Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper focuses on the design of fast algorithms for 3–8 point small-size DCT-VII (Discrete Cosine Transform Type VII). Based on a structural matrix decomposition approach, it proposes a series of efficient implementations for different transform lengths. By performing sign adjustments, reordering, decomposing the DCT-VII coefficient matrix into sparse components and cyclic convolution templates, the paper constructs algorithms with reduced computational complexity and provides the corresponding dataflow diagrams and pseudocode.
1. The structural decompositions do not offer a general form that can be extended to larger sizes (e.g., 16, 32, 64), whereas practical codecs often rely on larger transform dimensions.
2. Although the number of multiplications is reduced, some algorithms increase the number of additions, which may limit overall energy savings.
3. The matrix decompositions involve repeated sign permutations and approximate-zero terms, which may introduce cumulative numerical errors.
4. The approach relies on manually inspecting matrix structures, lacking automation or generality, which reduces its scalability.
5. A deeper comparison with DFT-pruning methods, sparse-matrix approximation techniques, and least-squares-based DST-VII/DCT-VIII approximations would be beneficial.
6. Although the paper focuses on N=3–8, it should clarify whether the proposed strategy can scale to larger sizes such as 16 or 32 points.
7. In image and video processing, improving the efficiency and robustness of local block transforms remains an important direction. Works such as "Re-cropping Framework: A Grid Recovery Method for Quantization Step Estimation in Non-aligned Recompressed Images" and "From simple to complex scenes: Learning robust feature representations for accurate human parsing" demonstrate that the recovery of structural information and the stability of local feature representations rely on interpretable transform-domain properties, which aligns with the motivation behind the paper’s fine-grained decomposition of small-size DCT-VII.
8. "Light-Field Image Multiple Reversible Robust Watermarking Against Geometric Attacks" and "Encrypt a Story: A Video Segment Encryption Method Based on the Discrete Sinusoidal Memristive Rulkov Neuron" highlight the value of lightweight transforms in watermarking and video security, further indicating that building efficient and implementable small-size orthogonal transforms (such as the fast DCT-VII proposed in this paper) is relevant to multimedia forensics, security, and coding systems.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1. The structural approach is described in vague, procedural terms (reshaping, reordering, sign changes, decomposition), but no formal proofs or general theorems are provided to guarantee correctness or efficiency across all sequence lengths.

2. The algorithms are only presented for very small input sizes (lengths 3–8). This is an extremely narrow scope, and the paper does not convincingly argue why such small block sizes are practically relevant in modern image/video coding standards, which typically employ larger block transforms (e.g., 8×8, 16×16, 32×32).

3. The reported reduction of multiplications by ~66% is misleading without a detailed breakdown of both arithmetic and memory access costs. In practice, additions dominate in many DSP implementations, yet the reduction in additions is negligible (~6%).

4. The paper does not compare its algorithms against state-of-the-art fast DCT implementations (e.g., recursive algorithms, Winograd-type approaches). Without such benchmarks, the claimed efficiency is unsubstantiated.

5. Some related works are recommended for citation:
   a. https://doi.org/10.1117/1.3556727
   b. https://doi.org/10.1117/12.632649

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have carefully revised the manuscript according to my comments. I recommend that the paper be accepted for publication.

Reviewer 2 Report

Comments and Suggestions for Authors

All problems have been addressed.