{"id":"cea1d1eb-784f-43c7-9a6c-10c2788b330a","arxiv_id":"2505.23618","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Sparse orthogonal adjustments around DCT-2-like transforms approximate DST-7 and DCT-8 closely enough that VVC coding efficiency is nearly unchanged while complexity drops by up to roughly 5x.","lead":"This paper shows how to approximate the large DST-7 and DCT-8 transforms in video coding using fast DCT-2 computations plus sparse correction stages, cutting computation and memory. If it holds up, video codecs can run large transforms much faster with nearly no compression loss, and 64-point transforms become practical for ultra-high-definition video.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (2) downweights high-frequency basis vectors by about 100:1, so the approximation leaves them essentially unconstrained; the 'practically identical coding efficiency' claim rests entirely on all-intra BD-rate tests that are not statistically characterized.","rationale":"The reader identified the weighted least-squares objective in Eq. (2) as the weakest assumption, and I agree that this is the most load-bearing point in the argument. The paper's central claim has two parts: approximation quality preserves coding efficiency, and complexity is significantly reduced. The complexity part is supported by throughput measurements and arithmetic-count references, though the detailed accounting is in JVET documents. The coding-efficiency part depends on the optimization proxy in Eq. (2) being sufficient, which is not a proven theorem. The paper's own all-intra BD-rate tables are consistent with the claim, but they are not statistically characterized, and the main text omits the inter-configuration and high-bitrate results that would be most sensitive to high-frequency basis-vector errors. I also noticed a potentially informative inconsistency between Table 2 and Table 3 regarding the 64-pt transform: the approximate 64-pt adjustment appears to report a larger average gain than the exact 64-pt transform, which is implausible unless the numbers have different sign conventions or are within noise. This reinforces the need for a controlled statistical comparison rather than a single table. I am not arguing that the method is wrong; the concern is that the current evidence does not establish the general claim. Since the reader's verdict is already CONDITIONAL and my analysis points to the same underlying weakness, the verdict should remain unchanged. Independent support in the paper includes the external JVET references, the throughput benchmark, and the fact that the adjustment matrices are orthogonal by construction; those are real strengths but they do not resolve the empirical question about high-frequency fidelity.","tokens_in":6803,"tokens_out":11373,"duration_ms":114016,"concrete_test":"Run the JVET CTC random-access and low-delay configurations, plus all-intra at very high bitrate, in VTM-3.0 with the proposed 8x8 sub-block adjustment, comparing against the exact DST-7/DCT-8 transform set at the same dimensions, with at least three QPs and repeated anchors to estimate per-sequence variance and confidence intervals. Also re-run the exact 64-pt DST-7/DCT-8 anchor under identical all-intra conditions to resolve the Table 2/3 sign inconsistency. If any configuration shows an average BD-rate loss greater than about 0.1% relative to the exact transform set, or if the approximate 64-pt adjustment's gain exceeds the exact 64-pt gain by more than the noise floor, the low-frequency weighting premise fails and the central coding-efficiency claim is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The design objective in Eq. (2) minimizes sum_{i,j} exp(-alpha*i)*(H_ij - D_ij)^2 with alpha = ln(100)/N. For i = N-1, the relative weight is about 0.01, so high-frequency basis vectors are effectively unconstrained. For the 8x8 post-adjustment, rows 8..N-1 of H are exactly rows of the DCT-2, not of DST-7/DCT-8 (since C = I except for the top-left 8x8 block). The paper never bounds the resulting high-frequency approximation error or its effect on quantization distortion. The only evidence that this is harmless is the BD-rate table, which is all-intra only in the main text; random-access, low-delay, and very-high-bitrate results are deferred to refs. [7,8]. Moreover, the numbers in Table 3 are not accompanied by confidence intervals or repeated-anchor statistics, and there is an apparent sign/consistency tension: the proposed 64-pt adjustment (Table 3, row '64', CTC average +0.08 with the 8x8 design) is reported as more beneficial than the exact 64-pt transform would be (Table 2: 2.78 vs 2.73, i.e., +0.05). Under either common BD-rate sign convention, an approximation should not outperform the exact transform unless the difference is noise. Thus the load-bearing premise, that low-frequency fidelity alone preserves coding gain, is supported only by an under-characterized subset of test conditions.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper describes a method for approximating the DST-7 and DCT-8 transforms used in VVC by composing an efficient DCT-2-family transform with sparse orthogonal \"adjustment\" matrices. The adjustment matrices are optimized with a weighted least-squares criterion (Eq. 2) that emphasizes low-frequency basis vectors. Two designs are presented: a band-matrix pre-adjustment before DST-3, and an 8x8 sub-block post-adjustment after DCT-2. Experiments in VTM-3.0 under all-intra CTC report BD-rate differences within roughly +/-0.1% of the reference, while Table 1 reports throughput improvements up to about 5.7x, and the conclusion states that enabling 64-point DST-7/DCT-8 does not increase worst-case complexity.","tokens_in":7205,"tokens_out":5038,"duration_ms":46565,"significance":"If the claims are correct, this is a practical and potentially influential complexity-reduction technique for multiple transform selection in video coding. The optimization framework is general and could be reused for other transform pairs, and the 8x8 sub-block design is a clever way to share computation between DST-7 and DCT-8. The reported throughput gains are substantial. However, the manuscript's evidence is narrower than its conclusions: only all-intra results are shown, no statistical characterization is provided, and one table appears internally inconsistent with the exact-transform baseline. The central modeling premise -- that low-frequency fidelity alone preserves coding gain -- is plausible but is not rigorously established in the text. The paper is clearly written and the mathematical framework is coherent, but the experimental support needs strengthening before the claims can be fully accepted.","major_comments":[{"comment":"The weighting alpha = ln(100)/N in Eq. (2) downweights the highest-frequency basis vectors by a factor of about 100 relative to the lowest-frequency ones, so the objective places essentially no constraint on high-frequency rows. For the 8x8 post-adjustment, where C is the identity except for the top-left 8x8 block, rows 8..N-1 of H are exactly rows of DCT-2, not DST-7 or DCT-8. The paper does not bound this high-frequency approximation error or analyze its effect on quantization distortion. Since the \"practically identical coding efficiency\" claim is the main result, the authors should either provide an analytical bound or present experiments (e.g., RA, LD, very-high-bitrate) that directly validate the low-frequency-only assumption. This is a load-bearing point, not a presentation issue.","section":"Section 2, Eq. (2) and Fig. 2"},{"comment":"There is an apparent inconsistency in the reported gains. Table 3, row \"64\" of the 8x8 sub-matrix adjustment, reports a CTC average of +0.08% over VTM-3.0. Table 2 shows that exact 64-point DST-7 and DCT-8 provide 2.78% versus 2.73%, i.e., +0.05%. Thus the approximate adjustment appears to outperform the exact transform by 0.03% on the same metric. Under either common BD-rate sign convention, an approximation should not beat the transform it approximates unless the difference is within measurement noise. Please reconcile this discrepancy and provide confidence intervals or repeated-anchor statistics to show the reported differences are meaningful.","section":"Table 3 vs. Table 2"},{"comment":"The main-text experimental evidence is exclusively all-intra under CTC; random-access, low-delay, and very-high-bitrate results are only cited to JVET documents [7, 8]. The conclusions in Section 4 state that the proposed methods provide \"negligible coding performance differences on VTM-3.0\" without restricting this statement to all-intra. Since complexity and coding-efficiency trade-offs can differ across configurations, the paper should include these additional results or explicitly narrow the scope of the conclusions. Furthermore, no confidence intervals are reported for any BD-rate numbers; with differences on the order of 0.01-0.08%, this level of statistical detail is necessary to support the claim of identical coding efficiency.","section":"Section 3, Table 3 and footnote 3"}],"minor_comments":[{"comment":"The conclusion contains a duplicated word: \"new method method\" should read \"new method.\"","section":"Section 4"},{"comment":"The caption sentence \"A long vertical direction are transforms used for computation (B), and along horizontal are the desired transforms (D)\" appears garbled; it should be rewritten as a complete, grammatical sentence, e.g., \"Along the vertical direction are the transforms used for computation (B), and along the horizontal direction are the desired transforms (D).\"","section":"Figure 1 caption"},{"comment":"The phrase \"same number of arithmetic operations as needed for one adjustment\" should be \"the same number of arithmetic operations as are needed for one adjustment\" for grammatical correctness.","section":"Section 2.3"},{"comment":"The optimized adjustment matrices are not included in the manuscript; the text refers to JVET documents [7, 8] for parameters. Because these matrices are the central artifact of the paper, please provide them in an appendix or as supplementary material so that the results can be reproduced without consulting external standards documents.","section":"Reproducibility"},{"comment":"The throughput ratios are reported relative to full matrix multiplication, but no absolute measured throughput or details of the benchmarking platform are given in the paper. A brief statement of the methodology, even if the full tool is described in [18], would help readers assess the practical significance.","section":"Table 1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript reads as a condensed summary of the authors' JVET contributions, and the editor may wish to consider whether the journal requires a more self-contained treatment. The sign inconsistency between Table 2 and Table 3 is the most serious technical issue; if it cannot be resolved with corrected numbers or statistical evidence, the central claim would be undermined. I recommend asking for the full configuration results and the actual matrices as supplementary material during revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one if you care about transform coding in VVC/AV1-class codecs. The paper is a consolidated write-up of the authors' JVET proposals for approximating DST-7/DCT-8 with sparse orthogonal adjustments around DCT-2; the genuinely new bits are the weighted least-squares formulation in Eq. (2), the simultaneous DCT-8/DST-7 computation via Eq. (5), and the throughput measurements in Table 1. The adjustment matrices themselves and the random-access/low-delay results live in the cited JVET documents, not here. The authors say so in Footnote 1 and Section 3, so this is not hidden novelty-stripping; it is a design note plus benchmark summary.\n\nThe method is sound in the engineering sense. For a fixed target transform, minimize weighted LS error between H=CBA and D, with low-frequency rows weighted ~100x more than the highest, under sparsity and orthogonality constraints. The 8x8 post-adjustment is clever: it leaves rows 8..N-1 as plain DCT-2, which is exactly where high-frequency basis vectors matter least for coding gain. Table 3 shows CTC-average BD-rate differences between -0.04 and +0.08 percentage points (with class A1 outliers up to +0.45), and Table 1 shows 5x+ throughput gains for the 8x8 design. That is a credible trade-off for hardware video codecs.\n\nThe soft spots are, in order. First, the load-bearing premise — low-frequency fidelity alone preserves coding gain — is only empirically supported, and the evidence in this paper is thinner than the conclusion. The main table is all-intra only; RA/LD and very-high-bitrate results are deferred to [7,8]. There are no error bars or repeated runs. Second, the sign tension the stress-test note flags is real: the proposed 64-pt 8x8 adjustment reports +0.08 CTC average while the exact 64-pt transform reports +0.05. An approximation should not beat the exact transform; 0.03 percentage points is likely noise, but the paper does not address it. Third, the actual matrices are not in the paper; reproducibility requires pulling JVET docs and VTM. That is acceptable for a standardization-derived paper but should be stated as such.\n\nWho this is for: people implementing VVC MTS in software or hardware, and researchers working on low-complexity trigonometric approximations. It is not a breakthrough; it is a useful engineering contribution with honest citations and a clean framework. I would send it to peer review, with the expectation that the authors add the missing matrices as an appendix or clearly indicate where they can be fetched, include RA/LD results, and comment on the Table 2/Table 3 discrepancy.","headline":"Solid engineering write-up of JVET transform-adjustment designs, with a clean optimization framework and real throughput gains; the coding-efficiency evidence is thinner than the conclusion.","tokens_in":7703,"tokens_out":5574,"would_cite":false,"duration_ms":48642,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Sparse orthogonal adjustment stages can replace VVC's DST-7 and DCT-8 with near-zero coding loss and a big complexity cut.","keywords":["transform coding","video compression","DST-7","DCT-8","low-complexity approximation","sparse orthogonal matrices","weighted least squares","asymmetric transforms"],"falsifier":"Encode a set of high-texture or noisy 4K sequences with the proposed 8x8 sub-block adjustment under VVC all-intra common test conditions and compare BD-rate against the full DST-7/DCT-8; if the loss exceeds the paper's reported noise margin by a clear amount, such as more than 0.5%, the low-frequency-weighting premise would be refuted.","tokens_in":6608,"feed_emoji":"🎥","tokens_out":15069,"duration_ms":118864,"temperature":0.7,"pith_summary":"This paper aims to establish that the asymmetric transforms used in Versatile Video Coding, DST-7 and DCT-8, can be replaced by cheap approximations built from a DCT-2-family transform plus sparse orthogonal correction stages without losing coding efficiency. The core argument is that only the low-frequency basis vectors of these transforms matter for compression, so an optimization with exponentially larger weights on low frequencies can fit those rows accurately and leave high-frequency rows approximate. In tests on the VVC reference software, the approximations hold BD-rate changes to within a few hundredths of a percent on average, while worst-case multiplications per coefficient fall from 64 to 36 and 64-point asymmetric transforms become affordable. If the claim holds, the practical cost of multiple-transform coding drops substantially, making the compression gains of DST-7/DCT-8 viable in hardware where full matrix transforms are too expensive.","feed_headline":"8x8 adjustment cuts worst-case transform cost to 36 multiplies","feed_subtitle":"DST-7 and DCT-8 can be swapped for DCT-2 plus sparse tweaks with nearly zero coding loss.","key_machinery":"The load-bearing object is the factored approximation $H = C B A \\approx D$, with $B$ chosen from the DCT-2 family of transforms that share the DCT-2's efficient computational structure, and $A$ or $C$ restricted to sparse orthogonal matrices: a $K$-tap band matrix in the pre-adjustment variant, or a top-left $8\\times 8$ sub-block in the post-adjustment variant. The optimization enforces orthogonality through products of Givens rotations and minimizes the weighted least-squares objective $\\sum_{i=0}^{N-1}\\sum_{j=0}^{N-1} e^{-\\alpha i}(H_{i,j}-D_{i,j})^2$ with $\\alpha = \\ln(10^2)/N$. Two algebraic identities carry extra weight: $T(C_8)=S T(S_7) R$ links DCT-8 to DST-7, and in the sub-block case $C(C_8)=S C(S_7) S$, so the encoder can compute both adjustments in one pass and leave most coefficients unchanged.","core_discovery":"The central discovery is that a desired orthogonal transform D can be factored approximately as H = C B A, where B is one of the efficiently computable DCT-2-type transforms (DCT-2, DCT-3, DST-2, or DST-3) and A and C are sparse orthogonal adjustment matrices, either a K-tap band matrix before B or a small top-left sub-block matrix after B. The adjustment parameters come from minimizing a weighted least-squares error that places exponentially larger weight on the low-frequency basis-vector rows, reflecting their dominant role in coding gain. Applied to DST-7, with DCT-8 obtained through the identity $T(C_8)=S T(S_7) R$, the method yields approximations whose low-frequency basis functions match the target almost exactly while high-frequency functions diverge in ways that do not hurt compression. The VVC reference software tests show essentially no coding loss, while the 8x8 sub-block adjustment lowers worst-case complexity to 36 multiplications per coefficient and enables 64-point asymmetric transforms without increasing that worst case.","pith_inferences":["The same weighted least-squares adjustment recipe could be exported to other compression transforms, such as DST-1 variants or non-separable secondary transforms, wherever a fast base transform exists and only low-frequency fidelity is rate-distortion-relevant.","Because the objective downweights high-frequency basis vectors exponentially, the approximation may lose more coding gain on content with unusually strong high-frequency residual energy; a targeted test on textured, noisy, or screen-content sequences would reveal whether the empirical safety margin covers that regime.","The reported complexity is in multiplications per coefficient and software throughput ratios; actual silicon area and energy savings depend on how the sparse adjustment stages are mapped to hardware, which the paper does not model."],"forward_implications":["With the 8x8 sub-block adjustment, worst-case complexity in the VVC reference software drops from 64 to 36 multiplications per coefficient, and memory decreases by about 1 kilobyte.","64-point DST-7 and DCT-8 can be enabled with no increase in worst-case complexity, adding up to 0.45% BD-rate gains on UHD content.","Average all-intra BD-rate differences versus the reference remain within roughly a tenth of a percent for typical classes, and the only class exceeding that range is A1, where the adjustment adds up to 0.45% gain on UHD content.","The DST-7/DCT-8 sign and flip relations let an encoder evaluate all horizontal/vertical transform combinations at the cost of one adjustment, with throughput more than five times that of full matrix multiplication in the 8x8 case."],"supporting_citations":[{"why":"Supplies the algebraic relations among DCT-2, DCT-3, DST-2, and DST-3 that justify using them as efficient building blocks.","marker":"[5]"},{"why":"Provides the band-matrix adjustment parameters and the standardization tests for the pre-adjustment variant.","marker":"[7]"},{"why":"Provides the sub-block matrix adjustment parameters, the complexity results, and the 64-point enabling experiments.","marker":"[8]"},{"why":"Contributes the Givens-rotation factorization used to enforce orthogonality in the non-convex optimization.","marker":"[10]"},{"why":"Describes the efficient simultaneous computation of DCT-8 and DST-7 combinations used by the encoder.","marker":"[14]"},{"why":"The VVC reference software used for all coding efficiency experiments.","marker":"[15]"},{"why":"Defines the common test conditions that fix sequences, bitrates, and encoder configuration for the reported BD-rate numbers.","marker":"[16]"},{"why":"Defines the BD-rate metric in which all coding gains and losses are reported.","marker":"[17]"},{"why":"Specifies the software benchmarking method that produces the throughput ratios in Table 1.","marker":"[18]"}],"fun_headline_variants":["Sparse adjustments make asymmetric transforms nearly free","DCT-2 factorisation makes DST-7 cheap with near-zero loss","36 multiplies per coefficient: low-complexity transform tweaks","Orthogonal adjustments slash transform cost without coding loss","Low-complexity transform approximations for VVC"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The approach relies on the assumption that reproducing the low-frequency basis vectors of DST-7 and DCT-8 with much higher fidelity than the high-frequency ones is enough to preserve the coding gain, so approximation errors in the high-frequency rows can be neglected.","fun_headline_variants_meta":{"raw":{"variants":["Sparse adjustments make asymmetric transforms nearly free","DCT-2 factorisation makes DST-7 cheap with near-zero loss","36 multiplies per coefficient: low-complexity transform tweaks","Orthogonal adjustments slash transform cost without coding loss","Low-complexity transform approximations for VVC"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000375,"raw_usage":{"total_tokens":1973,"prompt_tokens":888,"completion_tokens":1085,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":504,"completion_tokens_details":{"reasoning_tokens":1004}},"tokens_in":504,"tokens_out":1085,"duration_ms":9436,"temperature":1.0,"reasoning_tokens":1004,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T12:41:57.504380+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Encode a set of high-texture or noisy 4K sequences with the proposed 8x8 sub-block adjustment under VVC all-intra common test conditions and compare BD-rate against the full DST-7/DCT-8; if the loss exceeds the paper's reported noise margin by a clear amount, such as more than 0.5%, the low-frequency-weighting premise would be refuted.","supporting_citations":[{"cited_title":"Since the first approach has computations similar to bi- orthogonal filters, band matrices with at most K non-zero row elements are referred as K-tap adjustments","cited_arxiv_id":null,"evidence_quote":"Supplies the algebraic relations among DCT-2, DCT-3, DST-2, and DST-3 that justify using them as efficient building blocks."},{"cited_title":"The proposed methods are used to reduce the complexity of large DST-7 and DCT-8 and tested on a real codec (VTM-3.0)","cited_arxiv_id":null,"evidence_quote":"Provides the band-matrix adjustment parameters and the standardization tests for the pre-adjustment variant."},{"cited_title":"Improved H.264 intra coding bas ed on bi-directional intra prediction, directional transfor m, and adaptive coefficient scanning,","cited_arxiv_id":null,"evidence_quote":"Provides the sub-block matrix adjustment parameters, the complexity results, and the 64-point enabling experiments."},{"cited_title":"GBST: Separable transforms based on line graphs for predic - tive video coding,","cited_arxiv_id":null,"evidence_quote":"Contributes the Givens-rotation factorization used to enforce orthogonality in the non-convex optimization."},{"cited_title":"Co m- plexity reduction for adaptive multiple transforms (AMT) u s- ing adjustment stages,","cited_arxiv_id":null,"evidence_quote":"Describes the efficient simultaneous computation of DCT-8 and DST-7 combinations used by the encoder."},{"cited_title":"CE6: efficient implementations of MTS with transform adjustments,","cited_arxiv_id":null,"evidence_quote":"The VVC reference software used for all coding efficiency experiments."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the common test conditions that fix sequences, bitrates, and encoder configuration for the reported BD-rate numbers."},{"cited_title":"Highly efficient non-separable transforms for next generation video coding,","cited_arxiv_id":null,"evidence_quote":"Defines the BD-rate metric in which all coding gains and losses are reported."},{"cited_title":"Rotational transform for image and video compression,","cited_arxiv_id":null,"evidence_quote":"Specifies the software benchmarking method that produces the throughput ratios in Table 1."}],"review_version":1}