Related papers: Blind Deconvolution with Non-local Sparsity Reweig…

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…

Deep convolutional networks often append additive constant ("bias") terms to their convolution operations, enabling a richer repertoire of functional mappings. Biases are also used to facilitate training, by subtracting mean response over…

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

Visual recognition algorithms are required today to exhibit adaptive abilities. Given a deep model trained on a specific, given task, it would be highly desirable to be able to adapt incrementally to new tasks, preserving scalability as the…

We propose a new randomized coordinate descent method for a convex optimization template with broad applications. Our analysis relies on a novel combination of four ideas applied to the primal-dual gap function: smoothing, acceleration,…

There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…

We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…

Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these methods by integrating convex transformations of the…

Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…

Blind image deblurring is a long standing challenging problem in image processing and low-level vision. Recently, sophisticated priors such as dark channel prior, extreme channel prior, and local maximum gradient prior, have shown promising…

In this paper, we propose a Riemannian steepest descent method for solving a blind deconvolution problem. We prove that the proposed algorithm with an appropriate initialization will recover the exact solution with high probability when the…

The method described here performs blind deconvolution of the beamforming output in the frequency domain. To provide accurate blind deconvolution, sparsity priors are introduced with a smooth \ell_1/\ell_2 regularization term. As the mean…

Image restoration has seen great progress in the last years thanks to the advances in deep neural networks. Most of these existing techniques are trained using full supervision with suitable image pairs to tackle a specific degradation.…

A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…

Non-local self-similarity and sparsity principles have proven to be powerful priors for natural image modeling. We propose a novel differentiable relaxation of joint sparsity that exploits both principles and leads to a general framework…

There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…

We study the question of extracting a sequence of functions $\{\boldsymbol{f}_i, \boldsymbol{g}_i\}_{i=1}^s$ from observing only the sum of their convolutions, i.e., from $\boldsymbol{y} = \sum_{i=1}^s \boldsymbol{f}_i\ast…

In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…

We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…