9 research outputs found
Greedy Signal Recovery Review
The two major approaches to sparse recovery are L1-minimization and greedy
methods. Recently, Needell and Vershynin developed Regularized Orthogonal
Matching Pursuit (ROMP) that has bridged the gap between these two approaches.
ROMP is the first stable greedy algorithm providing uniform guarantees.
Even more recently, Needell and Tropp developed the stable greedy algorithm
Compressive Sampling Matching Pursuit (CoSaMP). CoSaMP provides uniform
guarantees and improves upon the stability bounds and RIC requirements of ROMP.
CoSaMP offers rigorous bounds on computational cost and storage. In many cases,
the running time is just O(NlogN), where N is the ambient dimension of the
signal. This review summarizes these major advances
Compressive Inverse Scattering I. High Frequency SIMO Measurements
Inverse scattering from discrete targets with the
single-input-multiple-output (SIMO), multiple-input-single-output (MISO) or
multiple-input-multiple-output (MIMO) measurements is analyzed by compressed
sensing theory with and without the Born approximation. High frequency analysis
of (probabilistic) recoverability by the -based
minimization/regularization principles is presented. In the absence of noise,
it is shown that the -based solution can recover exactly the target of
sparsity up to the dimension of the data either with the MIMO measurement for
the Born scattering or with the SIMO/MISO measurement for the exact scattering.
The stability with respect to noisy data is proved for weak or widely separated
scatterers. Reciprocity between the SIMO and MISO measurements is analyzed.
Finally a coherence bound (and the resulting recoverability) is proved for
diffraction tomography with high-frequency, few-view and limited-angle
SIMO/MISO measurements.Comment: A new section on diffraction tomography added; typos fixed; new
figures adde
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Greedy Signal Recovery Review
The two major approaches to sparse recovery are L1-minimization and greedy methods.
Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP)
that has bridged the gap between these two approaches. ROMP is the first stable greedy
algorithm providing uniform guarantees. Even more recently, Needell and Tropp developed the
stable greedy algorithm Compressive Sampling Matching Pursuit (CoSaMP). CoSaMP provides
uniform guarantees and improves upon the stability bounds and RIC requirements of ROMP.
CoSaMP offers rigorous bounds on computational cost and storage. In many cases, the running
time is just O(NlogN), where N is the ambient dimension of the signal. This review
summarizes these major advances