Related papers: Sparse synthesis regularization with deep neural n…

In this paper, we consider the minimization of a Tikhonov functional with an $\ell_1$ penalty for solving linear inverse problems with sparsity constraints. One of the many approaches used to solve this problem uses the Nemskii operator to…

Frames are the foundation of the linear operators used in the decomposition and reconstruction of signals, such as the discrete Fourier transform, Gabor, wavelets, and curvelet transforms. The emergence of sparse representation models has…

Deep neural networks have become very popular in modeling complex nonlinear processes due to their extraordinary ability to fit arbitrary nonlinear functions from data with minimal expert intervention. However, they are almost always…

Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norm, e.g., $L_1$ and $L_2$ norms. In this…

In the past decade, sparsity-driven regularization has led to advancement of image reconstruction algorithms. Traditionally, such regularizers rely on analytical models of sparsity (e.g. total variation (TV)). However, more recent methods…

Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few…

This work presents an approach for image reconstruction in clinical low-dose tomography that combines principles from sparse signal processing with ideas from deep learning. First, we describe sparse signal representation in terms of…

Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…

This paper introduces recovery thresholding hyperinterpolations, a novel class of methods for sparse signal reconstruction in the presence of noise. We develop a framework that integrates thresholding operators--including hard thresholding,…

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…

The extensive need for computational resources poses a significant obstacle to deploying large-scale Deep Neural Networks (DNN) on devices with constrained resources. At the same time, studies have demonstrated that a significant number of…

This work addresses the recovery and demixing problem of signals that are sparse in some general dictionary. Involved applications include source separation, image inpainting, super-resolution, and restoration of signals corrupted by…

We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…

Many regression and classification procedures fit a parameterized function $f(x;w)$ of predictor variables $x$ to data $\{x_{i},y_{i}\}_1^N$ based on some loss criterion $L(y,f)$. Often, regularization is applied to improve accuracy by…

It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…

This paper presents a novel hybrid algorithm for minimizing the sum of a continuously differentiable loss function and a nonsmooth, possibly nonconvex, sparse regularization function. The proposed method alternates between solving a…

$\ell_1$ based sparse regularization plays a central role in compressive sensing and image processing. In this paper, we propose $\ell_1$DecNet, as an unfolded network derived from a variational decomposition model incorporating $\ell_1$…

This paper presents a regularization technique incorporating a non-convex and non-smooth term, $\ell_{1}^{2}-\eta\ell_{2}^{2}$, with parameters $0<\eta\leq 1$ designed to address ill-posed linear problems that yield sparse solutions. We…