Related papers: Inferring Rankings Using Constrained Sensing
In this paper we show the use of the focal underdetermined system solver to recover sparse empirical quadrature rules for parametrized integrals from existing data, consisting of the values of given parametric functions sampled on a…
The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…
Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation…
This paper provides a theoretical analysis of a new learning problem for recommender systems where users provide feedback by comparing pairs of items instead of rating them individually. We assume that comparisons stem from latent user and…
This paper tackles algorithmic and theoretical aspects of dictionary learning from incomplete and random block-wise image measurements and the performance of the adaptive dictionary for sparse image recovery. This problem is related to…
In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…
In this paper we introduce a nonuniform sparsity model and analyze the performance of an optimized weighted $\ell_1$ minimization over that sparsity model. In particular, we focus on a model where the entries of the unknown vector fall into…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Finding the sparse solution of an underdetermined system of linear equations has many applications, especially, it is used in Compressed Sensing (CS), Sparse Component Analysis (SCA), and sparse decomposition of signals on overcomplete…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
We present a comprehensive analysis of an algorithm for evaluating high-dimensional polynomials that are invariant under permutations and rotations. The key bottleneck is the contraction of a high-dimensional symmetric and sparse tensor…
This paper considers the use of total variation regularization in the recovery of approximately gradient sparse signals from their noisy discrete Fourier samples in the context of compressed sensing. It has been observed over the last…
Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…
Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…
The null space condition for $\ell_1$ minimization in compressed sensing is a necessary and sufficient condition on the sensing matrices under which a sparse signal can be uniquely recovered from the observation data via $\ell_1$…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly…
Recovering latent structure from count data has received considerable attention in network inference, particularly when one seeks both cross-group interactions and within-group similarity patterns in bipartite networks, which is widely used…
We consider the problem of detecting the locations of targets in the far field by sending probing signals from an antenna array and recording the reflected echoes. Drawing on key concepts from the area of compressive sensing, we use an…