Joint Sparsity with Partially Known Support and Application to Ultrasound Imaging

We investigate the benefits of known partial support for the recovery of joint-sparse signals and demonstrate that it is advantageous in terms of recovery performance for both rank-blind and rank-aware algorithms. We suggest extensions of several joint-sparse recovery algorithms, e.g., simultaneous normalized iterative hard thresholding, subspace greedy methods and subspace-augmented multiple signal classification techniques. We describe a direct application of the proposed methods for compressive multiplexing of ultrasound (US) signals. The technique exploits the compressive multiplexer architecture for signal compression and relies on joint-sparsity of US signals in the frequency domain for signal reconstruction. We validate the proposed algorithms on numerical experiments and show their superiority against state-ofthe-art approaches in rank-defective cases. We also demonstrate that the techniques lead to a significant increase of the image quality on in vivo carotid images compared to reconstruction without partially known support. The supporting code is available on https://github.com/AdriBesson/spl2018_joint_sparse.