arXiv subjects

Shima Shabani

Publications and source records attributed to Shima Shabani.

5 recordsLinked to original sources

arXiv2026

Reservoir Zero-Coordinatewise Projected Subspace Search for Minimization Over Sparse Symmetric Sets in Machine Learning

We study a class of nonconvex cardinality-constrained optimization problems arising in sparse learning. These problems are NP-hard due to the combinatorial nature of sparsity constraints. We introduce a Reservoir Zero-Coordinatewise Projected Subspace Search (RZCW-PSS) algorithm, a simplex-style method on sparse manifolds that integrates coordinatewise search, symmetry-aware swap-based support updates, randomized low-dimensional subspace exploration, and zero-coordinatewise reservoir injection. The proposed method augments classical coordinate and swap moves with sparse-compatible subspace searches constructed from a dynamically maintained reservoir of previously accepted feasible points. A key feature of the approach is a refined reservoir initialization strategy that embeds sparse projection directly into a uniform sampling procedure, preserving geometric diversity within the feasible set. The algorithm also includes an optional support-identification safeguard that enforces full-support stabilization under a fixed support-change decrease threshold. We establish that, under the stated regularity, sampling, and subproblem-accuracy assumptions, every full-support accumulation point of the RZCW-PSS iterates is Beck--Hallak zero-coordinatewise stationary almost surely; with the safeguard and full-support initialization, this conclusion applies to all accumulation points. We further prove a conditional local linear convergence rate after support stabilization and derive the corresponding logarithmic local iteration complexity. Numerical experiments on synthetic sparse learning problems demonstrate that RZCW-PSS improves robustness and solution quality while remaining computationally competitive with Partial Simplex Search, Basic Feasible Search, and Zero-Coordinatewise Search methods.

math.OC↗

arXiv2025

Morphological Granulometric Analysis of Particle Imagery from Microgravity Experiments

The aim of our work is to analyze size distributions of particles and their agglomerates in imagery from astrophysical microgravity experiments. The data acquired in these experiments are given by sequences consisting of several hundred images. It is desirable to establish an automated routine that helps to assess size distributions of important image structures and their dynamics in a statistical way. The main technique we adopt to this end is the morphological granulometry. After preprocessing steps that facilitate granulometric analysis, we show how to extract useful information on size of particle agglomerates as well as underlying dynamics. At hand of the discussion of two different microgravity key experiments we demonstrate that the granulometric analysis enables to assess important experimental aspects. We conjecture that our developments are a useful basis for the quantitative assessment of microgravity particle experiments.

physics.ins-det↗

arXiv2025

Quality Versus Sparsity in Image Recovery by Dictionary Learning Using Iterative Shrinkage

Sparse dictionary learning (SDL) is a fundamental technique that is useful for many image processing tasks. As an example we consider here image recovery, where SDL can be cast as a nonsmooth optimization problem. For this kind of problems, iterative shrinkage methods represent a powerful class of algorithms that are subject of ongoing research. Sparsity is an important property of the learned solutions, as exactly the sparsity enables efficient further processing or storage. The sparsity implies that a recovered image is determined as a combination of a number of dictionary elements that is as low as possible. Therefore, the question arises, to which degree sparsity should be enforced in SDL in order to not compromise recovery quality. In this paper we focus on the sparsity of solutions that can be obtained using a variety of optimization methods. It turns out that there are different sparsity regimes depending on the method in use. Furthermore, we illustrate that high sparsity does in general not compromise recovery quality, even if the recovered image is quite different from the learning database.

cs.CV↗

arXiv2025

Semi-Monotone Goldstein Line Search Strategy with Application in Sparse Recovery

Line search methods are a prominent class of iterative methods to solve unconstrained minimization problems. These methods produce new iterates utilizing a suitable step size after determining proper directions for minimization. In this paper we propose a semi-monotone line search technique based on the Goldstein quotient for dealing with convex non-smooth optimization problems. The method allows to employ large step sizes away from the optimum thus improving the efficacy compared to standard Goldstein approach. For the presented line search method, we prove global convergence to a stationary point and local R-linear convergence rate in strongly convex cases. We report on some experiments in compressed sensing. By comparison with several state-of-the-art algorithms in the field, we demonstrate the competitive performance of the proposed approach and specifically its high efficiency.

math.OC↗

arXiv2025

Sparse Dictionary Learning for Image Recovery by Iterative Shrinkage

In this paper we study the sparse coding problem in the context of sparse dictionary learning for image recovery. To this end, we consider and compare several state-of-the-art sparse optimization methods constructed using the shrinkage operation. As the mathematical setting of these methods, we consider an online approach as algorithmical basis together with the basis pursuit denoising problem that arises by the convex optimization approach to the dictionary learning problem. By a dedicated construction of datasets and corresponding dictionaries, we study the effect of enlarging the underlying learning database on reconstruction quality making use of several error measures. Our study illuminates that the choice of the optimization method may be practically important in the context of availability of training data. In the context of different settings for training data as may be considered part of our study, we illuminate the computational efficiency of the assessed optimization methods.

cs.CV↗