Analysis of off-grid effects in wideband sonar images using compressive sensing

In this paper an analysis of sparse wideband sonar images, obtained using compressive sensing reconstruction methods, for generally positioned off-grid targets, is presented. An exact relation is derived for the expected squared error in the resulting sonar image reconstructed from a reduced set of measurements, assuming the sparsity constraint. The error depends on the number of available data, as compared to the complete set of data, and the assumed sparsity. Since the signal is not on the grid, it looses the property of sparsity in the transformation domain. The effects of random sampling and noise will be illustrated and checked on examples as well.

[1]  Srdjan Stankovic,et al.  Missing samples analysis in signals for applications to L-estimation and compressive sensing , 2014, Signal Process..

[2]  Thomas Strohmer,et al.  High-Resolution Radar via Compressed Sensing , 2008, IEEE Transactions on Signal Processing.

[3]  Xudong Zhang,et al.  Wideband sonar imaging via compressed sensing , 2014, OCEANS 2014 - TAIPEI.

[4]  Feng Liu,et al.  Wideband underwater sonar imaging via compressed sensing with scaling effect compensation , 2015, Science China Information Sciences.

[5]  Xudong Zhang,et al.  Compressed sensing radar imaging of off-grid sparse targets , 2015, 2015 IEEE Radar Conference (RadarCon).

[6]  Ljubiša Stankovíc,et al.  Nonsparsity Influence on the ISAR Recovery from a Reduced Set of Data , 2016 .

[7]  Milos Dakovic,et al.  On the reconstruction of nonsparse time-frequency signals with sparsity constraint from a reduced set of samples , 2018, Signal Process..

[8]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[9]  Massimo Fornasier,et al.  Compressive Sensing , 2015, Handbook of Mathematical Methods in Imaging.

[10]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[11]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[12]  Isidora Stanković,et al.  On the Errors in Randomly Sampled Nonsparse Signals Reconstructed With a Sparsity Assumption , 2017, IEEE Geoscience and Remote Sensing Letters.