Quantization Noise on Image Reconstruction Using Model-Based Compressive Sensing

The Compressive Sensing (CS) allows the acquisition of signals already compressed and the posterior reconstruction with much less number of measures than the minimum required by the Nyquist theorem. A subarea of CS which improves the performance at the reconstruction stage is named Model-Based CS. Some works have been developed within this subarea. However, most of them consider only the noise generated by sparse approximation, disregarding the noise generated by the quantization stage and its influence on efficiency and robustness of CS. The objective of this study is to investigate the influence of the noise generated by the quantization stage in Model-Based CS efficiency for images with different levels of sparsity and different distributions of coefficients in the frequency domain. In this work, the image acquisition stage is implemented using the partial Fourier matrix which results in a vector of measures. Then, different steps of uniform scalar quantization are added to this vector and the image reconstruction stage is performed using the Compressive Sampling Matching Pursuit (CoSaMP) on a quadtree model. PSNR and bits rate (BR) are then used to evaluate the efficiency of CoSaMP with quantization noise. The performance of this proposed Model-Based CS using different quantization steps were slightly better than other studies using the same model in terms of PSNR, but with the advantage of obtaining smaller values of bit rate (BR maior que 2 bpp).