Principal Component Wavelet Networks for Solving Linear Inverse Problems

In this paper we propose a novel learning-based wavelet transform and demonstrate its utility as representation in solving number of linear inverse problems—these are asymmetric problems, where the forward problem is easy to solve, but difficult often ill-posed. The decomposition comprised application an invertible 2D filter-bank comprising symmetric anti-symmetric filters, combination with set 1×1 convolution filters learnt from Principal Component Analysis (PCA). needed control size decomposition. We show that PCA across subbands way produces architecture equivalent separable Convolutional Neural Network (CNN), principal components forming subtraction mean bias terms. use filter bank (approximately) allows us create deep autoencoder very simply, avoids issues overfitting. investigate construction learning such networks, their problems via Alternating Direction Multipliers Method (ADMM). our network drop-in replacement for traditional discrete transform, using shrinkage projection operator. results good potential on compressive sensing, in-painting, denoising super-resolution, significantly close performance gap Generative Adversarial (GAN)-based methods.