Learning Based Regularization for Spatial Multiplexing Cameras

In this paper, we consider learning based regularization for compressive sensing reconstruction using focal plane array sensors. While many optimization algorithms employ proximal operators for regularization, they are often inadequate in fully capturing the characteristics of complex natural images. Recently, deep learning based approaches obtained promising results in different imaging problems, creating the possibility to use them for regularization in an optimization framework. Here, we utilize this approach in compressive sensing based spatial multiplexing cameras. This technique is motivated by the high cost of producing large focal plane arrays in infrared sensors. Reconstruction from undersampled measurements can be done using a spatial multiplexing camera which relies on multiple snapshots for super-resolving a scene. It acquires coded projections of a scene using a spatial light modulator and a low-resolution focal plane array. We first formulate the problem of finding a high resolution image from its undersampled measurements. Then, we develop a reconstruction method with learning based regularization to solve this problem using alternating direction method of multipliers framework. For this, we replace the proximal operator corresponding to the regularization function with a deep convolutional denoising network. We also enhance a previously proposed denoising network's training phase by introducing multiple noise realizations for each training patch, which results in better reconstruction performance. Numerical results for different imaging scenarios show successful recovery of high resolution images in terms of PSNR, SSIM and visual quality at significant noise levels.