Sparse image super-resolution via superset selection and pruning

This note extends the superset method for sparse signal recovery from bandlimited measurements to the two-dimensional case. The algorithm leverages translation-invariance of the Fourier basis functions by constructing a Hankel tensor, and identifying the signal subspace from its range space. In the noisy case, this method determines a superset which then needs to undergo pruning. The method displays reasonable robustness to noise, and unlike ℓ [subscript 1] minimization, always succeeds in the noiseless case.United States. Air Force Office of Scientific ResearchTOTAL (Firm)Alfred P. Sloan FoundationNational Science Foundation (U.S.)United States. Office of Naval Researc

ESPRIT for multidimensional general grids

We present a new method for complex frequency estimation in several variables, extending the classical (1d) ESPRIT-algorithm. We also consider how to work with data sampled on non-standard domains (i.e going beyond multi-rectangles)

Sampling and Exact Reconstruction of Pulses with Variable Width

Recent sampling results enable the reconstruction of signals composed of streams of fixed-shaped pulses. These results have found applications in topics as varied as channel estimation, biomedical imaging and radio astronomy. However, in many real signals, the pulse shapes vary throughout the signal. In this paper, we show how to sample and perfectly reconstruct Lorentzian pulses with variable width. Since a stream of Lorentzian pulses has a finite number of degrees of freedom per unit time, it belongs to the class of signals with finite rate of innovation (FRI). In the noiseless case, perfect recovery is guaranteed by a set of theorems. In addition, we verify that our algorithm is robust to model-mismatch and noise. This allows us to apply the technique to two practical applications: electrocardiogram (ECG) compression and bidirectional reflectance distribution function (BRDF) sampling. ECG signals are one dimensional, but the BRDF is a higher dimensional signal, which is more naturally expressed in a spherical coordinate system; this motivated us to extend the theory to the 2D and spherical cases. Experiments on real data demonstrate the viability of the proposed model for ECG acquisition and compression, as well as the efficient representation and low-rate sampling of specular BRDFs

Sparse approximation of functions using sums of exponentials and AAK theory

We consider the problem of approximating functions by sums of few exponentials functions, either on an interval or on the positive half-axis. We study both continuous and discrete cases, i.e. when the function is replaced by a number of equidistant samples. Recently, an algorithm has been constructed by Beylkin and Monzón for the discrete case. We provide a theoretical framework for understanding how this algorithm relates to the continuous case