Abstract
Sparse signals, encountered in many wireless and signal acquisition applications, can be acquired via compressed sensing (CS) to reduce computations and transmissions, crucial for resource-limited devices, e.g., wireless sensors. Since the information signals are often continuous-valued, digital communication of compressive measurements requires quantization. In such a quantized compressed sensing (QCS) context, we address remote acquisition of a sparse source through vector quantized noisy compressive measurements. We propose a deep encoder-decoder architecture, consisting of an encoder deep neural network (DNN), a quantizer, and a decoder DNN, that realizes low-complexity vector quantization aiming at minimizing the mean-square error of the signal reconstruction for a given quantization rate. We devise a supervised learning method using stochastic gradient descent and backpropagation to train the system blocks. Strategies to overcome the vanishing gradient problem are proposed. Simulation results show that the proposed non-iterative DNN-based QCS method achieves higher rate-distortion performance with lower algorithm complexity as compared to standard QCS methods, conducive to delay-sensitive applications with large-scale signals.
Highlights
I N A MYRIAD of wireless applications and signal acquisition tasks, information signals are sparse, i.e., they contain many zero-valued elements, either naturally or after a transformation [2]
We propose two strategies that are employed to facilitate the training of DeepVQCS: 1) asymptotic quantizer approximation16 that adjusts steepness coefficient h, and 2) gradient approximation thatadjusts the gradient pass through the soft-to-hard quantization (SHQ) layer
SIMULATION RESULTS Simulation results are presented to assess the rate-distortion performance and algorithm time complexity of the proposed DeepVQCS scheme summarized in Algorithm 1
Summary
I N A MYRIAD of wireless applications and signal acquisition tasks, information signals are sparse, i.e., they contain many zero-valued elements, either naturally or after a transformation [2]. The main design driver is that once trained offline, the non-iterative QCS method provides an extremely fast and low-complexity encoding-decoding stage for online communications, conducive to delay-sensitive applications with large-scale signals. [31], [44] address bitconstrained signal acquisition at a DNN-based decoder, whereas we consider bit-constrained source compression at a resource-limited encoder; our (CS-based) encoder undergoes the stringently bit-constrained quantization stage, imposed by, e.g., a low-resolution analog-to-digital converter (ADC) or/and rate-limited communications. To this end, we devise a deep joint encoder-decoder as a first attempt to apply DNN-based VQ in QCS. −e−x +e−x f (x) denotes differentiation of function f (x) with respect to x. · denotes rounding up to the nearest integer. a 0 counts the number of non-zero entries of vector a. · 1 and · 2 denote the 1-norm and 2-norm
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