Predictive Coding Machine for Compressed Sensing and Image Denoising

Sparse and low rank coding has widely received much attention in machine learning, multimedia and computer vision. Unfortunately, expensive inference restricts the power of coding models in real-world applications, e.g., compressed sensing and image deblurring. In order to avoid the expensive inference, we propose a predictive coding machine (PCM) which aims to train a deep neural network (DNN) encoder to approximate the codes. By this means, a test sample can be fast approximated by the well-trained DNN. However, DNN leads PCM to be a non-convex and non-smooth optimization problem, which is extremely hard to solve. To address this challenge, we extend accelerated proximal gradient for PCM by steering gradient descent of DNN. To the best of our knowledge, we are the first to propose a gradient descent algorithm guided by accelerated proximal gradient for solving the PCM problem. Besides, a sufficient condition is provided to ensure the convergence to a critical point. Moreover, when the coding models are convex in PCM, the convergence rate O(1/(m2√t)) can be held in which m is the iteration number of accelerated proximal gradient, and t is the epoch of training DNN. Numerical results verify the promising advantages of PCM in terms of effectiveness, efficiency and robustness.