Fractal functions and wavelet expansions based on several scaling functions
Journal of Approximation Theory
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Characterization of oblique dual frame pairs
EURASIP Journal on Applied Signal Processing
Blind multiband signal reconstruction: compressed sensing for analog signals
IEEE Transactions on Signal Processing
Sampling theorems for signals from the union of finite-dimensional linear subspaces
IEEE Transactions on Information Theory
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang–Fix
IEEE Transactions on Signal Processing
Theoretical Results on Sparse Representations of Multiple-Measurement Vectors
IEEE Transactions on Signal Processing
Nonlinear and Nonideal Sampling: Theory and Methods
IEEE Transactions on Signal Processing
A Theory for Sampling Signals From a Union of Subspaces
IEEE Transactions on Signal Processing
Sampling signals with finite rate of innovation
IEEE Transactions on Signal Processing
A minimum squared-error framework for generalized sampling
IEEE Transactions on Signal Processing - Part I
Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors
IEEE Transactions on Signal Processing - Part I
Sparse solutions to linear inverse problems with multiple measurement vectors
IEEE Transactions on Signal Processing
Minimum rate sampling and reconstruction of signals with arbitrary frequency support
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Block sparsity and sampling over a union of subspaces
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Uncertainty relations for shift-invariant analog signals
IEEE Transactions on Information Theory
Sampling piecewise sinusoidal signals with finite rate of innovation methods
IEEE Transactions on Signal Processing
Recovering signals from lowpass data
IEEE Transactions on Signal Processing
Time-delay estimation from low-rate samples: a union of subspaces approach
IEEE Transactions on Signal Processing
Block-sparse signals: uncertainty relations and efficient recovery
IEEE Transactions on Signal Processing
The Cramér-Rao bound for estimating a sparse parameter vector
IEEE Transactions on Signal Processing
Average case analysis of multichannel sparse recovery using convex relaxation
IEEE Transactions on Information Theory
Beyond Nyquist: efficient sampling of sparse bandlimited signals
IEEE Transactions on Information Theory
A sampling theorem for a 2d surface
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Rendering in shift-invariant spaces
Proceedings of Graphics Interface 2013
Hi-index | 35.94 |
A traditional assumption underlying most data converters is that the signal should be sampled at a rate exceeding twice the highest frequency. This statement is based on a worst-case scenario in which the signal occupies the entire available bandwidth. In practice, many signals are sparse so that only part of the bandwidth is used. In this paper, we develop methods for low-rate sampling of continuous-time sparse signals in shift-invariant (SI) spaces, generated by m kernels with period T. We model sparsity by treating the case in which only k out of the m generators are active, however, we do not know which k are chosen. We show how to sample such signals at a rate much lower than m/T, which is the minimal sampling rate without exploiting sparsity. Our approach combines ideas from analog sampling in a subspace with a recently developed block diagram that converts an infinite set of sparse equations to a finite counterpart. Using these two components we formulate our problem within the framework of finite compressed sensing (CS) and then rely on algorithms developed in that context. The distingnishing feature of our results is that in contrast to standard CS, which treats finite-length vectors, we consider sampling of analog signals for which no underlying finite-dimensional model exists. The proposed framework allows to extend much of the recent literature on CS to the analog domain.