Related papers: Stable Separation and Super-Resolution of Mixture …
This paper addresses the problem of reconstructing a high-resolution hyperspectral image from a low-resolution multispectral observation. While spatial super-resolution and spectral super-resolution have been extensively studied, joint…
Many problems arising in image processing and signal recovery with multi-regularization can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with…
We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval $[-\Omega, \Omega]$. This problem is known to be challenging in the regime where the spacing of the sources is…
Given an image generated by the convolution of point sources with a band-limited function, the deconvolution problem is to reconstruct the source number, positions, and amplitudes. This problem arises from many important applications in…
A method for spatial deconvolution of spectra is presented. It follows the same fundamental principles as the ``MCS image deconvolution algorithm'' (Magain, Courbin, Sohy, 1998) and uses information contained in the spectrum of a reference…
We study the inverse problem of locating point sources from far-field data under plane wave incidence. A direct computational method is developed based on multiple scattering theory, using a novel indicator function to avoid iterative…
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.…
In this paper, we employ fixed point theory and semidefinite programming to compute the performance bounds on convex block-sparsity recovery algorithms. As a prerequisite for optimal sensing matrix design, a computable performance bound…
We consider the problem of stable recovery of sparse signals of the form $$F(x)=\sum_{j=1}^d a_j\delta(x-x_j),\quad x_j\in\mathbb{R},\;a_j\in\mathbb{C}, $$ from their spectral measurements, known in a bandwidth $\Omega$ with absolute error…
Audio source separation is a difficult machine learning problem and performance is measured by comparing extracted signals with the component source signals. However, if separation is motivated by the ultimate goal of re-mixing then…
In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…
We consider the problem of resolving $ r$ point sources from $n$ samples at the low end of the spectrum when point spread functions (PSFs) are not known. Assuming that the spectrum samples of the PSFs lie in low dimensional subspace (let…
In some super-resolution techniques, adjacent points are illuminated at different times. Thereby, their locations and light intensities can be detected even if the images are very blurred due to diffraction. According to conventional…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…
Solving an optimization problem whose objective function is the sum of two convex functions has received considerable interests in the context of image processing recently. In particular, we are interested in the scenario when a…
Single image super resolution aims to enhance image quality with respect to spatial content, which is a fundamental task in computer vision. In this work, we address the task of single frame super resolution with the presence of image…
In this paper, we study the problem of reconstructing a 3D point source model from a set of 2D projections at unknown view angles. Our method obviates the need to recover the projection angles by extracting a set of rotation-invariant…
This paper considers the problem of recovering an ensemble of Diracs on a sphere from its low resolution measurements. The Diracs can be located at any location on the sphere, not necessarily on a grid. We show that under a separation…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…