Hard thresholding is the process of setting to zero the coefficients whose absolute values are lower than the threshold λ . Soft thresholding is another method by first setting to zero coefficients whose absolute values are lower than the threshold λ and then shrinking the nonzero coefficients toward zero.

The method is based on the representation of segments via characteristic functions. The method simply alternates two steps: convolution and thresholding. The algorithm has the optimal complexity O(NlogN) per iteration and fast convergence.