Robust Recovery for Graph Signal via l₀-Norm Regularization

Graph signal processing refers to dealing with irregularly structured data. Compared with traditional signal processing, it can preserve the complex interactions within irregular data. In this work, we devise a robust algorithm to recover band-limited graph signals in the presence of impulsive noise. First, the observed data vector is recast, such that the noise component is divided into two vectors, representing the dense-noise component and sparse outliers, respectively. We then exploit l(0)-norm to characterize the sparse vector as a regularization term. Alternating minimization is subsequently adopted as the solver for the resultant optimization problem. Besides, we suggest an approach to automatically update the penalty parameter of the l(0)-norm term. In addition, we analyze the computational complexity and the steady-state convergence of our algorithm. Experimental results on synthetic and temperature data exhibit the superiority of the developed method over state-of-the-art algorithms in impulsive noise environments in terms of recovery accuracy and convergence speed.