Quantization in Compressive Sensing: A Signal Processing Approach

Abstract

Influence of the finite-length registers and quantization effects on the reconstruction of sparse and approximately sparse signals is analyzed in this paper. For the nonquantized measurements, the compressive sensing (CS) framework provides highly accurate reconstruction algorithms that produce negligible errors when the reconstruction conditions are met. However, hardware implementations of signal processing algorithms involve the finite-length registers and quantization of the measurements. An analysis of the effects related to the measurements quantization with an arbitrary number of bits is the topic of this paper. A unified mathematical model for the analysis of the quantization noise and the signal nonsparsity on the CS reconstruction is presented. An exact formula for the expected energy of error in the CS-based reconstructed signal is derived. The theory is validated through various numerical examples with quantized measurements, including the cases of approximately sparse signals, noise folding, and floating-point arithmetics.

Sparse Analyzer Tool for Biomedical Signals

“…The reconstruction error may depend on the choice of the domain of sparsity and reconstruction algorithm, but in certain cases, it may also be the consequence of the quantization influence, as discussed in [47]. Namely, the limitations of the number of bits used for the representation of the available signal samples can affect the reconstruction performance.…”

“…, in order for product y = AX to produce amplitudes below 1 [47]. The reconstruction error related to the number of bits is given by [47] e 2 = 3.01 × log 2 K − 6.02B − 7.78.…”

“…, in order for product y = AX to produce amplitudes below 1 [47]. The reconstruction error related to the number of bits is given by [47] e 2 = 3.01 × log 2 K − 6.02B − 7.78. The proposed solution is designed for the 64-bit computer device, so the effects of quantization in this case can be considered negligible.…”

“…The ADMM, that is, a variation on the method of multipliers, is a special case of Douglas-Rachford splitting. The DR problem is defined as follows [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]:…”

RANSAC-Based Signal Denoising Using Compressive Sensing

“…In recent years, the reconstruction of sparse signals, based on a reduced set of random measurements, attracted significant research interest [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]. Within the compressive sensing (CS) framework, a rigorous mathematical foundation has been established to support this type of reconstruction, including the conditions that guarantee a successful and unique reconstruction result [2,5].…”