arXiv subjects

Sophie Marie Fosson

Publications and source records attributed to Sophie Marie Fosson.

3 recordsLinked to original sources

arXiv2026

Discrete-time feedback linearization control for nonsmooth constrained optimization

We propose a discrete-time feedback linearization control approach to solve nonsmooth linearly constrained composite optimization problems. By using proximal operators, we construct a dynamical system whose equilibria correspond to the stationary points of the optimization problem. Interpreting the Lagrange multipliers as control inputs, we employ feedback linearization control to steer the obtained dynamical system to a stable equilibrium. We analyze the convergence of the resulting closed-loop system both in the strongly convex setting and under the Polyak-Lojasiewicz condition. Finally, we illustrate the applicability of the approach through numerical experiments.

math.OC↗

arXiv2019

Analysis of SparseHash: an efficient embedding of set-similarity via sparse projections

Embeddings provide compact representations of signals in order to perform efficient inference in a wide variety of tasks. In particular, random projections are common tools to construct Euclidean distance-preserving embeddings, while hashing techniques are extensively used to embed set-similarity metrics, such as the Jaccard coefficient. In this letter, we theoretically prove that a class of random projections based on sparse matrices, called SparseHash, can preserve the Jaccard coefficient between the supports of sparse signals, which can be used to estimate set similarities. Moreover, besides the analysis, we provide an efficient implementation and we test the performance in several numerical experiments, both on synthetic and real datasets.

cs.DS↗

arXiv2018

Steerable Discrete Cosine Transform

In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms.

cs.IT↗