Multiquadric Radial Basis Function Approximation Scheme for Solution of Total Variation Based Multiplicative Noise Removal Model

This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimization functional and to show its application to image denoising containing multiplicative noise.These capabilities used within the proposed algorithm have not only the quality of image denoising,edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images.It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure.The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio(PSNR),signal-to-noise ratio(SNR),and structural similarity index(SSIM)corresponded to the current conventional TV-based schemes.

Review of Fresnel incoherent correlation holography with linear and non-linear correlations

Fresnel incoherent correlation holography(FINCH)is a well-established incoherent imaging technique.In FINCH,three selfinterference holograms are recorded with calculated phase differences between the two interfering,differently modulated object waves and projected into a complex hologram.The object is reconstructed without the twin image and bias terms by a numerical Fresnel back propagation of the complex hologram.A modified approach to implement FINCH by a single camera shot by pre-calibrating the system involving recording of the point spread function library and reconstruction by a nonlinear cross correlation has been introduced recently.The expression of the imaging characteristics from the modulation functions in original FINCH and the modified approach by pre-calibration in spatial and polarization multiplexing schemes are reviewed.The study reveals that a reconstructing function completely independent of the function of the phase mask is required for the faithful expression of the characteristics of the modulating function in image reconstruction.In the polarization multiplexing method by non-linear cross correlation,a partial expression was observed,while in the spatial multiplexing method by non-linear cross correlation,the imaging characteristics converged towards a uniform behavior.