Poisson noise (also known as shot or photon noise) arises due to the lack of information during the image acquisition phase, it is quite common in the field of microscopic or astronomical imaging applications. In this paper, we propose a non-local total variation regularization framework with a p-norm driven data-fidelity for denoising the Poissonian images. In precise, the energy functional is derived using a Maximum A Posteriori estimator of the Poisson probability density function. The diffusion amounts to a non-local total variation minimization process, which eventually preserves fine structures while denoising the data. The numerical solution is sought under a fast converging split-Bregman iterative scheme. The proposed model is compared visually and statistically with the state-of-the-art Poisson denoising models.

In 2009, Noor and Waseem studied an important third-order iterative method. The convergence order is obtained using Taylor expansion and assumptions on the derivatives of order up to four. In this paper, we have obtained convergence order three for this method using assumptions on the first and second derivatives of the involved operator. Further, we have extended the method to obtain a fifth- and a sixth-order methods. The dynamics of the methods are also provided in this study. Numerical examples are included. The same technique can be used to extend the utilization of other single or multistep methods.

In this article, we modify Mumford–Shah level-set model to handle speckles and blur in synthetic aperture radar (SAR) imagery. The proposed model is formulated using a non-local regularization framework. Hence, the model duly cares about local gradient oscillations (corresponding to the fine details/textures) during the evolution process. It is assumed that the speckle intensity is gamma distributed, while designing a maximum a posteriori estimator of the functional. The parameters of the gamma distribution (i.e. scale and shape) are estimated using a maximum likelihood estimator. The regularization parameter of the model is evaluated adaptively using these (estimated) parameters at each iteration. The split-Bregman iterative scheme is employed to improve the convergence rate of the model. The proposed and the state-of-the-art despeckling models are experimentally verified and compared using a large number of speckled and blurred SAR images. Statistical quantifiers are used to numerically evaluate the performance of various models under consideration.