关键词: 压缩感知, 量化, 率失真函数, 有损压缩, 信号重构

Abstract: Recent studies in Compressive Sensing (CS) have shown that sparse signals can be recovered from a small number of random measurements, which raises the question of whether random measurements can provide an efficient representation of sparse signals in an information-theoretic sense. To examine the influence of quantization errors, the average distortion introduced by quantizing compressive sensing measurements was studied using rate distortion theory. Both uniform quantization and non-uniform quantization were considered. The asymptotic rate-distortion functions were obtained when the signal was recovered from quantized measurements using different reconstruction algorithms. Both theoretical and experimental results shows that encoding a sparse signal through simple scalar quantization of random measurements incurs a significant penalty relative to direct or adaptive encoding of the sparse signal, but compressive sensing is able to exploit the sparsity to reduce the distortion, so quantized compressive sampling is suitable to be used to encode the low sparse signal.

Key words: Compressive Sensing (CS), quantization, rate distortion function, lossy compression, signal reconstruction