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Semantic segmentation consists of assigning a semantic label to each pixel according to predefined classes. This process facilitates the understanding of object appearance and spatial relationships, playing an important role in the global…

We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…

Semantic Image Segmentation facilitates a multitude of real-world applications ranging from autonomous driving over industrial process supervision to vision aids for human beings. These models are usually trained in a supervised fashion…

Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…

Many computer vision systems require low-cost segmentation algorithms based on deep learning, either because of the enormous size of input images or limited computational budget. Common solutions uniformly downsample the input images to…

Feature selection procedures for spatial point processes parametric intensity estimation have been recently developed since more and more applications involve a large number of covariates. In this paper, we investigate the setting where the…

In this work we develop a novel approach using deep neural networks to reconstruct the conductivity distribution in elliptic problems from one measurement of the solution over the whole domain. The approach is based on a mixed reformulation…

Nonconvex penalties are utilized for regularization in high-dimensional statistical learning algorithms primarily because they yield unbiased or nearly unbiased estimators for the parameters in the model. Nonconvex penalties existing in the…

Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…

Robustness and generalizability in medical image segmentation are often hindered by scarcity and limited diversity of training data, which stands in contrast to the variability encountered during inference. While conventional strategies --…

Semantic segmentation stands as a pivotal research focus in computer vision. In the context of industrial image inspection, conventional semantic segmentation models fail to maintain the segmentation consistency of fixed components across…

We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…

We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is…

Piecewise contractions (PCs) are piecewise smooth maps that decrease distance between pairs of points in the same domain of continuity. The dynamics of a variety of systems is described by PCs. During the last decade, a lot of effort has…

We introduce new finite-dimensional spaces specifically designed to approximate the solutions to high-frequency Helmholtz problems with smooth variable coefficients in dimension $d$. These discretization spaces are spanned by Gaussian…

Using a multiplicative reparametrization, I show that a subclass of $L_q$ penalties with $q\leq 1$ can be expressed as sums of $L_2$ penalties. It follows that the lasso and other norm-penalized regression estimates may be obtained using a…

The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…

Segmentation remains an important problem in image processing. For homogeneous (piecewise smooth) images, a number of important models have been developed and refined over the past several decades. However, these models often fail when…

A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study…

This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…