Analysis of noise and nonsparsity in the ISAR image recovery from a reduced set of data

摘要

Sparse inverse synthetic aperture radar (ISAR) images can be reconstructed using a reduced set of data and compressive sensing based theory. In real cases the ISAR images are noisy and only approximately sparse or not sparse. The influence of the additive input noise and nonsparsity of the ISAR data to the reconstructed images is analyzed in this paper. Simple and exact formula for the mean square error (MSE) in the reconstructed ISAR image is derived. Results are tested on examples and compared with statistical data in the cases of: 1) input additive noise and sparse ISAR images and 2) nonsparse ISAR images reconstructed assuming that they were sparse. Statistical data confirm the theoretical results.