Removal of Micro-Doppler Effect of ISAR Image Based on Laplacian Regularized Nonconvex Low-Rank Representation

The micro-Doppler (m-D) effect caused by micro-motion degrades the readability of the inverse synthetic aperture radar (ISAR) image. To achieve well-focused ISAR image of the target with the micro-motion part, this paper proposes a novel approach for the removal of m-D effect of ISAR image. Note that the range profiles of the rigid body are similar to each other, making the respective data matrix low-rank. Those of the micro-motion part, in contrary, generally fluctuate in different range cells, whose data matrix is sparse. Therefore, the removal of m-D effect can be naturally solved by the robust principal component analysis (RPCA)-a convenient convex program to decompose an auxiliary matrix into a low-rank matrix and a sparse one. In RPCA, the rank of a matrix is described by the nuclear norm, which is convex but leads to a suboptimal solution. To address it, we utilize a nonconvex surrogate, i.e., the summation of logistic function of the singular values of a matrix, to approximate the rank. Moreover, the range profiles of the rigid body are generally locally similar. To capture this geometric structured information, we further introduce a Laplacian regularization into the model. Then, the Laplacian regularized nonconvex low-rank (LRNL) model is solved efficiently by the linearized alternating direction method (ADM). Extensive experimental results based on both simulated and measured data demonstrate the effectiveness of the proposed approach on the removal of m-D effect of ISAR image.