Thresholded Smoothed Norm for Accelerated Sparse Recovery

Smoothed ℓ₀ norm (SL0) is a fast and complex domain extendible sparse recovery algorithm which is suitable for many practical real-time applications. In this letter, we propose an improved algorithm termed “Thresholded Smoothed ℓ₀ Norm (T-SL0)” for accelerating the iterative process of SL0. T-SL0 introduces an iterative efficiency indicator and compares it with a preset threshold in real time to determine whether or not the current iteration should be executed. Through identifying and bypassing low efficient iterations, our approach converges much faster than the original SL0 algorithm. Experimental results are presented to demonstrate that our approach can accelerate SL0 significantly without loss of accuracy.