Group polytope faces pursuit for recovery of block-sparse signals

This is the accepted version of the article. The final publication is available at link.springer.com. http://www.springerlink.com/content/e0r61416446277w0

Nonideal Sampling and Interpolation from Noisy Observations in Shift-Invariant Spaces

Digital analysis and processing of signals inherently relies on the existence of methods for reconstructing a continuous-time signal from a sequence of corrupted discrete-time samples. In this paper, a general formulation of this problem is developed that treats the interpolation problem from ideal, noisy samples, and the deconvolution problem in which the signal is filtered prior to sampling, in a unified way. The signal reconstruction is performed in a shift-invariant subspace spanned by the integer shifts of a generating function, where the expansion coefficients are obtained by processing the noisy samples with a digital correction filter. Several alternative approaches to designing the correction filter are suggested, which differ in their assumptions on the signal and noise. The classical deconvolution solutions (least-squares, Tikhonov, and Wiener) are adapted to our particular situation, and new methods that are optimal in a minimax sense are also proposed. The solutions often have a similar structure and can be computed simply and efficiently by digital filtering. Some concrete examples of reconstruction filters are presented, as well as simple guidelines for selecting the free parameters (e.g., regularization) of the various algorithms

A Multichannel Spatial Compressed Sensing Approach for Direction of Arrival Estimation

The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-642-15995-4_57ESPRC Leadership Fellowship EP/G007144/1EPSRC Platform Grant EP/045235/1EU FET-Open Project FP7-ICT-225913\"SMALL

On the distinguishability of random quantum states

We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of their Gram matrix. We use the latter to lower bound the asymptotic distinguishability of ensembles of n random quantum states in d dimensions, where n/d approaches a constant. In particular, for almost all ensembles of n states in n dimensions, p>0.72. An application to distinguishing Boolean functions (the "oracle identification problem") in quantum computation is given.Comment: 20 pages, 2 figures; v2 fixes typos and an error in an appendi

Measurement does not always aid state discrimination

We have investigated the problem of discriminating between nonorthogonal quantum states with least probability of error. We have determined that the best strategy for some sets of states is to make no measurement at all, and simply to always assign the most commonly occurring state. Conditions which describe such sets of states have been derived.Comment: 3 page

Minimum-error discrimination between symmetric mixed quantum states

We provide a solution of finding optimal measurement strategy for distinguishing between symmetric mixed quantum states. It is assumed that the matrix elements of at least one of the symmetric quantum states are all real and nonnegative in the basis of the eigenstates of the symmetry operator.Comment: 10 page

Mixed quantum state detection with inconclusive results

We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a sufficient condition for the scaled inverse measurement to maximize the probability of correct detection for the case in which the rate of inconclusive results exceeds a certain threshold. Using this condition we derive the optimal measurement for linearly independent pure-state sets, and for mixed-state sets with a broad class of symmetries. Specifically, we consider geometrically uniform (GU) state sets and compound geometrically uniform (CGU) state sets with generators that satisfy a certain constraint. We then show that the optimal measurements corresponding to GU and CGU state sets with arbitrary generators are also GU and CGU respectively, with generators that can be computed very efficiently in polynomial time within any desired accuracy by solving a semidefinite programming problem.Comment: Submitted to Phys. Rev.