Related papers: Iterative Reweighted Least Squares Networks With C…
Deep learning-based low-light image enhancers have made significant progress in recent years, with a trend towards achieving satisfactory visual quality while gradually reducing the number of parameters and improving computational…
This review discusses methods for learning parameters for image reconstruction problems using bilevel formulations. Image reconstruction typically involves optimizing a cost function to recover a vector of unknown variables that agrees with…
Motivated by the observation that a given signal $\boldsymbol{x}$ admits sparse representations in multiple dictionaries $\boldsymbol{\Psi}_d$ but with varying levels of sparsity across dictionaries, we propose two new algorithms for the…
Self-paced learning (SPL) mimics the cognitive mechanism of humans and animals that gradually learns from easy to hard samples. One key issue in SPL is to obtain better weighting strategy that is determined by minimizer function. Existing…
This work develops a robust diffusion recursive least squares algorithm to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. This algorithm minimizes an exponentially weighted…
This paper investigates the optimality analysis of the recursive least-squares (RLS) algorithm for autoregressive systems with exogenous inputs (ARX systems). A key challenge in analyzing is managing the potential unboundedness of the…
Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is…
Several regularization methods have recently been introduced which force the latent activations of an autoencoder or deep neural network to conform to either a Gaussian or hyperspherical distribution, or to minimize the implicit rank of the…
Many attempts took place to improve the adaptive filters that can also be useful to improve backpropagation (BP). Normalized least mean squares (NLMS) is one of the most successful algorithms derived from Least mean squares (LMS). However,…
Rank minimization (RM) is a wildly investigated task of finding solutions by exploiting low-rank structure of parameter matrices. Recently, solving RM problem by leveraging non-convex relaxations has received significant attention. It has…
Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…
We present an iterative support shrinking algorithm for $\ell_{p}$-$\ell_{q}$ minimization~($0 <p < 1 \leq q < \infty $). This algorithm guarantees the nonexpensiveness of the signal support set and can be easily implemented after being…
In this paper, we present a practical algorithm based on sparsity regularization to effectively solve nonlinear dynamic inverse problems that are encountered in subsurface model calibration. We use an iteratively reweighted algorithm that…
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the…
Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold…
Nonlocal image representation or group sparsity has attracted considerable interest in various low-level vision tasks and has led to several state-of-the-art image denoising techniques, such as BM3D, LSSC. In the past, convex optimization…
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…
Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…
We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…
Sparse reconstruction approaches using the re-weighted l1-penalty have been shown, both empirically and theoretically, to provide a significant improvement in recovering sparse signals in comparison to the l1-relaxation. However, numerical…