Image enhancement by curvelet, ridgelet, and wavelet transform

Abstract

Image Processing always aims at extracting maximum information from an image. To achieve this we have to analyze the image completely along its periphery. But the parts of an image are hardly straight, they contain continuously varying slopes. Wavelet based image processing gives low resolution when the image has largely varying slopes and they give redundant coefficients. If we tile the whole image, we get curve-lets meaning 'small curves'. If this tilling is optimum, we get parts of the curve which resemble to the straight lines. These straight lines are then analyzed and reconstructed using 'Curvelet Transform'. Curvelet Transform represents edges of a curve better than Wavelet Transform. This transform uses 'Ridgelet Transform' as a main processing. Ridgelet Transform is a two step process using Radon Transform and DWT. Radon transform analysis involves the mapping of rectangular coordinates into the polar or angular coordinates. With the increasing need for higher speed and lower memory requirement, we, in this paper propose to compute the Ridgelet coefficients without involving the conversion to angular coordinates. We have used Radon transforms our basic building block. As it will be seen taking 1-D DWT on Radon Transform results in Ridgelet Transform. At the end of the paper the images having many 'ridges', our transform gives better PSNR than Wavelet transform and many others. It also saves computational time by using fast FFT algorithm and avoiding operating on Tiles having less variation of pixels. The PSNR also depends on the algorithm used to perform DWT.