In this paper, we deal with l
0‐norm data fitting and total variation regularization for image compression and denoising. The l
0‐norm data fitting is used for measuring the number of non‐zero wavelet coefficients to be employed to represent an image. The regularization term given by the total variation is to recover image edges. Due to intensive numerical computation of using l
0‐norm, it is usually approximated by other functions such as the l
1‐norm in many image processing applications. The main goal of this paper is to develop a fast and effective algorithm to solve the l
0‐norm data fitting and total variation minimization problem. Our idea is to apply an alternating minimization technique to solve this problem, and employ a graph‐cuts algorithm to solve the subproblem related to the total variation minimization. Numerical examples in image compression and denoising are given to demonstrate the effectiveness of the proposed algorithm.
