SELECTIVE SENSING: A DATA-DRIVEN NONUNIFORM SUBSAMPLING APPROACH FOR COMPUTATION-FREE ON-SENSOR DATA DIMENSIONALITY REDUCTION Anonymous

Abstract

Designing an on-sensor data dimensionality reduction scheme for efficient signal sensing has always been a challenging task. Compressive sensing is a state-of-the-art sensing technique used for on-sensor data dimensionality reduction. However, the undesired computational complexity involved in the sensing stage of compressive sensing limits its practical application in resourceconstrained sensor devices or high-data-rate sensor devices dealing with highdimensional signals. In this paper, we propose a selective sensing framework that adopts the novel concept of data-driven nonuniform subsampling to reduce the dimensionality of acquired signals while retaining the information of interest in a computation-free fashion. Selective sensing adopts a co-optimization methodology to co-train a selective sensing operator with a subsequent information decoding neural network. We take image as the sensing modality and reconstruction as the information decoding task to demonstrate the 1st proof-ofconcept of selective sensing. The experiment results on CIFAR10, Set5 and Set14 datasets show that selective sensing can achieve an average reconstruction accuracy improvement in terms of PSNR/SSIM by 3.73dB/0.07 and 9.43dB/0.16 over compressive sensing and uniform subsampling counterparts across the dimensionality reduction ratios of 4-32x, respectively. Source code is available at https://figshare.com/s/519a923fae8f386d7f5b.

1. INTRODUCTION

In the era of Internet-of-things (IoT) data explosion (Biookaghazadeh et al., 2018) , efficient information acquisition and on-sensor data dimensionality reduction techniques are in great need. Compressive sensing is the state-of-the-art signal sensing technique that is applicable to on-sensor data dimensionality reduction. However, directly performing compressive sensing in the digital domain as a linear transformation of signals can be computationally costly, especially when the signal dimension n is high and/or a data-driven sensing matrixMousavi et al. 2018) is used. To mitigate this problem, several approaches have been proposed to reduce the computational complexity of compressive sensing by constraining the sensing matrices to be sparse, binary, or ternary (Wang et al., 2016; Nguyen et al., 2017; Zhao et al., 2018; Hong et al., 2019) . While these approaches can reduce the computational complexity by a constant factor (O(cn 2 ), where c can be as low as 10 -2 ), such reduced computational complexity can be still too high to be affordable for resource-constrained sensor devices, e.g., low-cost IoT sensors (Djelouat et al., 2018) , or high-data-rate sensor devices dealing with high-dimensional signals, e.g., LiDAR and depth map (Chodosh et al., 2019) . Other approaches (Duarte et al., 2008; Robucci et al., 2010) propose to implement compressive sensing in the analog domain instead, eliminating or reducing the computation cost of compressive sensing through custom hardware implementation. However, such custom hardware implementation inevitably increases the cost of the sensor and is often specific to the sensor design, thereby cannot be generally applied to other sensors or applications. In this paper, we propose a selective sensing framework to address the above-mentioned problem by adopting the novel concept of data-driven nonuniform subsampling to reduce the dimensionality of acquired signals while retaining the information of interest in a computation-free fashion. Specifically, the data dimensionality reduction in selective sensing is a nonuniform subsampling (or selection) process that simply selects the most informative entries of a signal vector based on an optimized, stationary selection index vector informed by training data. Since no computation is involved for any form of data encoding, the computational complexity of the selective sensing operator is simply O(1), leading to the computation-free data dimensionality reduction during the selective sensing process.foot_0 Selective sensing adopts a co-optimization methodology to co-train a selective sensing operator with a subsequent information decoding neural network. As the trainable parameters of the sensing operator (the selection index) and the information decoding neural network are discrete-and continuous-valued, respectively, the co-optimization problem in selective sensing is a mixed discrete-continuous optimization problem that is inherently difficult to solve. We propose a feasible solution to solve it by transforming the mixed discrete-continuous optimization problem into two continuous optimization subproblems through interpolation and domain extension techniques. Both of the subproblems can then be efficiently solved using gradient-descent-based algorithms. We take images as the sensing modality and reconstruction as the information decoding task to demonstrate the 1st proof-of-concept of selective sensing. The experiments on CIFAR10, Set5 and Set14 datasets show that the selective sensing framework can achieve an average reconstruction accuracy improvement in terms of PSNR/SSIM by 3.73dB/0.07 and 9.43dB/0.16 over compressive sensing and uniform subsampling counterparts across the dimensionality reduction ratios of 4-32x, respectively. The contributions of this paper are summarized as follows: 1. We propose a new on-sensor data dimensionality reduction method called selective sensing. Selective sensing efficiently reduces the dimensionality of acquired signals in a computation-free fashion while retaining information of interest. The computation-free nature of selective sensing makes it a highly suitable solution for performing on-sensor data dimensionality reduction on resourceconstrained sensor devices or high-data-rate sensor devices dealing with high-dimensional signals. 2. We propose and apply the novel concept of data-driven nonuniform subsampling. Specifically, we first formulate the problem of co-optimizing a selective sensing operator with a subsequent information decoding neural network as a mixed discrete-continuous optimization problem. Furthermore, we propose a viable solution that transforms the problem into two continuous optimization subproblems that can be efficiently solved by gradient-descent-based algorithms, which makes the co-training feasible. 3. We empirically show that data-driven nonuniform subsampling can well preserve signal information under the presence of a co-trained information decoding network.

2. RELATED WORK

2.1 NONUNIFORM SUBSAMPLING Model-based nonuniform subsampling has been proposed in Chepuri et al. (2016) in the name of sparse sensing. Sparse sensing requires a hand-crafted sparsity model of a signal as prior knowledge. Differently, selective sensing requires no prior knowledge about the sparsity model of a signal, as all the necessary information needed for reconstruction can be learned from data through the training process. Therefore, selective sensing has a much broader range of applications, especially in IoT, than sparse sensing, considering a vast majority of IoT signals are not well studied nor understood yet, but huge amounts of IoT data are already available for training and learning. Dadkhahi & Duarte (2014) proposes to generate an image mask that can preserve the manifold structure presented in image data. Differently, we focus on the task of single image sensing and reconstruction in this paper. Baldassarre et al. (2016); Weiss et al. (2019); Gözcü et al. (2018); Bahadir et al. (2019; 2020) propose to perform MRI image nonuniform subsampling in k-space (frequency domain). As many spatial-domain signals are much sparser in the frequency domain, e.g., natural images and MRI images, the existing nonuniform subsampling approaches performed in k-space are insufficient



For temporal signals, the selection operation can be simply implemented in the digital domain with a counter and a mux that already exists in the control logic of most sensors. We consider such operations as control rather than data computation as no data is computed during the selective sensing process. For spatial signals such as images, the selective sensing operator can also be implemented as a low-cost masked sensor array with no computation involved. In addition,Mayberry et al. (2014); Centeye (2020) present image sensor architectures for embedded systems that can provide pixel-level control of image sensors.



(2017; 2018); Lohit et al. (2018); Wu et al. (

