Eficiência de Compressive Sensing em modelo quadtree em imagens na presença de ruído

Abstract

This work is an experimental quantitative research and it investigated how much the eciency of the CoSaMP algorithm modied according to the theory that advocates the changes of the QuadTree model{based Compressive Sensing (CS) when applied to images with quantization and sparsity approximation noise. The aim of this study was to evaluate the impact of quantization and sparsity approximation noise to the eciency of image reconstruction and to compare the eciency between the Quadtree model{ based CoSaMP and the traditional CoSaMP. For this, a thorough literature review of the state of the art in image compression, theory of conventional CS and theory of model{based CS was done. After the review stage, MatlabTM routines were built and several tests varying values of M measurements, S sparsity levels and Q quantization steps were applied to four images with different sparsity levels and resolutions. Results showed that the quantization errors are not perceived when the sparsity approximation error level is high. On the other hand, when the sparsity approximation error level is low we observed better performance for steps 1, 2, 4 and 8. The results also showed that the ratio between the number of measurements and the sparsity approximation level meets the following criteria: 3:00 ≤ M=S ≤ 3:75. In this case, the values of M=S ranged from the lowest to highest, as the images varied from less to more sparsely scattered. It was observed that the eciency of the algorithm does not depend on the N stacked image size, but rather the S sparsity approximation level. Furthermore, we observed that the Quadtree CoSaMP outperforms the CoSaMP for all M measurements and performances better than the conventional CS when we take less measurements.