2017/11/28 by Alireza Hosseini, Hosseini, Alireza
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Medical Image Segmentation Techniques #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1711.10534
openalex publication_date 2017/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a new regularization term is proposed to solve mathematical\nimage problems. By using difference operators in the four directions;\nhorizontal, vertical and two diagonal directions, an estimation of derivative\namplitude is found. Based on the new obtained estimation, a new regularization\nterm will be defined, which can be viewed as a new discretized total variation\n(TVprn) model. By improving TVprn, a more effective regularization term is\nintroduced. By finding conjugate of TVprn and producing vector fields with\nspecial constraints, a new discretized TV for two dimensional discrete\nfunctions is proposed (TVnew). The capability of the new TV model to solve\nmathematical image problems is examined in some numerical experiments. It is\nshown that the new proposed TV model can reconstruct the edges and corners of\nthe noisy images better than other TVs. Moreover, two test experiments of\nresolution enhancement problem are solved and compared with some other\ndifferent TVs.\n