Signal Reconstruction From Modulo Observations We consider the problem of reconstructing a signal from underdetermined modulo observations (or measurements). This observation model is inspired by a (relatively) less wellknown imaging mechanism called modulo imaging, which can be used to extend the dynamic range of imaging systems; variations of this model have also been studied under the category of phase unwrapping. Signal reconstruction in the underdetermined regime with modulo observations is a challenging illposed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to solving the inverse problem limited to two modulo periods, inspired by recent advances in algorithms for phase retrieval under sparsity constraints. We show that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal and provides improved performance over other existing algorithms. We also provide experiments validating our approach on both synthetic and real data to depict its superior performance.

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 superresolving a scene. It acquires coded projections of a scene using a spatial light modulator and a lowresolution 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 networkxe2x80x99s 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.