arXiv subjects

Kazuki Matsumoto

Publications and source records attributed to Kazuki Matsumoto.

5 recordsLinked to original sources

arXiv2026

Prox-Friendly Log-Magnitude Prior on Complex-Valued Signal

The logarithmic transform is essential in audio signal processing since human auditory perception is approximately logarithmic with respect to magnitude. However, directly incorporating prior knowledge about signals (e.g., harmonic structure) in the log-magnitude domain into optimization problems solved by standard proximal splitting algorithms remains challenging. To address this issue, this paper proposes a novel regularizer termed EPILOG (Exponential Penalty for Imposing priors on LOG-magnitude). EPILOG indirectly imposes prior knowledge on the log-magnitude of a complex-valued signal through regularization of an auxiliary variable that is shown to be linked with the log-magnitude. Furthermore, we derive its variable-wise proximity operators and develop a proximal splitting algorithm using these operators. Experiments on speech dereverberation demonstrate the effectiveness of the proposed regularizer, particularly in promoting cepstral-domain sparsity.

cs.SD↗

arXiv2026

LipSSM: Structurally Lipschitz-Bounded Cascaded State-Space Model via Metric Transfer between Consecutive SSM Layers

Lipschitz continuity is a fundamental principle in the design of certifiably robust deep neural networks (DNNs), wherein adjusting the Lipschitz constant, which quantifies network robustness, is of central theoretical importance. A standard approach to enforcing Lipschitz continuity requires each layer of a DNN to be Lipschitz continuous, thereby guaranteeing overall Lipschitz continuity. However, this layer-wise approach typically imposes overly conservative restrictions by producing a loose estimate of the overall Lipschitz constant, which limits the expressive capacity of the DNN and degrades empirical performance at a prescribed level of robustness. To overcome this loose estimation, the recently proposed LipKernel transfers information across layers to yield a much tighter overall Lipschitz bound than conventional layer-wise construction. In this paper, we extend this concept to cascaded state-space models (SSMs) to construct Lipschitz-continuous DNNs capable of modeling longer-term dependencies. The proposed architecture, named LipSSM, is theoretically justified and empirically evaluated.

cs.LG↗

arXiv2026

LipsAM: Lipschitz-continuous Neural Networks for Convergent Plug-and-Play Audio Signal Recovery

The Lipschitz continuity of deep neural networks (DNNs) is essential for establishing theoretical guarantees regarding their behavior. From both theoretical and practical perspectives, various methods have been proposed to construct Lipschitz-continuous architectures and control their Lipschitz constants. However, several DNN architectures common in audio signal processing fall outside the scope of existing theoretical frameworks, hindering the development of Lipschitz-continuous models in acoustic applications. In particular, despite their widespread adoption, DNNs that separately process the magnitude and phase of complex-valued signals cannot be Lipschitz continuous under existing frameworks. In this paper, to address this limitation, we establish a theoretical foundation for constructing amplitude modifiers (AMs), a class of DNN architectures that operate solely on the magnitude of a complex-valued input, with provable Lipschitz continuity. Specifically, we derive a necessary and sufficient condition for an AM to be Lipschitz continuous and propose LipsAMs (Lipschitz-continuous AMs) corresponding to common architectures for audio signals, including time-frequency masking. Furthermore, we develop an efficient framework for evaluating their Lipschitz constants and analytically derive these constants for some of the proposed architectures. As an application, we propose CoReM-LipsAM (Controlled Residual Maps via LipsAM) for plug-and-play (PnP) audio signal recovery, integrating a DNN as a data-driven prior within a model-based signal processing algorithm. The convergence of the obtained PnP algorithm is structurally guaranteed by the CoReM-LipsAM architecture and empirically validated through speech dereverberation experiments.

cs.SD↗

arXiv2026

LipsAM: Lipschitz-Continuous Amplitude Modifier for Audio Signal Processing and its Application to Plug-and-Play Dereverberation

The robustness of deep neural networks (DNNs) can be certified through their Lipschitz continuity, which has made the construction of Lipschitz-continuous DNNs an active research field. However, DNNs for audio processing have not been a major focus due to their poor compatibility with existing results. In this paper, we consider the amplitude modifier (AM), a popular architecture for handling audio signals, and propose its Lipschitz-continuous variants, which we refer to as LipsAM. We prove a sufficient condition for an AM to be Lipschitz continuous and propose two architectures as examples of LipsAM. The proposed architectures were applied to a Plug-and-Play algorithm for speech dereverberation, and their improved stability is demonstrated through numerical experiments.

cs.SD↗

arXiv2025

Subband Splitting: Simple, Efficient and Effective Technique for Solving Block Permutation Problem in Determined Blind Source Separation

Solving the permutation problem is essential for determined blind source separation (BSS). Existing methods, such as independent vector analysis (IVA) and independent low-rank matrix analysis (ILRMA), tackle the permutation problem by modeling the co-occurrence of the frequency components of source signals. One of the remaining challenges in these methods is the block permutation problem, which may cause severe performance degradation. In this paper, we propose a simple and effective technique for solving the block permutation problem. The proposed technique splits the entire frequency bands into several overlapping subbands and sequentially applies BSS methods (e.g., IVA, ILRMA, or any other method) to each subband. Since the splitting reduces the size of the problem, the BSS methods can effectively work in each subband. Then, the permutations among the subbands are aligned by using the separation result in one subband as the initial values for the other subbands. Additionally, we propose SS-IVA and SS-ILRMA by combining subband splitting (SS) with IVA and ILRMA. Experimental results demonstrated that our technique remarkably improves the separation performance without increasing computational cost. In particular, our SS-ILRMA achieved the separation performance comparable to the oracle method (frequency-domain independent component analysis with the ideal permutation solver). Moreover, SS-ILRMA converged faster than conventional IVA and ILRMA.

cs.SD↗