Total variation reconstruction for Kronecker compressive sensing with a new regularization

Edge-preserving nonlocal weighting scheme for total variation based compressive sensing recovery

“…Utilizing nonlocal structure of image through NLM is an effective solution to preserve image details [7]. Since human visual system is more sensitive to the difference in intensity than absolute pixel values, it is expected to obtain better performance if the gradient image is handled well.…”

“…Since human visual system is more sensitive to the difference in intensity than absolute pixel values, it is expected to obtain better performance if the gradient image is handled well. Therefore, it is also important to preserve the nonlocal structures which also exist in the gradient domain [7]. To address all these requirements, we apply NLM in the gradient domain (named as TVNL) by iteratively filtering gradient images.…”

“…Compressive sensing (CS) is an emerging sensing paradigm which allows to sample a signal at much lower rate than the Nyquist's sampling rate Total variation (TV) -based regularization is proved to have a tendency of preserving edge locations well [3], and it is being widely used in CS recovery [6][7][8][9][10]. The anisotropic TV optimization is given as:…”

“…Fortunately, in natural images, there might exist many pixels which are very similar to each other in values but spatially far away from a current pixel. This phenomenon is named as the nonlocal structure [2] which was successfully utilized to reduce staircase artifact of TV-based CS reconstruction by applying the nonlocal means filter (NLM) via regularization [7]. In this paper, this nonlocal structure is utilized for denoising while preserving image details.…”

Multi-Resolution Kronecker Compressive Sensing

“…One of the widely used CS reconstruction methods is the total variation (TV) technique [5][6][7], which can achieve good CS recovery performance while preserving edges of images well. However, in case of a very low subrate, such as 0.05, it has very poor recovery performance, as depicted in Fig.…”