This book explores the application of alternative multiplier method in image processing, and selects two areas, that is motion blurred image restoration and fusion of remote sensed images for detailed study. The book conducts simulation experiment through MATLAB, effectively solves complex convex optimization problem by alternative multiplier method, investigates the robust algorithms of masked facial recognition and the relationship between intra-class and inter-class variances of facial images and robust algorithms. The book also explores efficient distributed optimization methods. The distributed computing framework CoCoA is applied to various problems in machine learning and signal processing.