PENDANTSS: PEnalized Norm-Ratios Disentangling Additive Noise, Trend and Sparse Spikes

Zheng, Paul; Chouzenoux, Émilie; Duval, Laurent

doi:10.1109/lsp.2023.3251891

Cited by 2 publications

(1 citation statement)

References 24 publications

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“…SOOT penalty was shown in [34] to suitably enhance the restoration of sparse signals in the context of blind deconvolution, when compared to standard ℓ 1 -based formulation. It was later on generalized in [35,36] to tackle signal processing tasks arising in chemistry, and hereagain showed superior results when compared to various state-of-the-art sparsity priors. Function d C denotes the Euclidean distance to a set C. If C is non-empty and convex, function 1 2 d 2 C is convex and 1-Lipschitz differentiable [37].…”

Section: Problem Formulationmentioning

confidence: 99%

Convergence analysis of block majorize-minimize subspace approach

Chouzenoux,

Fest

2023

Optim Lett

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We consider the minimization of a differentiable Lipschitz gradient but non necessarily convex, function F defined on R N . We propose an accelerated gradient descent approach which combines three strategies, namely (i) a variable metric derived from the majorization-minimization principle ; (ii) a subspace strategy incorporating information from the past iterates ; (iii) a block alternating update. Under the assumption that F satisfies the Kurdyka-Łojasiewicz property, we give conditions under which the sequence generated by the resulting block majorize-minimize subspace algorithm converges to a critical point of the objective function, and we exhibit convergence rates for its iterates.

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Section: Problem Formulationmentioning

confidence: 99%

Convergence analysis of block majorize-minimize subspace approach

Chouzenoux,

Fest

2023

Optim Lett

Self Cite

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Unrolled Deep Networks for Sparse Signal Restoration in Analytical Chemistry

Gharbi,

Villa,

Chouzenoux

et al. 2024

2024 IEEE 34th International Workshop on Machine Learning for Signal Processing (MLSP)

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This paper addresses the problem of sparse signal recovery from linearly transformed and noisy measurements. We propose to adopt the recent 'deep unrolling' paradigm, which consists in creating a deep neural network inspired from an iterative algorithm initially built for penalized loss minimization. The iterations of the algorithm are recast as neural network layers. The use of deep learning frameworks ensures an efficient implementation and the possibility to learn the algorithm native hyperparameters, through the minimization of a task-oriented loss. For a given application, choosing an adequate iterative scheme to unroll, and fine-tuning the architecture is a challenging task. In this work, we present three deep unrolled architectures dedicated to sparse signal recovery. We then perform their comprehensive comparative study, through the motivating application, arising in analytical chemistry, of peak retrieval from blurred and noisy chromatography acquisitions.

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PENDANTSS: PEnalized Norm-Ratios Disentangling Additive Noise, Trend and Sparse Spikes

Cited by 2 publications

References 24 publications

Convergence analysis of block majorize-minimize subspace approach

Convergence analysis of block majorize-minimize subspace approach

Unrolled Deep Networks for Sparse Signal Restoration in Analytical Chemistry

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