Year: 2010
Type: article
Abstract: 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 L 1 -based minimization/regularization principles is presented. In the absence of noise, it is shown that the L 1 -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.
Source: Inverse Problems
Author: Albert C Fannjiang
Institution: University of California, Davis
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1594848653