Related papers: A stochastic optimisation unadjusted Langevin meth…
In this paper we are concerned with fully automatic and locally adaptive estimation of functions in a "signal + noise"-model where the regression function may additionally be blurred by a linear operator, e.g. by a convolution. To this end,…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
We present a method for supervised learning of sparsity-promoting regularizers for image denoising. Sparsity-promoting regularization is a key ingredient in solving modern image reconstruction problems; however, the operators underlying…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…
In this work, we propose a first-order sampling method called the Metropolis-adjusted Preconditioned Langevin Algorithm for approximate sampling from a target distribution whose support is a proper convex subset of $\mathbb{R}^{d}$. Our…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
Blind image deblurring is a challenging low-level vision task that involves estimating the unblurred image when the blur kernel is unknown. In this paper, we present a self-supervised multi-scale blind image deblurring method to jointly…
This study addresses the blind deconvolution problem with modulated inputs, focusing on a measurement model where an unknown blurring kernel $\boldsymbol{h}$ is convolved with multiple random modulations…
Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…
We propose a blind deconvolution method for signals on graphs, with the exact sparseness constraint for the original signal. Graph blind deconvolution is an algorithm for estimating the original signal on a graph from a set of blurred and…
We propose a general alternating minimization algorithm for nonconvex optimization problems with separable structure and nonconvex coupling between blocks of variables. To fix our ideas, we apply the methodology to the problem of blind…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…
Image deblurring is an ill-posed problem with multiple plausible solutions for a given input image. However, most existing methods produce a deterministic estimate of the clean image and are trained to minimize pixel-level distortion. These…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…
This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly…
In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…
The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have…