Quantization Effect in Nonuniform Nonsparse Signal Reconstruction

This paper examines the influence of quantization on the compressive sensing theory applied to the nonuniformly sampled nonsparse signals with reduced set of randomly positioned measurements. The error of the reconstruction will be generalized to exact expected squared error expression. The aim is to connect the generalized random sampling strategy with the quantization effect, finding the resulting error of the reconstruction. Small sampling deviations correspond to the imprecisions of the sampling strategy, while completely random sampling schemes causes large sampling deviations. Numerical examples provide an agreement between the statistical results and theoretical values.