Improving weighted ℓ1 regularization for image and sparse signal recovery using a multi-measurement vector approach

Much  research  has  been  recently  been  devoted  to  sparse  signal  recovery  and  image  reconstruction from multiple measurement vectors (MMV). The assumption that the underlying signals or images have some common features with sparse representation suggests that using a joint sparsity approach to recover each individual  signal  or  image  can  be  more  effective  than  recovering  each  signal  or  image  separately  using standard  sparse  recovery  techniques.  Joint  sparsity  reconstruction  is  typically  performed  using $\ell_{2,1}$ minimization, and although the process often yields better results than separate recoveries, the inherent coupling makes the algorithm computationally intensive, since it is difficult to parallelize. It is also not robust to outliers or bad data.  In this talk we introduce an algorithm based on the observation that the pixel-wise variance of the signals convey information about their shared support.  This observation motivates the introduction of a weighted $\ell_{p}$, $p = 1,2$ joint sparsity algorithm, where the weights depend on information learned from the calculated variance.  These spatially varying weights may also be determined by determining the magnitude of the features in the sparse domain.   Specifically, the sparsity enforcing regularization term should be more heavily penalized in regions where it is likely that no signal is present.  We demonstrate the accuracy, robustness, and cost efficiency of our new method.  It can also be used where some of the measurement vectors may misrepresent the unknown signals or images of interest.  Such "false data" problems appear in applications including state estimation of electrical power grids, large scale sensor network estimation, and synthetic aperture radar automated target recognition.

Friday, January 24, 2020 - 15:30

704 Thackeray Hall

Speaker Information
Anne Gelb
Dartmouth College