Compressive Sensing Spectroscopy Using a Residual Convolutional Neural Network Compressive sensing (CS) spectroscopy is well known for developing a compact spectrometer which consists of two parts: compressively measuring an input spectrum and recovering the spectrum using reconstruction techniques. Our goal here is to propose a novel residual convolutional neural network (ResCNN) for reconstructing the spectrum from the compressed measurements. The proposed ResCNN comprises learnable layers and a residual connection between the input and the output of these learnable layers. The ResCNN is trained using both synthetic and measured spectral datasets. The results demonstrate that ResCNN shows better spectral recovery performance in terms of average root mean squared errors (RMSEs) and peak signal to noise ratios (PSNRs) than existing approaches such as the sparse recovery methods and the spectral recovery using CNN. Unlike sparse recovery methods, ResCNN does not require a priori knowledge of a sparsifying basis nor prior information on the spectral features of the dataset. Moreover, ResCNN produces stable reconstructions under noisy conditions. Finally, ResCNN is converged faster than CNN.

Compressed Sensing: From Research to Clinical Practice With Deep Neural Networks: Shortening Scan Times for Magnetic Resonance Imaging Compressed sensing (CS) reconstruction methods leverage sparse structure in underlying signals to recover highresolution images from highly undersampled measurements. When applied to magnetic resonance imaging (MRI), CS has the potential to dramatically shorten MRI scan times, increase diagnostic value, and improve the overall patient experience. However, CS has several shortcomings that limit its clinical translation. These include 1) artifacts arising from inaccurate sparse modeling assumptions, 2) extensive parameter tuning required for each clinical application, and 3) clinically infeasible reconstruction times. Recently, CS has been extended to incorporate deep neural networks as a way of learning complex image priors from historical exam data. Commonly referred to as unrolled neural networks, these techniques have proven to be a compelling and practical approach to address the challenges of sparse CS. In this tutorial, we review the classical CS formulation and outline steps needed to transform this formulation into a deeplearningbased reconstruction framework. Supplementary opensource code in Python is used to demonstrate this approach with open databases. Further, we discuss considerations in applying unrolled neural networks in the clinical setting.