Abstract: In this talk we investigate accurate and efficient l_1 regularization methods for generating images from noisy and under-sampled Fourier data. As a prototype, we will consider synthetic aperture radar (SAR).
While l_1 regularization algorithms are already employed in many imaging applications, practical and efficient implementation in terms of real time imaging often remain a challenge. Here we demonstrate that fast numerical operators can be used to robustly implement high order l_1 regularization methods that are as or more efficient than traditional approaches such as back projection, while providing superior image quality. We also develop a joint sparsity model which naturally combines the joint sparsity methodology used for multi-measurement vectors (MMV) with composite imaging methods. Our technique is able to reduce the effects of speckle and other noisy artifacts with little additional computational cost.
In the second part of this talk we demonstrate how it possible to reduce the effects of bad data measurements using a new technique called variance based weighted joint sparsity (VBJS) method. Joint sparsity techniques typically rely on minimizing the l_2,1 norm, but this can be computationally intensive and it requires fine tuning of parameters. The VBJS method uses weighted l_1 regularization, where the weights depend on the pixel-wise variance between the reconstruction of the sparse features of the underlying image. The VBJS method is accurate, robust, cost efficient, and reduces the effects of false data on both image reconstruction and sparse signal recovery.