Related papers: Structured FISTA for Image Restoration
We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a…
We consider to design a new efficient and easy-to-implement algorithm to solve a general group sparse optimization model with a class of non-convex non-Lipschitz regularizations, named as fast iterative thresholding and support-and-scale…
In this paper, we consider an LQR design problem for distributed control systems. For large-scale distributed systems, finding a solution might be computationally demanding due to communications among agents. To this aim, we deal with LQR…
Structured pruning of filters or neurons has received increased focus for compressing convolutional neural networks. Most existing methods rely on multi-stage optimizations in a layer-wise manner for iteratively pruning and retraining which…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
Single-pixel imaging (SPI) is a potential computational imaging technique which produces image by solving an illposed reconstruction problem from few measurements captured by a single-pixel detector. Deep learning has achieved impressive…
In this note, we propose a FISTA-type first order algorithm, VAR-FISTA, to solve a composite optimization problem. A distinctive feature of VAR-FISTA is its ability to exploit the convexity of the function in the problem, resulting in an…
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, where the numerator can be written as the sum of a continuously differentiable convex function whose gradient is Lipschitz continuous and a proper…
Image restoration problems are typically ill-posed requiring the design of suitable priors. These priors are typically hand-designed and are fully instantiated throughout the process. In this paper, we introduce a novel framework for…
In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the…
The recently developed data-driven eigenmatrix method shows very promising reconstruction accuracy in sparse recovery for a wide range of kernel functions and random sample locations. However, its current implementation can lead to…
Many large-scale optimization problems can be expressed as composite optimization models. Accelerated first-order methods such as the fast iterative shrinkage-thresholding algorithm (FISTA) have proven effective for numerous large composite…
We introduce a fast iterative non-local shrinkage algorithm to recover MRI data from undersampled Fourier measurements. This approach is enabled by the reformulation of current non-local schemes as an alternating algorithm to minimize a…
This paper proposes a new backtracking strategy based on the FISTA accelerated algorithm for multiobjective optimization problems. The strategy focuses on solving the problem of Lipschitz constant being unknown. It allows estimate parameter…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
This paper is concerned with convex composite minimization problems in a Hilbert space. In these problems, the objective is the sum of two closed, proper, and convex functions where one is smooth and the other admits a computationally…
The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex…
Motivated by the limitation of analyzing oscillatory signals composed of multiple components with fast-varying instantaneous frequency, we approach the time-frequency analysis problem by optimization. Based on the proposed adaptive harmonic…