The Tail-Normalized Iterative Hard Thresholding Algorithm for Compressed Sensing

The tail-l(1) minimization algorithm significantly enhances the recovery capability of sparse signals compared to the l(1) minimization algorithm. However, solving the tail-l(1) minimization problem requires high computational costs and a considerable amount of time. The normalized iterative hard thresholding (NIHT) algorithm, an improvement over the traditional IHT algorithm, exhibits good computational efficiency. Inspired by the NIHT algorithm, this paper introduces an enhanced NIHT algorithm, namely the tail-NIHT algorithm. The tail-NIHT algorithm retains the computational speed of the NIHT algorithm, greatly improving the efficiency of solving the tail-l(1) minimization problem. Additionally, the tail-NIHT algorithm enhances the sparse signal recovery capability of the NIHT algorithm. Experimental results demonstrate that this algorithm is a promising approach in compressed sensing.