  Multilook processing is a widely used speckle reduction approach in synthetic
aperture radar (SAR) imaging. Conventionally, it is achieved by incoherently
summing of some independent low-resolution images formulated from overlapping
subbands of the SAR signal. However, in the context of compressive sensing (CS)
SAR imaging, where the samples are collected at sub-Nyquist rate, the data
spectrum is highly aliased that hinders the direct application of the existing
multilook techniques. In this letter, we propose a new CS-SAR imaging method
that can realize multilook processing simultaneously during image
reconstruction. The main idea is to replace the SAR observation matrix by the
inverse of multilook procedures, which is then combined with random sampling
matrix to yield a multilook CS-SAR observation model. Then a joint sparse
regularization model, considering pixel dependency of subimages, is derived to
form multilook images. The suggested SAR imaging method can not only
reconstruct sparse scene efficiently below Nyquist rate, but is also able to
achieve a comparable reduction of speckles during reconstruction. Simulation
results are finally provided to demonstrate the effectiveness of the proposed
method.
