Speckles are introduced in the ultrasound data due to constructive and destructive interference of the probing signals that are used for capturing the characteristics of the tissue being imaged. There are a plethora of models discussed in the literature to improve the contrast and resolution of the ultrasound images by despeckling them. There is a class of models that assumes that the noise is multiplicative in its original form, and transforming the model to a log domain makes it an additive one. Nevertheless, such a transformation duly oversimplifies the scenario and does not capture the inherent properties of the data-correlated nature of speckles. Therefore, it results in poor reconstruction. This problem is addressed to a considerable extent in the subsequent works by adopting various models to address the data-correlated nature of the noise and its distributions. This work introduces a weberized non-local total bounded variational model based on the noise distribution built on the Retinex theory. This perceptually inspired model apparently restores and improves the contrast of the images without compromising much on the details inherently present in the data. The numerical implementation of the model is carried out using the Bregman formulation to improve the convergence rate and reduce the parameter sensitivity. The experimental results are highlighted and compared to demonstrate the efficiency of the model.

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A new mathematical algorithm is reported for the accurate and efficient analysis of pore properties of nanoporous anodic alumina (NAA) membranes using scanning electron microscope (SEM) images. NAA membranes of the desired pore size were fabricated using a two-step anodic oxidation process. Surface morphology of the NAA membranes with different pore properties was studied using SEM images along with computerized image processing and analysis. The main objective was to analyze the SEM images of NAA membranes quantitatively, systematically, and quickly. The method uses a regularized shock filter for contrast enhancement, mathematical morphological operators, and a segmentation process for efficient determination of pore properties. The algorithm is executed using MATLAB, which generates a statistical report on the morphology of NAA membrane surfaces and performs accurate quantification of the parameters such as average pore-size distribution, porous area fraction, and average interpore distances. A good comparison between the pore property measurements was obtained using our algorithm and ImageJ software. This algorithm, with little manual intervention, is useful for optimizing the experimental process parameters during the fabrication of such nanostructures. Further, the algorithm is capable of analyzing SEM images of similar or asymmetrically porous nanostructures where sample and background have distinguishable contrast.

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