ACTIVE DEEP PROBABILISTIC SUBSAMPLING

Abstract

Subsampling a signal of interest can reduce costly data transfer, battery drain, radiation exposure and acquisition time in a wide range of problems. The recently proposed Deep Probabilistic Subsampling (DPS) method effectively integrates subsampling in an end-to-end deep learning model, but learns a static pattern for all datapoints. We generalize DPS to a sequential method that actively picks the next sample based on the information acquired so far; dubbed Active-DPS (A-DPS). We validate that A-DPS improves over DPS for MNIST classification at high subsampling rates. We observe that A-DPS learns to actively adapt based on the previously sampled elements, yielding different sampling sequences across the dataset. Moreover, we demonstrate strong performance in active acquisition Magnetic Resonance Image (MRI) reconstruction, outperforming DPS and other deep learning methods.

1. INTRODUCTION

Present-day technologies produce and consume vast amounts of data, which is typically acquired using an analog-to-digital converter (ADC). The amount of data digitized by an ADC is determined not only by the temporal sampling rate, but also by the manner in which spatial acquisitions are taken, e.g. by using a specific design of sensor arrays. Reducing the number of sample acquisitions needed, can lead to meaningful reductions in scanning time, e.g. in Magnetic Resonance Imaging (MRI), radiation exposure, e.g. in Computed Tomography (CT), battery drain, and bandwidth requirements. While the Nyquist theorem is traditionally used to provide theoretical bounds on the sampling rate, in recent years signal reconstruction from sub-Nyquist sampled data has been achieved through a framework called Compressive Sensing (CS). First proposed by Donoho (2006) , and later applied for MRI by Lustig et al. (2007) , CS leverages structural signal priors, specifically sparsity under some known transform. By taking compressive measurements followed by iterative optimization of a linear system under said sparsity prior, reconstruction of the original signal is possible while sampling at sub-Nyquist rates. Researchers have employed CS with great success in a wide variety of applications, such as radar (Baraniuk & Steeghs, 2007; Ender, 2010) , seismic surveying (Herrmann et al., 2012) , spectroscopy (Sanders et al., 2012) , and medical imaging (Han et al., 2016; Lai et al., 2016) . However, both the need to know the sparsifying basis of the data, and the iterative nature of the reconstruction algorithms, still hamper practical applicability of CS in many situations. These limitations can be overcome by the use of deep learning reconstruction models that make the sparsity assumption implicit, and facilitate non-iterative inference once trained. Moreover, the (typically random) nature of the measurement matrix in CS does, despite adhering to the given assumptions, not necessarily result in an optimal measurement given the underlying data statistics and the downstream system task. This has recently been tackled by algorithms that learn the sampling scheme from a data distribution. In general, these data-driven sampling algorithms can be divided into two categories: algorithms that learn sampling schemes which are fixed once learned (Huijben et al., 2020a; b; c; Ravishankar & Bresler, 2011; Sanchez et al., 2020; Bahadir et al., 2019; Bahadir et al., 2020; Weiss et al., 2019) , and algorithms that learn to actively sample (Ji et al., 2008; Zhang et al., 2019; Jin et al., 2019; Pineda et al., 2020; Bakker et al., 2020) ; selecting new samples based on sequential acquisition of the information. The former type of algorithms learn a sampling scheme that -on averageselects informative samples of all instances originating from the training distribution. However,

