3-D Sherlet Transform for Biomedical Applications

G. Guru Prasad, K. S. Chakradhar K. S. Chakradhar, Dr. T. Rama sree Dr. T. Rama sree
2011 Indian Journal Of Applied Research  
It is now widely acknowledged that analyzing the intrinsic geometrical features of an underlying image is essentially needed in image processing. The shearlets are an affine system with a single generating mother shearlet function parameterized by a scaling, shear, and translation parameter the shear parameter capturing the direction of singularities. This transform can even be regarded as matrix coefficients from a group representation of a shearlet group, thereby providing an extensive
more » ... tical framework for its theory. The Shearlet representation is a multi scale pyramid of well-localized waveforms defined at various locations and orientations, which was introduced to overcome the limitations of traditional multi scale systems in dealing with multidimensional data. While the shearlet approach shares the general philosophy of curvelets and surfacelets, it is based on a very different mathematical framework, which is derived from the theory of affine systems and uses shearing matrices rather than rotations. This allows a natural transition from the continuous setting to the digital setting and a more flexible mathematical structure. The 3-D digital shearlet transform algorithm proposed in this paper consists in a cascade of multi scale decomposition and a directional filtering stage. The filters employed in this decomposition are implemented as finite-length filters, and this ensures that the transform is local and numerically efficient. To illustrate its performance, the 3-D discrete shearlet transform is applied to problems of video denoising and enhancement, and compared against other state-of-the-art multi scale techniques, including curvelets and surfacelets. Many important results about the theory and applications of shearlets have been derived during the past 5 years. Yet, there is a need to extend this approach and its applications to higher dimensions, especially 3D, where important problems such as video processing and analysis of biological data in native resolution require the use of 3D representations. The focus of this thesis is the study of shearlet representations in 3D, including their numerical implementation and application to problems of data denoising and enhancement. Compared to other competing methods like 3D curvelet and surfacelet, our numerical experiments show better Peak Signal to Noise Ratio (abbreviated as PSNR) and visual quality.
doi:10.15373/2249555x/sept2013/71 fatcat:xyaoac52tjdkbd5gwudnz5xv34