arXiv subjects

Samuel Fernández-Menduiña

Publications and source records attributed to Samuel Fernández-Menduiña.

14 recordsLinked to original sources

arXiv2026

Rate-distortion optimization for full-reference image quality metrics via stochastic Hessian estimates

Block-based video codecs select coding parameters based on the input by optimizing a rate-distortion trade-off. The conventional distortion choice, the sum of squared errors (SSE), simplifies parameter selection: the SSE is the sum of block-wise SSEs, so rate-distortion optimization (RDO) can treat blocks independently. Alternatively, full-reference image quality assessment (FR-IQA) metrics such as MS-SSIM or LPIPS often align better with the human visual system than SSE, but they cannot be used in-loop: they do not decompose block-wise and typically require the fully decoded image as input. Building on existing results in metric quadratization, we approximate a broad class of FR-IQA metrics by an input-dependent quadratic distortion (IDQD), whose quadratic form matrix is derived from the Hessian of the metric evaluated at the source video. To make the distortion computable block-wise, we propose two approximations of the Hessian matrix: 1) keeping the block-diagonal, and 2) keeping only its diagonal. We propose estimators for both that require only matrix-vector products with the Hessian obtained by automatic differentiation. Across five metrics for Kodak and CLIC in VVC, IDQD-RDO achieves 14.2-36.7 % BD-rate savings under the target metric with no decoder changes and incurs 10-30 % encoding complexity overhead.

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arXiv2026

Spend Bits Where Queries Look: KV Cache Vector Quantization with Attention-Preserving Transforms

Long-context LLM decoding reads the key-value (KV) cache at every step. Loading it takes longer than computing attention over it, so throughput is bandwidth-bound. Hence, reducing the cache size can raise both decoding speed and serving capacity. The challenge is to reduce cache size while preserving the attention products, keeping reconstruction cheap, and using a fixed per-token bit count. At two bits per element, the most competitive methods rely on orthogonal transforms. However, existing techniques are either data-oblivious or use the query statistics without deriving the transform from a distortion criterion. Moreover, they rely on transforms built on top of random or Hadamard rotations, which equalize variances across entries rather than compacting energy, and fixed-width scalar quantizers, which are suboptimal at low rates. In this paper, we formulate KV cache quantization as a transform coding problem in which distortion is the error in the attention products. We derive closed-form optimal transforms for keys and values from calibration statistics, under a high-resolution model. We show that the optimal key transform is not orthogonal and satisfies a generalized Parseval relation: the attention-aware distortion becomes mean-squared error (MSE) in the transform domain. Thus, we can use MSE-optimal vector quantizers applied directly to the transformed key coefficients. To meet the fixed-width layout requirement, we show that grouping coefficients into equal-volume partitions makes equal-size codebooks attain the variable-rate optimum under the same high-resolution model. At two bits per element, our method, termed NOVA-KV, recovers most of the long-context retrieval accuracy lost by scalar quantization methods at comparable throughput.

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arXiv2026

L2G-Net: Local to Global Spectral Graph Neural Networks via Cauchy Factorizations

Despite their theoretical advantages, spectral methods based on the graph Fourier transform (GFT) are seldom used in graph neural networks (GNNs) due to the cost of computing the eigenbasis and the lack of vertex-domain locality in the resulting representations. As a result, most GNNs rely on local approximations such as polynomial Laplacian filters or message passing, which limit their ability to model long-range dependencies. In this paper, we introduce an exact factorization of the GFT into operators acting on subgraphs, which are then combined via a sequence of Cauchy matrices. Building on this factorization, we propose a new class of spectral GNNs, termed L2G-Net (Local to Global Net). Unlike existing spectral methods, which are either fully global (when using the GFT) or local (when using polynomial filters), L2G-Net operates by processing the spectral representations of subgraphs and then combining them via structured matrices. Our algorithm avoids full eigendecompositions, exploiting graph topology to construct the factorization with quadratic complexity in the number of nodes, scaled by the maximum cut size between subgraphs. Experiments stressing long-range dependencies on large graphs show that L2G-Net scales to regimes out of reach for the standard GFT, and is competitive with state-of-the-art methods with orders of magnitude fewer learnable parameters.

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arXiv2026

FaSST: Fast Sparsifying Secondary Transform

Data-dependent secondary transforms, which aim to decorrelate coefficients of a separable primary transform, can improve residual coding efficiency; however, their deployment is often constrained by computational complexity. Recent video codecs use variants of the low-frequency non-separable transform (LFNST), which discards some high-frequency secondary transform coefficients, limiting achievable coding gains. Moreover, existing data-dependent secondary transforms lack explicit rate-distortion (RD) optimal design criteria. In this work, we propose a framework for designing low-complexity data-dependent secondary transforms, termed Fast Sparsifying Secondary Transforms (FaSSTs). Our approach approximates data-driven sparse orthonormal transforms (SOTs) by factorizing them into a sequence of Givens rotations. The rotations are efficiently determined using an alternating minimization strategy combined with an approximate Givens factorization procedure. Our method adapts the number of rotations based on the prediction mode, further reducing computational complexity. We design mode-dependent secondary transforms for intra-prediction residuals in AV2 using FaSST. Experimental results show that mode-adaptive FaSST matches the RD performance of LFNST while reducing the number of computations by 83.67%. Moreover, by avoiding fixed-coefficient truncation, FaSST achieves up to 1.80% BD-rate savings relative to LFNST while operating at 66.24% lower complexity.

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arXiv2026

Rate-Distortion Optimization for Ensembles of Non-Reference Metrics

Non-reference metrics (NRMs) can assess the visual quality of images and videos without a reference, making them well-suited for the evaluation of user-generated content. Nonetheless, rate-distortion optimization (RDO) in video coding is still mainly driven by full-reference metrics, such as the sum of squared errors, which treat the input as an ideal target. A way to incorporate NRMs into RDO is through linearization (LNRM), where the gradient of the NRM with respect to the input guides bit allocation. While this strategy improves the quality predicted by some metrics, we show that it can yield limited gains or degradations when evaluated with other NRMs. We argue that NRMs are highly non-linear predictors with locally unstable gradients that can compromise the quality of the linearization; furthermore, optimizing a single metric may exploit model-specific biases that do not generalize across quality estimators. Motivated by this observation, we extend the LNRM framework to optimize ensembles of NRMs and, to further improve robustness, we introduce a smoothing-based formulation that stabilizes NRM gradients prior to linearization. Our framework is well-suited to hybrid codecs, and we advocate for its use with overfitted codecs, where it avoids iterative evaluations and backpropagation of neural network-based NRMs, reducing encoder complexity relative to direct NRM optimization. We validate the proposed approach on AVC and Cool-chic, using the YouTube UGC dataset. Experiments demonstrate consistent bitrate savings across multiple NRMs with no decoder complexity overhead and, for Cool-chic, a substantial reduction in encoding runtime compared to direct NRM optimization.

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arXiv2026

Wrapper-Aware Rate-Distortion Optimization in Feature Coding for Machines

Feature coding for machines (FCM) is a lossy compression paradigm for split-inference. The transmitter encodes the outputs of the first part of a neural network before sending them to the receiver for completing the inference. Practical FCM methods ``sandwich'' a traditional codec between pre- and post-processing neural networks, called wrappers, to make features easier to compress using video codecs. Since traditional codecs are non-differentiable, the wrappers are trained using a proxy codec, which is later replaced by a standard codec after training. These codecs perform rate-distortion optimization (RDO) based on the sum of squared errors (SSE). Because the RDO does not consider the post-processing wrapper, the inner codec can invest bits in preserving information that the post-processing later discards. In this paper, we modify the bit-allocation in the inner codec via a wrapper-aware weighted SSE metric. To make wrapper-aware RDO (WA-RDO) practical for FCM, we propose: 1) temporal reuse of weights across a group of pictures and 2) fixed, architecture- and task-dependent weights trained offline. Under MPEG test conditions, our methods implemented on HEVC match the VVC-based FCM state-of-the-art, effectively bridging a codec generation gap with minimal runtime overhead relative to SSE-RDO HEVC.

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arXiv2025

INT-DTT+: Low-Complexity Data-Dependent Transforms for Video Coding

Discrete trigonometric transforms (DTTs), such as the DCT-2 and the DST-7, are widely used in video codecs for their balance between coding performance and computational efficiency. In contrast, data-dependent transforms, such as the Karhunen-Loève transform (KLT) and graph-based separable transforms (GBSTs), offer better energy compaction but lack symmetries that can be exploited to reduce computational complexity. This paper bridges this gap by introducing a general framework to design low-complexity data-dependent transforms. Our approach builds on DTT+, a family of GBSTs derived from rank-one updates of the DTT graphs, which can adapt to signal statistics while retaining a structure amenable to fast computation. We first propose a graph learning algorithm for DTT+ that estimates the rank-one updates for rows and column graphs jointly, capturing the statistical properties of the overall block. Then, we exploit the progressive structure of DTT+ to decompose the kernel into a base DTT and a structured Cauchy matrix. By leveraging low-complexity integer DTTs and sparsifying the Cauchy matrix, we construct an integer approximation to DTT+, termed INT-DTT+. This approximation significantly reduces both computational and memory complexities with respect to the separable KLT with minimal performance loss. We validate our approach in the context of mode-dependent transforms for the VVC standard, following a rate-distortion optimized transform (RDOT) design approach. Integrated into the explicit multiple transform selection (MTS) framework of VVC in a rate-distortion optimization setup, INT-DTT+ achieves more than 3% BD-rate savings over the VVC MTS baseline, with complexity comparable to the integer DCT-2 once the base DTT coefficients are available.

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arXiv2025

Avoiding Quality Saturation in UGC Compression Using Denoised References

Video-sharing platforms must re-encode large volumes of noisy user-generated content (UGC) to meet streaming demands. However, conventional codecs, which aim to minimize the mean squared error (MSE) between the compressed and input videos, can cause quality saturation (QS) when applied to UGC, i.e., increasing the bitrate preserves input artifacts without improving visual quality. A direct approach to solve this problem is to detect QS by repeatedly evaluating a non-reference metric (NRM) on videos compressed with multiple codec parameters, which is inefficient. In this paper, we re-frame UGC compression and QS detection from the lens of noisy source coding theory: rather than using a NRM, we compute the MSE with respect to the denoised UGC, which serves as an alternative reference (D-MSE). Unlike MSE measured between the UGC input and the compressed UGC, D-MSE saturates at non-zero values as bitrates increase, a phenomenon we term distortion saturation (DS). Since D-MSE can be computed at the block level in the transform domain, we can efficiently detect D-MSE without coding and decoding with various parameters. We propose two methods for DS detection: distortion saturation detection (DSD), which relies on an input-dependent threshold derived from the D-MSE of the input UGC, and rate-distortion saturation detection (RDSD), which estimates the Lagrangian at the saturation point using a low-complexity compression method. Both methods work as a pre-processing step that can help standard-compliant codecs avoid QS in UGC compression. Experiments with AVC show that preventing encoding in the saturation region, i.e., avoiding encoding at QPs that result in QS according to our methods, achieves BD-rate savings of 8%-20% across multiple different NRMs, compared to a naïve baseline that encodes at the given input QP while ignoring QS.

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arXiv2025

Image Coding for Machines via Feature-Preserving Rate-Distortion Optimization

Many images and videos are primarily processed by computer vision algorithms, involving only occasional human inspection. When this content requires compression before processing, e.g., in distributed applications, coding methods must optimize for both visual quality and downstream task performance. We first show theoretically that an approach to reduce the effect of compression for a given task loss is to perform rate-distortion optimization (RDO) using the distance between features, obtained from the original and the decoded images, as a distortion metric. However, optimizing directly such a rate-distortion objective is computationally impractical because it requires iteratively encoding and decoding the entire image-plus feature evaluation-for each possible coding configuration. We address this problem by simplifying the RDO formulation to make the distortion term computable using block-based encoders. We first apply Taylor's expansion to the feature extractor, recasting the feature distance as a quadratic metric involving the Jacobian matrix of the neural network. Then, we replace the linearized metric with a block-wise approximation, which we call input-dependent squared error (IDSE). To make the metric computable, we approximate IDSE using sketches of the Jacobian. The resulting loss can be evaluated block-wise in the transform domain and combined with the sum of squared errors (SSE) to address both visual quality and computer vision performance. Simulations with AVC and HEVC across multiple feature extractors and downstream networks show up to 17 % bit-rate savings for the same task accuracy compared to RDO based on SSE, with no decoder complexity overhead and a small (7.86 %) encoder complexity increase.

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arXiv2025

Rate-Distortion Optimization with Non-Reference Metrics for UGC Compression

Service providers must encode a large volume of noisy videos to meet the demand for user-generated content (UGC) in online video-sharing platforms. However, low-quality UGC challenges conventional codecs based on rate-distortion optimization (RDO) with full-reference metrics (FRMs). While effective for pristine videos, FRMs drive codecs to preserve artifacts when the input is degraded, resulting in suboptimal compression. A more suitable approach used to assess UGC quality is based on non-reference metrics (NRMs). However, RDO with NRMs as a measure of distortion requires an iterative workflow of encoding, decoding, and metric evaluation, which is computationally impractical. This paper overcomes this limitation by linearizing the NRM around the uncompressed video. The resulting cost function enables block-wise bit allocation in the transform domain by estimating the alignment of the quantization error with the gradient of the NRM. To avoid large deviations from the input, we add sum of squared errors (SSE) regularization. We derive expressions for both the SSE regularization parameter and the Lagrangian, akin to the relationship used for SSE-RDO. Experiments with images and videos show bitrate savings of more than 30\% over SSE-RDO using the target NRM, with no decoder complexity overhead and minimal encoder complexity increase.

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arXiv2024

Fast DCT+: A Family of Fast Transforms Based on Rank-One Updates of the Path Graph

This paper develops fast graph Fourier transform (GFT) algorithms with O(n log n) runtime complexity for rank-one updates of the path graph. We first show that several commonly-used audio and video coding transforms belong to this class of GFTs, which we denote by DCT+. Next, starting from an arbitrary generalized graph Laplacian and using rank-one perturbation theory, we provide a factorization for the GFT after perturbation. This factorization is our central result and reveals a progressive structure: we first apply the unperturbed Laplacian's GFT and then multiply the result by a Cauchy matrix. By specializing this decomposition to path graphs and exploiting the properties of Cauchy matrices, we show that Fast DCT+ algorithms exist. We also demonstrate that progressivity can speed up computations in applications involving multiple transforms related by rank-one perturbations (e.g., video coding) when combined with pruning strategies. Our results can be extended to other graphs and rank-k perturbations. Runtime analyses show that Fast DCT+ provides computational gains over the naive method for graph sizes larger than 64, with runtime approximately equal to that of 8 DCTs.

eess.SP↗

arXiv2023

Image Coding via Perceptually Inspired Graph Learning

Most codec designs rely on the mean squared error (MSE) as a fidelity metric in rate-distortion optimization, which allows to choose the optimal parameters in the transform domain but may fail to reflect perceptual quality. Alternative distortion metrics, such as the structural similarity index (SSIM), can be computed only pixel-wise, so they cannot be used directly for transform-domain bit allocation. Recently, the irregularity-aware graph Fourier transform (IAGFT) emerged as a means to include pixel-wise perceptual information in the transform design. This paper extends this idea by also learning a graph (and corresponding transform) for sets of blocks that share similar perceptual characteristics and are observed to differ statistically, leading to different learned graphs. We demonstrate the effectiveness of our method with both SSIM- and saliency-based criteria. We also propose a framework to derive separable transforms, including separable IAGFTs. An empirical evaluation based on the 5th CLIC dataset shows that our approach achieves improvements in terms of MS-SSIM with respect to existing methods.

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arXiv2022

PRNU Emphasis: a Generalization of the Multiplicative Model

The photoresponse non-uniformity (PRNU) is a camera-specific pattern, widely adopted to solve multimedia forensics problems such as device identification or forgery detection. The theoretical analysis of this fingerprint customarily relies on a multiplicative model for the denoising residuals. This setup assumes that the nonlinear mapping from the scene irradiance to the preprocessed luminance, that is, the composition of the Camera Response Function (CRF) with the optical and digital preprocessing pipelines, is a gamma correction. Yet, this assumption seldom holds in practice. In this letter, we improve the multiplicative model by including the influence of this nonlinear mapping on the denoising residuals. We also propose a method to estimate this effect. Results evidence that the response of typical cameras deviates from a gamma correction. Experimental device identification with our model increases the TPR by a $4.93\, \%$ on average for a fixed FPR of $0.01$.

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arXiv2020

On the Information Leakage of Camera Fingerprint Estimates

Camera fingerprints based on sensor PhotoResponse Non-Uniformity (PRNU) have gained broad popularity in forensic applications due to their ability to univocally identify the camera that captured a certain image. This fingerprint of a given sensor is extracted through some estimation method that requires a few images known to be taken with such sensor. In this paper, we show that the fingerprints extracted in this way leak a considerable amount of information from those images used in the estimation, thus constituting a potential threat to privacy. We propose to quantify the leakage via two measures: one based on the Mutual Information, and another based on the output of a membership inference test. Experiments with practical fingerprint estimators on a real-world image dataset confirm the validity of our measures and highlight the seriousness of the leakage and the importance of implementing techniques to mitigate it. Some of these techniques are presented and briefly discussed.

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