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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.

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Within the compressive sensing paradigm, sparse signals can be reconstructed based on a reduced set of measurements. The reliability of the solution is determined by its uniqueness. With its mathematically tractable and feasible calculation, the coherence index is one of very few CS metrics with considerable practical importance. In this paper, we propose an improvement of the coherence-based uniqueness relation for the matching pursuit algorithms. Starting from a simple and intuitive derivation of the standard uniqueness condition, based on the coherence index, we derive a less conservative coherence indexbased lower bound for signal sparsity. The results are generalized to the uniqueness condition of the l0-norm minimization for a signal represented in two orthonormal bases.

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