Related papers: Multi-dimensional Sparse Super-resolution
We propose a Bayesian methodology for estimating spiked covariance matrices with jointly sparse structure in high dimensions. The spiked covariance matrix is reparametrized in terms of the latent factor model, where the loading matrix is…
This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as…
Blind image restoration is a non-convex problem which involves restoration of images from an unknown blur kernel. The factors affecting the performance of this restoration are how much prior information about an image and a blur kernel are…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by…
Parsimony in signal representation is a topic of active research. Sparse signal processing and representation is the outcome of this line of research which has many applications in information processing and has shown significant…
We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a…
Super-resolution imaging aims at improving the resolution of an image by enhancing it with other images or data that might have been acquired using different imaging techniques or modalities. In this paper we consider the task of doubling,…
Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit…
This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal…
We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…
Motivated by the application of neural networks in super resolution microscopy, this paper considers super resolution as the mapping of trigonometric moments of a discrete measure on $[0,1)^d$ to its support and weights. We prove that this…
The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm…
Two-dimensional (2D) fully-addressed arrays can conveniently realize three-dimensional (3D) ultrasound imaging while fully controlled such arrays usually demands thousands of independent channels, which is costly. Sparse array technique…
The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…
High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…
$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many…
The conventional methods for estimating camera poses and scene structures from severely blurry or low resolution images often result in failure. The off-the-shelf deblurring or super-resolution methods may show visually pleasing results.…
The problem of estimating a sparse signal from low dimensional noisy observations arises in many applications, including super resolution, signal deconvolution, and radar imaging. In this paper, we consider a sparse signal model with…
A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…