Image reconstruction via L0 gradient and L1 wavelet coefficients minimization

In this paper, we address the problem of image reconstruction from highly undersampled Fourier measurements. In order to promote inherent sparsity in gradient and wavelet transform domain, we proposed a new reconstruction scheme via minimizing L₀ norm of gradients and L₁ norm of wavelet coefficients. L₀ gradient minimization can control the number of non-zero gradients to enforce the sparsity in gradient, which results in edge preserving reconstruction. The reconstruction is casted into optimization framework and alternating direction method of multipliers (ADMM) algorithm is utilized to efficiently solve the proposed optimization problem. Experimental results demonstrate the superior performance of the proposed method in comparison with the L₁ gradient reconstruction method.