Khodabandeh Zahra, Rabbani Hossein, Dehnavi Alireza Mehri, Sarrafzadeh Omid
Department of Bioelectrics and Biomedical Engineering, School of Advanced Technologies in Medicine, Isfahan University of Medical Sciences, Mashhad, Iran.
Student Research Committee, School of Advanced Technologies in Medicine, Isfahan University of Medical Sciences, Mashhad, Iran.
J Med Signals Sens. 2019 Aug 29;9(3):145-157. doi: 10.4103/jmss.JMSS_42_17. eCollection 2019 Jul-Sep.
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.
The main goal of this article is expanding the circlet to a new one with elliptical basis functions.
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.
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.
自然图像中有相当数量的重要物体具有圆形和椭圆形形状。例如，大多数生物细胞的细胞核是圆形的，并且一些寄生虫如蛲虫在微观图像中呈椭圆形。因此，基于圆和椭圆的二维（2D）基函数的原子表示对于处理这些图像可能是有用的。该领域的首批研究是通过引入圆小波变换来进行的。
本文的主要目标是将圆小波扩展为具有椭圆基函数的新小波。
在本文中，我们首先引入一种名为椭圆小波的新变换，然后在图像去噪应用中将其与其他X小波变换进行比较，包括二维离散小波变换、双树复小波、曲波、轮廓波、可控金字塔和圆小波变换。
实验结果表明，对于30以下的噪声，在峰值信噪比方面，椭圆小波比其他几何X小波更好，特别是对于包含更多圆形结构的Lena图像。然而，对于纹理中有精细结构的Barbara图像，其结果比双树复小波和可控金字塔更差。
