QISTA-ImageNet: A Deep Compressive Image Sensing Framework Solving ℓ q-Norm Optimization Problem

Gang-Xuan Lin, Shih-Wei Hu, Chun-Shien Lu

Abstract: In this paper, we study how to reconstruct the original images from the given sensed samples/measurements by proposing a so-called deep compressive image sensing framework. This framework, dubbed QISTA-ImageNet, is built upon a deep neural network to realize our optimization algorithm QISTA ( $$\ell _q$$ -ISTA) in solving image recovery problem. The unique characteristics of QISTA-ImageNet are that we (1) introduce a generalized proximal operator and present learning-based proximal gradient descent (PGD) together with an iterative algorithm in reconstructing images, (2) analyze how QISTA-ImageNet can exhibit better solutions compared to state-of-the-art methods and interpret clearly the insight of proposed method, and (3) conduct empirical comparisons with state-of-the-art methods to demonstrate that QISTA-ImageNet exhibits the best performance in terms of image reconstruction quality to solve the $$\ell _q$$ -norm optimization problem.