Enhanced iterative hard thresholding for the estimation of discrete-valued sparse signals

摘要

In classical Compressed Sensing, real-valued sparse vectors have to be estimated from an underdetermined system of linear equations. However, in many applications such as sensor networks, the elements of the vector to be estimated are discrete-valued or from a finite set. Hence, specialized algorithms which perform the reconstruction with respect to this additional knowledge are required. Starting from the well-known iterative hard thresholding algorithm, a new algorithm is developed. To this end, knowledge from communications engineering is transferred to Compressed Sensing, resulting in a powerful though low-complexity algorithm. Via numerical results the benefit of the proposed algorithm is covered.