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arxiv: 2605.11475 · v1 · submitted 2026-05-12 · 💻 cs.CV

Recognition: 2 theorem links

· Lean Theorem

Deep Probabilistic Unfolding for Quantized Compressive Sensing

Gang Qu , Ping Wang , Siming Zheng , Xin Yuan
Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:14 UTC · model grok-4.3

classification 💻 cs.CV
keywords quantized compressive sensingdeep unfoldinglikelihood gradient projectionMamba moduleprobabilistic guidanceimage reconstructionmulti-scale feature fusion
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The pith

A closed-form likelihood gradient projection respects true quantization physics within deep unfolding for compressive sensing.

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

The paper develops a deep probabilistic unfolding model for quantized compressive sensing that improves reconstruction accuracy and efficiency over prior unfolding approaches. It replaces standard L2 projections on measurements with a derived closed-form, numerically stable likelihood gradient projection. This step converts the hard quantization constraint into soft probabilistic guidance that aligns with the actual physics of quantization. The model pairs this projection with a dual-domain Mamba module that captures and fuses multi-scale local and global features from correlated regions. Experiments indicate the resulting reconstructions outperform previous methods.

Core claim

By deriving a closed-form, numerically stable likelihood gradient projection inside an unfolding framework, the model respects the true quantization physics of compressive sensing and converts the hard quantization constraint into soft probabilistic guidance. An efficient dual-domain Mamba module is added to dynamically capture and fuse multi-scale local and global features while modeling interactions between distant but correlated regions, yielding state-of-the-art reconstruction performance.

What carries the argument

The closed-form likelihood gradient projection that supplies soft probabilistic guidance from true quantization physics, together with the dual-domain Mamba module that fuses multi-scale local and global features.

If this is right

  • Reconstructions align more closely with physical quantization effects instead of relying on L2 approximation.
  • Multi-scale correlations across distant image regions are modeled through dynamic feature fusion.
  • Overall accuracy and efficiency improve for quantized compressive sensing tasks.
  • Real-world deployment of quantized compressive sensing becomes more practical due to higher performance.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same closed-form projection technique could be adapted to other inverse problems that involve discretization.
  • Mamba-based dual-domain fusion may transfer to additional image reconstruction settings that require both local detail and long-range context.
  • Iterative stability of the projection supports scaling to deeper unfolding networks.

Load-bearing premise

The closed-form likelihood gradient projection stays accurate and stable across unfolding iterations while the dual-domain Mamba module captures required multi-scale correlations without artifacts.

What would settle it

Reconstruction error or numerical instability appearing when the model is tested on varying quantization bit depths or different sensing matrices, relative to standard L2-projection baselines.

Figures

Figures reproduced from arXiv: 2605.11475 by Gang Qu, Ping Wang, Siming Zheng, Xin Yuan.

Figure 1
Figure 1. Figure 1: The pipline of the proposed DPUNet. (a) The overall architecture of the pro￾posed QCS reconstruction model, which is a DUN framework with K stages. (b) The design of deep denoiser in (a). (c) The proposed dual-domain Mamba block in (b). Likelihood Gradient Projection. Our method explicitly incorporates a closed￾form quantized likelihood data-consistency projection: we use Mills-ratio-based expressions for … view at source ↗
Figure 2
Figure 2. Figure 2: The reconstruction results from 1-bit measurements of CelebA dataset (64×64, the sampling number is 4000). where g ∈ {1, ..., G} indexes channel groups with Cg = C/G channels per group, R ∈ N is the low-rank number, αg ∈ R is a learned coupling scale for group g, λ(t) ∈ [0, 1] is a warmup factor at optimization step t, Ug,r(ω), Vg,r(ω) ∈ C are learned complex frequency basis functions, and the global spect… view at source ↗
Figure 3
Figure 3. Figure 3: The reconstruction results from 1-bit measurements of FFHQ dataset (256 × 256 × 3, the sampling number is 24576). where p(y|zi) follow Eq. (9) and Eq. (13) for multi-bit and 1-bit cases, respec￾tively. Thus, the final objective of the proposed DPUNet is: \label {eq:} \mathcal {L}=||X_K-X_{gt}||_2 + \alpha \mathcal {L}_{\rm NLL}, (29) where α is empirically set to 0.05 in experiment. 4 Simulation Results We… view at source ↗
Figure 4
Figure 4. Figure 4: The reconstruction results of CelebA dataset from multi-bit measurements (64 × 64 × 3, the sampling number is 4000) [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The reconstruction results of FFHQ dataset from multi-bit measurements (256 × 256 × 3, the sampling number is 24576). 5.2 Comparison of Computational Complexity. Then, we further make a comparison on the average PSNR, the number of pa￾rameters, FLOPs, and inference time with previous unfolding designs (image size is 256 × 256 × 3) of different methods, as presented in Tab. 3. Benefiting from the efficient … view at source ↗
Figure 6
Figure 6. Figure 6: The OOD reconstruction results of CSet8 dataset from one- and two-bit mea￾surements (256 × 256 × 3, the sampling number is 24576) [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
read the original abstract

We propose a deep probabilistic unfolding model to address the classical quantized compressive sensing problem that leverages an unfolding framework to enhance the reconstruction accuracy and efficiency. Unlike previous unfolding methods that apply L2 projection to measurements, we derive a closed-form, numerically stable likelihood gradient projection, which allows the model to respect the true quantization physics, turning the hard quantization constraint into a soft probabilistic guidance. Furthermore, an efficient, dual-domain Mamba module is specifically designed to dynamically capture and fuse the multi-scale local and global features, ensuring the interactions between the distant but correlated regions. Extensive experiments demonstrate the state-of-the-art performance of the proposed method over previous works, which is capable of promoting the application of quantized compressive sensing in real life.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a deep probabilistic unfolding model for quantized compressive sensing. It derives a closed-form, numerically stable likelihood gradient projection to replace L2 projections, converting hard quantization constraints into soft probabilistic guidance within the unfolding iterations. A dual-domain Mamba module is introduced to capture and fuse multi-scale local and global features. Extensive experiments are reported to demonstrate state-of-the-art reconstruction performance over prior methods.

Significance. If the closed-form derivation is correct and the projection remains stable, the approach could meaningfully advance quantized CS by better respecting quantization physics rather than relying on heuristic projections, with the Mamba integration offering efficiency gains for multi-scale correlations. This has potential for practical sensing applications if the SOTA claims hold under rigorous validation.

major comments (2)
  1. [Method (derivation of likelihood gradient projection)] The central claim of a closed-form, numerically stable likelihood gradient projection (abstract and method) requires explicit verification that it does not accumulate errors or become unstable across unfolding iterations. No iteration-wise error monitoring, finite-difference gradient comparisons, or ablations on iteration count/bit-depth are described, which is load-bearing for the claim that the model respects true quantization physics without drift.
  2. [Experiments and ablation studies] The dual-domain Mamba module's ability to capture multi-scale correlations without artifacts or extra distributional assumptions is asserted but not load-bearing tested via controlled ablations (e.g., vs. standard attention or CNN baselines) in the experiments section; this underpins the efficiency and SOTA claims.
minor comments (2)
  1. [Abstract] The abstract claims 'state-of-the-art performance' but should include specific quantitative metrics (e.g., PSNR/SSIM gains) and dataset details for immediate clarity.
  2. [Method] Notation for the projection operator and likelihood gradient should be defined more explicitly with equation numbers to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments. We address each major point below and will revise the manuscript to incorporate additional verification and ablation studies as outlined.

read point-by-point responses

  1. Referee: [Method (derivation of likelihood gradient projection)] The central claim of a closed-form, numerically stable likelihood gradient projection (abstract and method) requires explicit verification that it does not accumulate errors or become unstable across unfolding iterations. No iteration-wise error monitoring, finite-difference gradient comparisons, or ablations on iteration count/bit-depth are described, which is load-bearing for the claim that the model respects true quantization physics without drift.

    Authors: We thank the referee for emphasizing the importance of empirical verification for the stability claim. The closed-form likelihood gradient projection is derived to ensure numerical stability by replacing direct L2 operations with a bounded probabilistic update that respects quantization intervals without matrix inversion. While the paper presents the derivation and overall performance, we acknowledge the absence of the requested diagnostics. In the revised manuscript, we will add iteration-wise error monitoring, finite-difference gradient comparisons, and ablations across iteration counts and bit-depths to demonstrate that errors do not accumulate and the projection remains faithful to quantization physics. revision: yes

  2. Referee: [Experiments and ablation studies] The dual-domain Mamba module's ability to capture multi-scale correlations without artifacts or extra distributional assumptions is asserted but not load-bearing tested via controlled ablations (e.g., vs. standard attention or CNN baselines) in the experiments section; this underpins the efficiency and SOTA claims.

    Authors: We agree that controlled ablations are essential to validate the dual-domain Mamba module's contributions. The current experiments demonstrate overall SOTA results, but we will strengthen the manuscript by adding targeted ablations in the revised version: replacing the Mamba blocks with standard attention and CNN baselines while keeping other components fixed, and reporting reconstruction quality, runtime, and parameter efficiency. Feature map visualizations will also be included to illustrate multi-scale fusion without artifacts or additional assumptions. revision: yes

Circularity Check

0 steps flagged

No circularity: closed-form derivation starts from quantization likelihood

full rationale

The paper's central step is deriving a closed-form numerically stable likelihood gradient projection directly from the quantization likelihood function, which converts the hard constraint into soft probabilistic guidance inside the unfolding iterations. This is presented as a first-principles derivation rather than a fit to data or a self-citation. No equations reduce by construction to fitted parameters, prior self-cited results, or renamed empirical patterns. The dual-domain Mamba module is an architectural choice for feature fusion, not a load-bearing mathematical claim that collapses to inputs. The derivation chain remains independent of the target reconstruction performance, consistent with the reader's assessment of no obvious reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of modeling quantization via a likelihood function whose gradient can be computed in closed form and remains stable inside unfolding iterations; the Mamba module adds learned parameters whose behavior depends on training data.

free parameters (1)
  • neural network weights and Mamba parameters
    Learned during end-to-end training; their values are not fixed by the derivation.
axioms (1)
  • domain assumption The quantization process admits a likelihood function whose gradient projection is closed-form and numerically stable.
    Invoked to replace L2 projection with the proposed soft probabilistic guidance.

pith-pipeline@v0.9.0 · 5413 in / 1246 out tokens · 52389 ms · 2026-05-13T01:14:22.662292+00:00 · methodology

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Reference graph

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