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The Gap Between Principle and Practice of Lossy Image Coding

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Lossy image coding's shortfall to Shannon's rate-distortion limit splits into five named effects, and an estimated upper bound beats VTM by 35% on Kodak.

desk verdict The five-effect taxonomy and scaling experiments are useful, but the 35% RD upper bound omits the hyperlatent rate and is not a valid upper bound. read the letter →

arxiv 2501.12330 v1 pith:3PLUAHDM submitted 2025-01-21 cs.IT cs.LGmath.IT

Haotian Zhang , Dong Liu This is my paper · ORCID
classification cs.ITcs.LGmath.IT MSC 94A3494A08
keywords informationtheorylearnedimagecodinglossyrate-distortionfunctionamortizationeffectdigitizationquantizationsurrogateper-sampleoptimization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Lossy image compression is bounded in principle by Shannon's rate-distortion function—the minimum bitrate needed to reconstruct a source within a given distortion—but practical codecs do not know how far they sit from that bound. This paper argues the shortfall is not one inefficiency but five distinct effects: modeling, approximation, amortization, digitization, and asymptotic, each with its own cause. Quantitatively, it reports that an estimated upper bound on the rate-distortion function, computed from continuous Gaussian latent variables without quantization, achieves 35% rate savings over the VVC reference codec VTM on Kodak, while the best empirical quantized model reaches 24%. If the bound is tight, current codecs—traditional and learned—still have large headroom, and the five-effect taxonomy says which bottleneck to attack next.

What carries the argument

The argument is carried by the contrast between two optimization objectives. Eq. (5), a continuous stochastic latent system, treats the latent as a Gaussian random variable and uses a KL divergence as the rate estimate; because it avoids quantization and entropy coding, it serves as an upper-bound estimator of the true rate-distortion function. Eq. (6), the deterministic quantized system used by practical codecs, treats the latent as a discrete variable obtained by rounding and uses its entropy as the rate. Per-sample optimization (Eqs. (7)-(8)) turns the amortization effect into a measured quantity: the rate-distortion gain from optimizing latents for each image rather than using shared network parameters. The residual gap between the estimated and empirical curves is then attributed to the digitization effect, while one-shot coding bounds place the asymptotic effect.

What would settle it

Hold the network architecture, entropy model, and loss fixed and train one version with continuous Gaussian latents and the Eq. (10) rate plus another with quantization and the Eq. (6) entropy rate; if the BD-rate gap between the two curves is much smaller than the residual gap reported in Fig. 4, the magnitudes attributed to digitization are not supported.

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Extended reading notes

Core claim

The paper's central claim is that the gap between the ideal rate-distortion function and the empirical rate-distortion function of state-of-the-art learned image coding decomposes into five effects: a modeling effect from imperfect entropy models and lossy synthesis, an approximation effect from restricting the form of the encoder mapping, an amortization effect from sharing one network across all images instead of optimizing per image, a digitization effect from quantization and its training surrogates, and an asymptotic effect from coding finite-length images in one shot. The paper quantifies the last three by comparing a continuous stochastic latent system whose rate is computed as a KL divergence (Eq. 10) with a deterministic quantized system whose rate is an entropy, and by turning on per-sample optimization. The estimated rate-distortion function achieves 35% rate savings over VTM on Kodak, extending a previously reported 30% bound, while the empirical deterministic system achieves up to 24% rate savings; under MS-SSIM the corresponding savings are 36% and 22%. This is presented as a new benchmark that reveals substantial untapped potential in lossy image coding.

Load-bearing premise

The quantitative estimates of the digitization effect assume the difference between the smooth stochastic model and the quantized practical model is mainly the act of quantization, even though the two systems also differ in architecture, noise model, and training objective.

Editorial extensions

If this is right

  • If the estimated upper bound is tight, the 35% rate saving over VTM on Kodak means conventional codecs operate well above Shannon's limit, so a codec that realizes the bound would need roughly one-third fewer bits at the same PSNR.
  • Per-sample optimization consistently improves both the estimated and empirical rate-distortion curves, with gains shrinking as model size grows; amortization is therefore a real but declining overhead that larger transforms gradually absorb.
  • The residual gap between the estimated and empirical curves, attributed to digitization, widens with model complexity in the Res-hyper family and shrinks when a stronger context entropy model is added, so the digitization effect is architecture-dependent rather than a fixed tax.
  • Because the asymptotic effect is negligible for deterministic systems that entropy-code discrete latents, practical learned codecs are not meaningfully limited by finite-blocklength effects; the room for improvement lies in modeling, approximation, amortization, and digitization.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The five-effect decomposition should transfer to neural video, audio, and other latent-based source codecs; repeating the estimated-versus-empirical comparison on video would show whether learned video codecs have headroom comparable to the 35% reported here.
  • A practical stochastic coder that communicates continuous Gaussian latents with relative entropy coding would test whether the estimated bound is reachable in one shot; if its rate approaches the estimated curve, the digitization and asymptotic effects are removable in principle rather than fundamental.
  • The widening estimated-empirical gap with model size hints at a digitization wall: as transforms and entropy models improve, the quantization surrogate may become the binding constraint, so better surrogates could unlock further gains without larger networks.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes that the gap between Shannon's rate-distortion function and the performance of practical learned image codecs is caused by five effects: modeling, approximation, amortization, digitization, and asymptotic. It formalizes these effects in a latent-variable optimization framework, then reports experiments on the Kodak dataset using two learned image coding architectures with varying capacity, with and without per-sample optimization. The estimated rate-distortion bound is reported to achieve up to 35% rate savings over VTM, and the empirical deterministic system up to 24%; the paper interprets these gaps as quantifying the amortization, digitization, and asymptotic effects.

Significance. If the central benchmark were valid, the 35% rate-savings claim would be an important reference point for learned image coding, and the five-effect taxonomy would provide a useful language for discussing why practical codecs fall short of the Shannon bound. The paper's strengths include systematic scaling experiments over model size, the use of per-sample optimization to probe the amortization effect, and comparisons against VTM and recent learned codecs on a standard dataset. The taxonomy is reasonable as an organizational contribution. However, the quantitative headline is not currently supported because the estimated-rate calculation in Eq. (10) omits the mandatory hyperlatent cost, and the digitization-effect quantification is confounded by architectural and objective differences.

major comments (3)
  1. [IV.A.3 and Eq. (10)] The rate in Eq. (10) is computed only for the main latent Y, as KL(P_{Y|X=x} || Q_Y) / log(2). However, Sec. IV.A.3 states that both Y and Z are per-sample optimized, and in the hyperprior architecture the parameters of Q_Y are supplied by the hyperlatent Z; a decoder cannot reconstruct Q_Y without receiving Z. The estimated rate should therefore include a side-information term for Z, for example KL(P_{Y,Z|X=x} || Q_{Y,Z}) or an equivalent cost. Omitting Z means Eq. (10) is not a valid upper bound on the rate-distortion function, and the 35% rate-savings claim in Sec. IV.B is not established. The sentence in Sec. III-C about not regarding the asymptotic effect concerns one-shot coding overhead, not the cost of transmitting the hyperlatent, so it does not justify the omission.
  2. [IV.B and Fig. 4] The gap between the estimated RD curve (stochastic Gaussian latents, no quantization) and the empirical RD curve (deterministic quantized latents under Eq. (6)) is used to quantify the digitization effect. These two systems differ not only in the presence of quantization but also in the form of PY|X (Gaussian noise versus deterministic rounding), in the training objective (Eq. (5) versus Eq. (6)), and in the inference procedure. The measured gap therefore also contains approximation and modeling differences, so the reported magnitudes for the digitization effect are not isolated. The paper's phrase 'provide some insights' is more cautious, but the surrounding analysis and Figs. 3-4 present the gap as the digitization effect; this requires either a controlled comparison or a clear downgrading of the quantitative claim.
  3. [III.A] The five effects are identified and defined by construction rather than derived as a formal decomposition of the total gap. In particular, the boundaries between the modeling effect, approximation effect, and amortization effect depend on the choice of the reference optimal PY|X and on the restricted feasible set A, which are not made operational. This is acceptable for a conceptual taxonomy, but the paper should state explicitly that the effects are not shown to be disjoint or exhaustive; otherwise the reader may infer a quantitative decomposition that the theoretical analysis does not provide.
minor comments (5)
  1. [Abstract and Sec. I] The word 'quantitively' should be 'quantitatively' in the Abstract and in Sec. I.
  2. [IV.A.2] The passage introducing Eq. (10) is unfinished: 'We calculated the estimated rate as For x ~ PX ...' should be rewritten as a complete derivation.
  3. [III.A.2] The sentence containing Eq. (4) has a grammatical error ('Equation 4 is minimized it over all feasible'); please revise.
  4. [III.B] The claim that the asymptotic effect is negligible in current advanced deterministic schemes is asserted without quantitative support; a short calculation of the one-shot overhead for the coded image sizes would strengthen the claim.
  5. [Figs. 2-4] Please clarify whether the reported 'up to' rate savings refer to the best image, the best model, or the dataset average, since the text uses both 'up to' and averaged BD-rate values.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the five-effect taxonomy and the RD upper-bound estimate are externally grounded; self-citations are peripheral.

full rationale

The central claim—that an estimated rate-distortion upper bound built from a continuous stochastic latent model achieves roughly 35% rate savings over VTM on Kodak—does not reduce by construction to the paper's own assumptions. The bound is computed by minimizing Eq. (5), whose rate term is the KL divergence in Eq. (10); this is the standard variational upper-bound objective from Yang and Mandt [4], and the comparison is against an external codec (VTM-22.01) and external learned codecs ([30], [31]). Per-sample optimization on the Kodak evaluation set is a legitimate way to tighten a variational upper bound for an empirical source; it is not a fitted parameter being relabeled as a prediction, because the paper explicitly reports it as an estimated upper bound, not as a parameter-free forecast of codec performance. The main caveats are correctness issues, not circularity: Eq. (10) does not include the hyperlatent Z term even though Sec. IV.A.3 states that both Y and Z are optimized together (so the quoted rate may undercount the true cost of communicating QY's parameters), and the digitization-effect comparison in Sec. IV.B mixes architectural and training differences, so the quantitative magnitude of the digitization effect is not isolated. These would weaken the quantitative conclusions but do not make the derivation circular. The paper contains multiple self-citations ([35], [44], [45], [51], [66], [71]), but they are used for peripheral points—transform architectures, quantization-surrogate training details, and lists of prior entropy models—and none is invoked as a uniqueness theorem or as the sole justification for the 35% claim. The five-effect taxonomy reorganizes known concepts (amortization gap, train-test mismatch, one-shot overhead) with external citations to Cremer et al. and Li-Gamal; it is a synthesis, not a renaming that does predictive work. Thus no circular step meeting the quoted-evidence threshold is present.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claims rest on domain assumptions about natural images, the validity of the variational upper bound, and the interpretability of the gap between stochastic and deterministic systems. The free parameters are the trained models and the per-sample optimization applied to the evaluation set, which directly influence the reported rates.

free parameters (4)
  • Neural network weights (Res-hyper / Res-context) = Not reported exactly; 8 Res-hyper variants with increasing depth/width
    The estimated and empirical RD curves depend on these trained weights; the 35% figure is tied to the specific trained models.
  • Per-sample optimized latents (Y, Z) = Optimized on each Kodak image for 5000 Adam iterations
    Per-sample optimization on the evaluation set tightens the estimated upper bound; this is a fit to the test data.
  • Training lambda values = {0.0018, 0.0054, 0.0162, 0.0483}
    Selected by the authors to span the rate-distortion operating range; BD-rate is interpolated across these points.
  • Training hyperparameters = Adam, initial lr 5e-5, batch size 8, 500 epochs, fixed seed
    A single seed is used; no variance estimate across seeds is provided.
assumptions (6)
  • standard math Rate-distortion function is the fundamental limit of lossy source coding (Shannon's theorem).
    Basis of the whole analysis; well-established in information theory.
  • domain assumption Natural images are samples from a source with a well-defined rate-distortion function.
    The paper evaluates a finite dataset (Kodak) and treats images as samples from a natural image distribution; the R(D) of a finite set is not standard.
  • domain assumption The variational objective in Eq. (5) provides an upper bound on the true rate-distortion function.
    From Yang and Mandt [4]; the tightness depends on model capacity and optimization.
  • ad hoc to paper The difference between the estimated (stochastic, continuous) RD curve and the empirical (deterministic, quantized) RD curve is primarily attributable to the digitization effect.
    The two systems differ in multiple ways, so the comparison does not isolate digitization; this is the paper's central experimental inference.
  • domain assumption Arithmetic coding overhead is negligible for images of Kodak size.
    Used to state that the asymptotic effect is negligible for deterministic systems; reasonable for typical image sizes.
  • standard math The one-shot achievability bound I <= R <= I + log(I+1) + O(1) applies.
    Cited theorem (Li and Gamal [55]) used to bound the asymptotic effect.

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Cite this review

Pith. "Pith review of The Gap Between Principle and Practice of Lossy Image Coding." pith.science (2026). https://pith.science/paper/3PLUAHDM

@misc{pith2026250112330,
  author       = {Pith},
  title        = {Pith review of: The Gap Between Principle and Practice of Lossy Image Coding},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3PLUAHDM}},
  note         = {Machine review of arXiv:2501.12330}
}
read the original abstract

Lossy image coding is the art of computing that is principally bounded by the image's rate-distortion function. This bound, though never accurately characterized, has been approached practically via deep learning technologies in recent years. Indeed, learned image coding schemes allow direct optimization of the joint rate-distortion cost, thereby outperforming the handcrafted image coding schemes by a large margin. Still, it is observed that there is room for further improvement in the rate-distortion performance of learned image coding. In this article, we identify the gap between the ideal rate-distortion function forecasted by Shannon's information theory and the empirical rate-distortion function achieved by the state-of-the-art learned image coding schemes, revealing that the gap is incurred by five different effects: modeling effect, approximation effect, amortization effect, digitization effect, and asymptotic effect. We design simulations and experiments to quantitively evaluate the last three effects, which demonstrates the high potential of future lossy image coding technologies.

Figures

Figures reproduced from arXiv: 2501.12330 by the authors.

Figure 1
Figure 1. (a) Illustration of a virtual channel PXˆ|X for lossy source coding; X is the source and Xˆ is the reconstruction. (b) Illustration of instantiating PXˆ|X by a latent-based model; Y refers to the latents. minimization of the mutual information is performed over all feasible PXˆ|X under the distortion constraint. The rate￾distortion function is determined by the source distribution PX and the pre-defined distortion m… view at source ↗
Figure 2
Figure 2. The compression efficiency of the estimated and empirical rate [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. The compression efficiency gain provided by the per-sample opti [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: The compression efficiency gap between the estimated and the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

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Reference graph

Works this paper leans on

90 extracted references · 70 canonical work pages

  1. [1]

    Coding theorems for a discrete source with a fidelity criterion,

    C. E. Shannon, “Coding theorems for a discrete source with a fidelity criterion,” International Convention Record , vol. 7, pp. 325–350, 1959

    1959

  2. [2]

    Variational image compression with a scale hyperprior,

    J. Ball ´e, D. Minnen, S. Singh, S. J. Hwang, and N. Johnston, “Variational image compression with a scale hyperprior,” in International Conference on Learning Representations (ICLR) , 2018

    2018

  3. [3]

    Auto-encoding variational bayes,

    D. P. Kingma and M. Welling, “Auto-encoding variational bayes,” in International Conference on Learning Representations (ICLR) , 2014

    2014

  4. [4]

    Towards empirical sandwich bounds on the rate-distortion function,

    Y . Yang and S. Mandt, “Towards empirical sandwich bounds on the rate-distortion function,” in International Conference on Learning Rep- resentations (ICLR), 2022

    2022

  5. [5]

    An improved upper bound on the rate-distortion function of images,

    Z. Duan, J. Ma, J. He, and F. Zhu, “An improved upper bound on the rate-distortion function of images,” in IEEE International Conference on Image Processing (ICIP) , 2023, pp. 246–250

    2023

  6. [6]

    T. M. Cover and J. A. Thomas, Rate Distortion Theory , 2005, ch. 10, pp. 301–346

    2005

  7. [7]

    An introduction to arithmetic coding,

    G. G. Langdon, “An introduction to arithmetic coding,” IBM Journal of Research and Development , vol. 28, no. 2, pp. 135–149, 1984

    1984

  8. [8]

    Compressing images by encoding their latent representations with relative entropy coding,

    G. Flamich, M. Havasi, and J. M. Hern ´andez-Lobato, “Compressing images by encoding their latent representations with relative entropy coding,” in Advances in Neural Information Processing Systems , 2020, pp. 16 131–16 141

    2020

Show all 90 references
  1. [9]

    Theoretical foundations of transform coding,

    V . Goyal, “Theoretical foundations of transform coding,” IEEE Signal Processing Magazine, vol. 18, no. 5, pp. 9–21, 2001

    2001

  2. [10]

    The JPEG still picture compression standard,

    G. K. Wallace, “The JPEG still picture compression standard,” Commu- nications of the ACM , vol. 34, no. 4, pp. 30–44, 1991

    1991

  3. [11]

    The JPEG 2000 still image compression standard,

    A. Skodras, C. Christopoulos, and T. Ebrahimi, “The JPEG 2000 still image compression standard,” IEEE Signal Processing Magazine , vol. 18, no. 5, pp. 36–58, 2001

    2000

  4. [12]

    BPG Image Format,

    F. Bellard, “BPG Image Format,” http://bellard.org/bpg/, 2015

    2015

  5. [13]

    Overview of the versatile video coding (VVC) standard and its applications,

    B. Bross, Y .-K. Wang, Y . Ye, S. Liu, J. Chen, G. J. Sullivan, and J.- R. Ohm, “Overview of the versatile video coding (VVC) standard and its applications,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 31, no. 10, pp. 3736–3764, 2021

    2021

  6. [14]

    End-to-end optimization of nonlinear transform codes for perceptual quality,

    J. Ball ´e, V . Laparra, and E. P. Simoncelli, “End-to-end optimization of nonlinear transform codes for perceptual quality,” in Picture Coding Symposium (PCS) , 2016, pp. 1–5

    2016

  7. [15]

    End-to-end optimized image compression,

    J. Ball ´e, V . Laparra, and E. P. Simoncelli, “End-to-end optimized image compression,” in International Conference on Learning Representations (ICLR), 2017

    2017

  8. [16]

    Soft-to-hard vector quantization for end- to-end learning compressible representations,

    E. Agustsson, F. Mentzer, M. Tschannen, L. Cavigelli, R. Timofte, L. Benini, and L. V . Gool, “Soft-to-hard vector quantization for end- to-end learning compressible representations,” in Advances in Neural Information Processing Systems , 2017, pp. 1141–1151

    2017

  9. [17]

    Unified multivariate gaussian mixture for efficient neural image compression,

    X. Zhu, J. Song, L. Gao, F. Zheng, and H. T. Shen, “Unified multivariate gaussian mixture for efficient neural image compression,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 2022, pp. 17 591–17 600

    2022

  10. [18]

    Nvtc: Nonlinear vector transform coding,

    R. Feng, Z. Guo, W. Li, and Z. Chen, “Nvtc: Nonlinear vector transform coding,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 2023, pp. 6101–6110

    2023

  11. [19]

    Lvqac: Lattice vector quantization coupled with spatially adaptive companding for efficient learned image compression,

    X. Zhang and X. Wu, “Lvqac: Lattice vector quantization coupled with spatially adaptive companding for efficient learned image compression,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023, pp. 10 239–10 248

    2023

  12. [20]

    Variable rate image com- pression with recurrent neural networks,

    G. Toderici, S. M. O’Malley, S. J. Hwang, D. Vincent, D. Minnen, S. Baluja, M. Covell, and R. Sukthankar, “Variable rate image com- pression with recurrent neural networks,” in International Conference on Learning Representations (ICLR) , 2016

    2016

  13. [21]

    Full resolution image compression with recurrent neural networks,

    G. Toderici, D. Vincent, N. Johnston, S. J. Hwang, D. Minnen, J. Shor, and M. Covell, “Full resolution image compression with recurrent neural networks,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , 2017, pp. 5435–5443

    2017

  14. [22]

    Improved lossy image compres- sion with priming and spatially adaptive bit rates for recurrent networks,

    N. Johnston, D. Vincent, D. Minnen, M. Covell, S. Singh, T. Chinen, S. Jin Hwang, J. Shor, and G. Toderici, “Improved lossy image compres- sion with priming and spatially adaptive bit rates for recurrent networks,” in IEEE/CVF Conference on Computer Vision and Pattern Recognit...

    2018

  15. [23]

    A spatial RNN codec for end-to- end image compression,

    C. Lin, J. Yao, F. Chen, and L. Wang, “A spatial RNN codec for end-to- end image compression,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 2020, pp. 13 266–13 274

    2020

  16. [24]

    End-to- end learnt image compression via non-local attention optimization and improved context modeling,

    T. Chen, H. Liu, Z. Ma, Q. Shen, X. Cao, and Y . Wang, “End-to- end learnt image compression via non-local attention optimization and improved context modeling,” IEEE Transactions on Image Processing , vol. 30, pp. 3179–3191, 2021

    2021

  17. [25]

    Learned image com- pression with discretized Gaussian mixture likelihoods and attention modules,

    Z. Cheng, H. Sun, M. Takeuchi, and J. Katto, “Learned image com- pression with discretized Gaussian mixture likelihoods and attention modules,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 2020, pp. 7936–7945

    2020

  18. [26]

    Causal contextual prediction for learned image compression,

    Z. Guo, Z. Zhang, R. Feng, and Z. Chen, “Causal contextual prediction for learned image compression,” IEEE Transactions on Circuits and Systems for Video Technology , vol. 32, no. 4, pp. 2329–2341, 2022

    2022

  19. [27]

    Neural image compression via attentional multi-scale back projection and frequency decomposition,

    G. Gao, P. You, R. Pan, S. Han, Y . Zhang, Y . Dai, and H. Lee, “Neural image compression via attentional multi-scale back projection and frequency decomposition,” in IEEE/CVF International Conference on Computer Vision (ICCV) , 2021, pp. 14 657–14 666

    2021

  20. [28]

    The devil is in the details: Window- based attention for image compression,

    R. Zou, C. Song, and Z. Zhang, “The devil is in the details: Window- based attention for image compression,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 2022, pp. 17 471– 17 480

    2022

  21. [29]

    Transformer-based transform coding,

    Y . Zhu, Y . Yang, and T. Cohen, “Transformer-based transform coding,” in International Conference on Learning Representations (ICLR) , 2022

    2022

  22. [30]

    Learned image compression with mixed Transformer-CNN architectures,

    J. Liu, H. Sun, and J. Katto, “Learned image compression with mixed Transformer-CNN architectures,” inIEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 2023, pp. 14 388–14 397

    2023

  23. [31]

    Frequency-aware transformer for learned image compression,

    H. Li, S. Li, W. Dai, C. Li, J. Zou, and H. Xiong, “Frequency-aware transformer for learned image compression,” in International Conference on Learning Representations (ICLR) , 2024

    2024

  24. [32]

    End-to-end optimized versatile image compression with wavelet-like transform,

    H. Ma, D. Liu, N. Yan, H. Li, and F. Wu, “End-to-end optimized versatile image compression with wavelet-like transform,” IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 44, no. 3, pp. 1247– 1263, 2022

    2022

  25. [33]

    Lossy image compression with normalizing flows,

    L. Helminger, A. Djelouah, M. Gross, and C. Schroers, “Lossy image compression with normalizing flows,” arXiv preprint arXiv:2008.10486, Tech. Rep., 2020

    2008 arXiv

  26. [34]

    Enhanced invertible encoding for learned image compression,

    Y . Xie, K. L. Cheng, and Q. Chen, “Enhanced invertible encoding for learned image compression,” in ACM International Conference on Multimedia, 2021, p. 162–170

    2021

  27. [35]

    Wavelet-like transform-based technology in response to the call for proposals on neural network-based image coding,

    C. Dong, H. Ma, H. Zhang, C. Gao, L. Li, and D. Liu, “Wavelet-like transform-based technology in response to the call for proposals on neural network-based image coding,” arXiv preprint arXiv:2403.05937, Tech. Rep., 2024

    2024 arXiv

  28. [36]

    Joint autoregressive and hier- archical priors for learned image compression,

    D. Minnen, J. Ball ´e, and G. Toderici, “Joint autoregressive and hier- archical priors for learned image compression,” in Advances in Neural Information Processing Systems , 2018, pp. 10 794–10 803. 10

    2018

  29. [37]

    Context-adaptive entropy model for end- to-end optimized image compression,

    J. Lee, S. Cho, and S. Beack, “Context-adaptive entropy model for end- to-end optimized image compression,” in International Conference on Learning Representations (ICLR) , 2019

    2019

  30. [38]

    Channel-wise autoregressive entropy models for learned image compression,

    D. Minnen and S. Singh, “Channel-wise autoregressive entropy models for learned image compression,” in IEEE International Conference on Image Processing (ICIP) , 2020, pp. 3339–3343

    2020

  31. [39]

    Learning end-to-end lossy image compression: A benchmark,

    Y . Hu, W. Yang, Z. Ma, and J. Liu, “Learning end-to-end lossy image compression: A benchmark,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 44, no. 8, pp. 4194–4211, 2022

    2022

  32. [40]

    Entroformer: A Transformer-based entropy model for learned image compression,

    Y . Qian, M. Lin, X. Sun, Z. Tan, and R. Jin, “Entroformer: A Transformer-based entropy model for learned image compression,” in International Conference on Learning Representations (ICLR) , 2022

    2022

  33. [41]

    ELIC: Efficient learned image compression with unevenly grouped space-channel con- textual adaptive coding,

    D. He, Z. Yang, W. Peng, R. Ma, H. Qin, and Y . Wang, “ELIC: Efficient learned image compression with unevenly grouped space-channel con- textual adaptive coding,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 2022, pp. 5708–5717

    2022

  34. [42]

    M2T: Masking Transform- ers twice for faster decoding,

    F. Mentzer, E. Agustson, and M. Tschannen, “M2T: Masking Transform- ers twice for faster decoding,” in IEEE/CVF International Conference on Computer Vision (ICCV) , 2023, pp. 5317–5326

    2023

  35. [43]

    MLIC: Multi-reference entropy model for learned image compression,

    W. Jiang, J. Yang, Y . Zhai, P. Ning, F. Gao, and R. Wang, “MLIC: Multi-reference entropy model for learned image compression,” in ACM International Conference on Multimedia , 2023, pp. 7618–7627

    2023

  36. [44]

    Flexible coding order for learned image compression,

    Y . Li, H. Zhang, and D. Liu, “Flexible coding order for learned image compression,” in IEEE International Conference on Visual Communica- tions and Image Processing (VCIP) , 2023, pp. 1–5

    2023

  37. [45]

    Learned image compression with Gaussian- Laplacian-Logistic mixture model and concatenated residual modules,

    H. Fu, F. Liang, J. Lin, B. Li, M. Akbari, J. Liang, G. Zhang, D. Liu, C. Tu, and J. Han, “Learned image compression with Gaussian- Laplacian-Logistic mixture model and concatenated residual modules,” IEEE Transactions on Image Processing , vol. 32, pp. 2063–2076, 2023

    2023

  38. [46]

    Lossy image com- pression with compressive autoencoders,

    L. Theis, W. Shi, A. Cunningham, and F. Husz ´ar, “Lossy image com- pression with compressive autoencoders,” in International Conference on Learning Representations (ICLR) , 2017

    2017

  39. [47]

    Estimating or propagating gradients through stochastic neurons for conditional computation,

    Y . Bengio, N. L ´eonard, and A. Courville, “Estimating or propagating gradients through stochastic neurons for conditional computation,” arXiv preprint arXiv:1308.3432, Tech. Rep., 2013

    2013 arXiv

  40. [48]

    Universally quantized neural compression,

    E. Agustsson and L. Theis, “Universally quantized neural compression,” in Advances in Neural Information Processing Systems , 2020, pp. 12 367–12 376

    2020

  41. [49]

    Soft then hard: Rethinking the quantization in neural image compression,

    Z. Guo, Z. Zhang, R. Feng, and Z. Chen, “Soft then hard: Rethinking the quantization in neural image compression,” in International Conference on Machine Learning (ICML) , 2021, pp. 3920–3929

    2021

  42. [50]

    Improving inference for neural image compression,

    Y . Yang, R. Bamler, and S. Mandt, “Improving inference for neural image compression,” in Advances in Neural Information Processing Systems, 2020, pp. 573–584

    2020

  43. [51]

    On uniform scalar quantization for learned image compression,

    H. Zhang, L. Li, and D. Liu, “On uniform scalar quantization for learned image compression,” arXiv preprint arXiv:2309.17051, Tech. Rep., 2023

    2023 arXiv

  44. [52]

    Comprehensive comparisons of uniform quantization in deep image compression,

    K. Tsubota and K. Aizawa, “Comprehensive comparisons of uniform quantization in deep image compression,” IEEE Access , vol. 11, pp. 4455–4465, 2023

    2023

  45. [53]

    Nonlinear transform coding,

    J. Ball ´e, P. A. Chou, D. Minnen, S. Singh, N. Johnston, E. Agustsson, S. J. Hwang, and G. Toderici, “Nonlinear transform coding,” IEEE Journal of Selected Topics in Signal Processing , vol. 15, no. 2, pp. 339–353, 2021

    2021

  46. [54]

    On the advantages of stochastic encoders,

    L. Theis and E. Agustsson, “On the advantages of stochastic encoders,” arXiv preprint arXiv:2102.09270, Tech. Rep., 2021

    2021 arXiv

  47. [55]

    Strong functional representation lemma and applications to coding theorems,

    C. T. Li and A. E. Gamal, “Strong functional representation lemma and applications to coding theorems,” IEEE Transactions on Information Theory, vol. 64, no. 11, pp. 6967–6978, 2018

    2018

  48. [56]

    Computation of channel capacity and rate-distortion func- tions,

    R. Blahut, “Computation of channel capacity and rate-distortion func- tions,” IEEE Transactions on Information Theory , vol. 18, no. 4, pp. 460–473, 1972

    1972

  49. [57]

    An algorithm for computing the capacity of arbitrary dis- crete memoryless channels,

    S. Arimoto, “An algorithm for computing the capacity of arbitrary dis- crete memoryless channels,” IEEE Transactions on Information Theory , vol. 18, no. 1, pp. 14–20, 1972

    1972

  50. [58]

    Estimation of the rate–distortion function,

    M. T. Harrison and I. Kontoyiannis, “Estimation of the rate–distortion function,” IEEE Transactions on Information Theory , vol. 54, no. 8, pp. 3757–3762, 2008

    2008

  51. [59]

    Neural estimation of the rate-distortion function with applications to operational source coding,

    E. Lei, H. Hassani, and S. Saeedi Bidokhti, “Neural estimation of the rate-distortion function with applications to operational source coding,” IEEE Journal on Selected Areas in Information Theory , vol. 3, no. 4, pp. 674–686, 2022

    2022

  52. [60]

    Estimating the rate- distortion function by wasserstein gradient descent,

    Y . Yang, S. Eckstein, M. Nutz, and S. Mandt, “Estimating the rate- distortion function by wasserstein gradient descent,” in Advances in Neural Information Processing Systems , 2023, pp. 2768–2794

    2023

  53. [61]

    Beta-V AE: Learning basic visual concepts with a constrained variational framework,

    I. Higgins, L. Matthey, A. Pal, C. P. Burgess, X. Glorot, M. M. Botvinick, S. Mohamed, and A. Lerchner, “Beta-V AE: Learning basic visual concepts with a constrained variational framework,” in Interna- tional Conference on Learning Representations (ICLR) , 2017

    2017

  54. [62]

    Lossy source coding,

    T. Berger and J. Gibson, “Lossy source coding,” IEEE Transactions on Information Theory , vol. 44, no. 6, pp. 2693–2723, 1998

    1998

  55. [63]

    Neural networks optimally compress the sawbridge,

    A. B. Wagner and J. Ball ´e, “Neural networks optimally compress the sawbridge,” in Data Compression Conference (DCC) , 2021, pp. 143– 152

    2021

  56. [64]

    An introduction to neural data compression,

    Y . Yang, S. Mandt, L. Theis et al. , “An introduction to neural data compression,” F oundations and Trends® in Computer Graphics and Vision, vol. 15, no. 2, pp. 113–200, 2023

    2023

  57. [65]

    Generative adversarial networks for extreme learned image compres- sion,

    E. Agustsson, M. Tschannen, F. Mentzer, R. Timofte, and L. Van Gool, “Generative adversarial networks for extreme learned image compres- sion,” in IEEE/CVF International Conference on Computer Vision (ICCV), 2019, pp. 221–231

    2019

  58. [66]

    End-to-end image com- pression with probabilistic decoding,

    H. Ma, D. Liu, C. Dong, L. Li, and F. Wu, “End-to-end image com- pression with probabilistic decoding,” arXiv preprint arXiv:2109.14837, Tech. Rep., 2021

    2021 arXiv

  59. [67]

    Lossy image compression with conditional dif- fusion models,

    R. Yang and S. Mandt, “Lossy image compression with conditional dif- fusion models,” in Advances in Neural Information Processing Systems , 2023

    2023

  60. [68]

    Inference suboptimality in varia- tional autoencoders,

    C. Cremer, X. Li, and D. Duvenaud, “Inference suboptimality in varia- tional autoencoders,” in International Conference on Machine Learning (ICML), 2018, pp. 1078–1086

    2018

  61. [69]

    Optimal entropy-constrained scalar quanti- zation of a uniform source,

    A. Gyorgy and T. Linder, “Optimal entropy-constrained scalar quanti- zation of a uniform source,” IEEE Transactions on Information Theory , vol. 46, no. 7, pp. 2704–2711, 2000

    2000

  62. [70]

    Rate-distortion-optimization for deep image compression,

    M. Sch ¨afer, S. Pientka, J. Pfaff, H. Schwarz, D. Marpe, and T. Wiegand, “Rate-distortion-optimization for deep image compression,” in IEEE International Conference on Image Processing (ICIP) , 2021, pp. 3737– 3741

    2021

  63. [71]

    Ensemble learning-based rate-distortion optimization for end-to-end image compression,

    Y . Wang, D. Liu, S. Ma, F. Wu, and W. Gao, “Ensemble learning-based rate-distortion optimization for end-to-end image compression,” IEEE Transactions on Circuits and Systems for Video Technology , vol. 31, no. 3, pp. 1193–1207, 2021

    2021

  64. [72]

    Semi- amortized variational autoencoders,

    Y . Kim, S. Wiseman, A. Miller, D. Sontag, and A. Rush, “Semi- amortized variational autoencoders,” in International Conference on Machine Learning (ICML) , 2018, pp. 2678–2687

    2018

  65. [73]

    Iterative amortized inference,

    J. Marino, Y . Yue, and S. Mandt, “Iterative amortized inference,” in International Conference on Machine Learning (ICML) , 2018, pp. 3403– 3412

    2018

  66. [74]

    Content adaptive optimization for neural image compression,

    J. Campos, S. Meierhans, A. Djelouah, and C. Schroers, “Content adaptive optimization for neural image compression,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), 2019

    2019

  67. [75]

    Simple statistical gradient-following algorithms for connectionist reinforcement learning,

    R. J. Williams, “Simple statistical gradient-following algorithms for connectionist reinforcement learning,” Machine Learning , vol. 8, pp. 229–256, 1992

    1992

  68. [76]

    A unified framework for one-shot achievability via the poisson matching lemma,

    C. T. Li and V . Anantharam, “A unified framework for one-shot achievability via the poisson matching lemma,” IEEE Transactions on Information Theory , vol. 67, no. 5, pp. 2624–2651, 2021

    2021

  69. [77]

    On universal quantization,

    J. Ziv, “On universal quantization,” IEEE Transactions on Information Theory, vol. 31, no. 3, pp. 344–347, 1985

    1985

  70. [78]

    On universal quantization by randomized uniform/lattice quantizers,

    R. Zamir and M. Feder, “On universal quantization by randomized uniform/lattice quantizers,” IEEE Transactions on Information Theory , vol. 38, no. 2, pp. 428–436, 1992

    1992

  71. [79]

    Algorithms for the communication of samples,

    L. Theis and N. Y . Ahmed, “Algorithms for the communication of samples,” in International Conference on Machine Learning (ICML) , 2022, pp. 21 308–21 328

    2022

  72. [80]

    Asymmetric numeral systems: entropy coding combining speed of Huffman coding with compression rate of arithmetic coding,

    J. Duda, “Asymmetric numeral systems: entropy coding combining speed of Huffman coding with compression rate of arithmetic coding,” arXiv preprint arXiv:1311.2540, Tech. Rep., 2013

    2013 arXiv

  73. [81]

    Understanding is compression,

    Z. Li, C. Huang, X. Wang, H. Hu, C. Wyeth, D. Bu, Q. Yu, W. Gao, X. Liu, and M. Li, “Understanding is compression,” arXiv preprint arXiv:2407.07723, Tech. Rep., 2024

    2024 arXiv

  74. [82]

    Lossy compres- sion with Gaussian diffusion,

    L. Theis, T. Salimans, M. D. Hoffman, and F. Mentzer, “Lossy compres- sion with Gaussian diffusion,” arXiv preprint arXiv:2206.08889, Tech. Rep., 2022

    2022 arXiv

  75. [83]

    Variational inference with normalizing flows,

    D. Rezende and S. Mohamed, “Variational inference with normalizing flows,” in International conference on machine learning (ICML) , 2015, pp. 1530–1538

    2015

  76. [84]

    Neural video compression with diverse contexts,

    J. Li, B. Li, and Y . Lu, “Neural video compression with diverse contexts,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 2023, pp. 22 616–22 626. 11

    2023

  77. [85]

    Run, don’t walk: Chasing higher FLOPS for faster neural networks,

    J. Chen, S.-h. Kao, H. He, W. Zhuo, S. Wen, C.-H. Lee, and S.- H. G. Chan, “Run, don’t walk: Chasing higher FLOPS for faster neural networks,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 2023, pp. 12 021–12 031

    2023

  78. [86]

    Xception: Deep learning with depthwise separable convolu- tions,

    F. Chollet, “Xception: Deep learning with depthwise separable convolu- tions,” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017, pp. 1800–1807

    2017

  79. [87]

    A unified end-to-end framework for efficient deep image compression,

    J. Liu, G. Lu, Z. Hu, and D. Xu, “A unified end-to-end framework for efficient deep image compression,” arXiv preprint arXiv:2002.03370, Tech. Rep., 2020

    2002 arXiv

  80. [88]

    Adam: A method for stochastic optimization,

    D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” in International Conference on Learning Representations (ICLR) , 2015

    2015

  81. [89]

    Kodak lossless true color image suite,

    E. Kodak, “Kodak lossless true color image suite,” http://r0k.us/graphics/ kodak/

  82. [90]

    Calculation of average psnr differences between rd- curves,

    G. Bjontegaard, “Calculation of average psnr differences between rd- curves,” ITU SG16 Doc. VCEG-M33, Tech. Rep., 2001

    2001

Pith tools

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