Information Capacity and Sampling Ratios for Compressed Sensing-Based SAR Imaging

Compressed sensing (CS) techniques can reduce the sampling rates required in synthetic aperture radar (SAR). However, it is difficult to use the restricted isometry property to theoretically analyze the performance. Therefore, in this letter, information theory is applied to set necessary bounds on sampling ratios in CS-based SAR imaging. The system is viewed as a multi-input/multi-output (MIMO) channel, with information capacity quantified for a given measurement matrix and signal-to-noise ratio (SNR). According to the source-channel coding theorem, the lower bound of the sampling ratios is derived in terms of sparsity ratio, SNR, bandwidth, and radar pulse duration. Simulation studies are performed to test and analyze the information-theoretical bounds.