Isidora Stanković

Ljubisa Stankovic, Milos Brajovic, Danilo Mandic et al.

Within the Compressive Sensing (CS) paradigm, sparse signals can be reconstructed based on a reduced set of measurements. Reliability of the solution is determined by the uniqueness condition. With its mathematically tractable and feasible calculation, coherence index is one of very few CS metrics with a 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 index-based lower bound for signal sparsity. The results are generalized to the uniqueness condition of the $l_0$-norm minimization for a signal represented in two orthonormal bases.

Isidora Stanković

This paper investigates the possibility of reconstruction of images considering that they are sparse in the DCT transformation domain. Two approaches are considered. One when the image is pre-processed in the DCT domain, using 8x8 blocks. The image is made sparse by setting the smallest DCT coefficients to zero. In the other case the original image is considered without pre-processing, assuming the sparsity as intrinsic property of the analyzed image. A gradient based algorithm is used to recover a large number of missing pixels in the image. The case of a salt-and-paper noise affecting a large number of pixels is easily reduced to the case of missing pixels and considered within the same framework. The reconstruction of images affected with salt-and-paper impulsive is compared with the images filtered using a median filter. The same algorithm can be used considering transformation of the whole image. Reconstructions of black and white and colour images are considered.