Background:A fair amount of important objects in natural images have circular and elliptical shapes. For example, the nucleus of most of the biological cells is circular, and a number of parasites such as Oxyuris have elliptical shapes in microscopic images. Hence, atomic representations by two-dimensional (2D) basis functions based on circle and ellipse can be useful for processing these images. The first researches have been done in this domain by introducing circlet transform.Methods:The main goal of this article is expanding the circlet to a new one with elliptical basis functions.Results:In this article, we first introduce a new transform called ellipselet and then compare it with other X-let transforms including 2D-discrete wavelet transform, dual-tree complex wavelet, curvelet, contourlet, steerable pyramid, and circlet transform in the application of image denoising.Conclusion:Experimental results show that for noises under 30, the ellipselet is better than other geometrical X-lets in terms of Peak Signal to Noise Ratio, especially for Lena which contains more circular structures. However, for Barbara which has fine structures in its texture, it has worse results than dual-tree complex wavelet and steerable pyramid.

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Multiple sclerosis (MS) is one of the most prevalent chronic inflammatory diseases caused by demyelination and axonal damage in the central nervous system. Structural retinal imaging via optical coherence tomography (OCT) shows promise as a biomarker for monitoring of MS. There are successful reports regarding application of Artificial Intelligence (AI) in analysis of cross-sectional OCTs in ophthalmologic diseases. However, the alteration of sub-retinal thicknesses in MS are noticeably subtle compared to other ophthalmologic diseases. Therefore, raw cross-sectional OCTs are replaced with multilayer segmented OCTs for discrimination of MS and heathy controls (HCs). To conform to the principles of trustworthy AI, interpretability is provided by visualizing regional layer contribution to classification performance with proposed occlusion sensitivity approach. The robustness of the classification is also guaranteed by showing the effectiveness of the algorithm while being tested on the new independent (but similar) dataset. The most discriminative features from different topologies of the multilayer segmented OCTs are selected by dimension reduction methods. Support vector machine (SVM), random forest (RF), and artificial neural network (ANN) are used for classification. Patient-wise cross-validation (CV) is utilized to evaluate the performance of the algorithm, where the training and test folds contain records from different subjects. The most discriminative topology is determined to be squares with side of 40 pixels and the most influential sub-retinal layers are ganglion cell and inner plexiform layer (GCIPL) and inner nuclear layer (INL). Linear SVM resulted in 88% Accuracy, 78% precision and 63% recall in discrimination of MS and HCs using macular multilayer segmented OCTs.

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