Related papers: Estimating Sparse Signals with Smooth Support via …
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
In this paper the problem of image restoration (denoising and inpainting) is approached using sparse approximation of local image blocks. The local image blocks are extracted by sliding square windows over the image. An adaptive block size…
The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in various areas of signal processing such as parallel…
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…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…
Optical flow is the pattern of apparent motion of objects in a scene. The computation of optical flow is a critical component in numerous computer vision tasks such as object detection, visual object tracking, and activity recognition.…
We propose a unified fractional regularization framework for sparse signal recovery based on the $\ell_1/\ell_p^q$ model. This model generalizes several widely used sparsity-promoting regularizers and provides additional flexibility through…
Several important classes of images such as text, barcode and pattern images have the property that pixels can only take a distinct subset of values. This knowledge can benefit the restoration of such images, but it has not been widely…
The L1 norm regularized least squares method is often used for finding sparse approximate solutions and is widely used in 1-D signal restoration. Basis pursuit denoising (BPD) performs noise reduction in this way. However, the shortcoming…
In numerous substitution models for the $\l_{0}$-norm minimization problem $(P_{0})$, the $\l_{p}$-norm minimization $(P_{p})$ with $0<p<1$ have been considered as the most natural choice. However, the non-convex optimization problem…
In many linear regression problems, including ill-posed inverse problems in image restoration, the data exhibit some sparse structures that can be used to regularize the inversion. To this end, a classical path is to use $\ell_{12}$ block…
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…
In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of…
We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an $\ell_2$ data-fidelity term and a…
This paper discusses the incorporation of local sparsity information, e.g. in each pixel of an image, via minimization of the $\ell^{1,\infty}$-norm. We discuss the basic properties of this norm when used as a regularization functional and…
This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…
This paper presents a novel L1-norm semi-supervised learning algorithm for robust image analysis by giving new L1-norm formulation of Laplacian regularization which is the key step of graph-based semi-supervised learning. Since our L1-norm…
Sparse regression methods have been proven effective in a wide range of signal processing problems such as image compression, speech coding, channel equalization, linear regression and classification. In this paper a new convex method of…
We present novel analysis and algorithms for solving sparse phase retrieval and sparse principal component analysis (PCA) with convex lifted matrix formulations. The key innovation is a new mixed atomic matrix norm that, when used as…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…