1,009 research outputs found
Precise Semidefinite Programming Formulation of Atomic Norm Minimization for Recovering d-Dimensional () Off-the-Grid Frequencies
Recent research in off-the-grid compressed sensing (CS) has demonstrated
that, under certain conditions, one can successfully recover a spectrally
sparse signal from a few time-domain samples even though the dictionary is
continuous. In particular, atomic norm minimization was proposed in
\cite{tang2012csotg} to recover -dimensional spectrally sparse signal.
However, in spite of existing research efforts \cite{chi2013compressive}, it
was still an open problem how to formulate an equivalent positive semidefinite
program for atomic norm minimization in recovering signals with -dimensional
() off-the-grid frequencies. In this paper, we settle this problem by
proposing equivalent semidefinite programming formulations of atomic norm
minimization to recover signals with -dimensional () off-the-grid
frequencies.Comment: 4 pages, double-column,1 Figur
Super-resolution Line Spectrum Estimation with Block Priors
We address the problem of super-resolution line spectrum estimation of an
undersampled signal with block prior information. The component frequencies of
the signal are assumed to take arbitrary continuous values in known frequency
blocks. We formulate a general semidefinite program to recover these
continuous-valued frequencies using theories of positive trigonometric
polynomials. The proposed semidefinite program achieves super-resolution
frequency recovery by taking advantage of known structures of frequency blocks.
Numerical experiments show great performance enhancements using our method.Comment: 7 pages, double colum
Structure-Based Bayesian Sparse Reconstruction
Sparse signal reconstruction algorithms have attracted research attention due
to their wide applications in various fields. In this paper, we present a
simple Bayesian approach that utilizes the sparsity constraint and a priori
statistical information (Gaussian or otherwise) to obtain near optimal
estimates. In addition, we make use of the rich structure of the sensing matrix
encountered in many signal processing applications to develop a fast sparse
recovery algorithm. The computational complexity of the proposed algorithm is
relatively low compared with the widely used convex relaxation methods as well
as greedy matching pursuit techniques, especially at a low sparsity rate.Comment: 29 pages, 15 figures, accepted in IEEE Transactions on Signal
Processing (July 2012
- …