A New Approach to Ridgelet Transform

Wavelet transform is suitable for expressing local characteristics of the object which has isotropic singularity. but to the anisotropic singularity, wavelet is not the best tool because it will cause the blur of image edges and details. Ridgelet transform actually is a wavelet basis function with a added parameter which is characterized direction. It has the same ability in local timefrequency resolution as wavelet transform. Meanwhile, ridgelet transform has a strong ability to identify and choose the direction. So it is an effective method to express the local characteristics of the object which has anisotropic singularity. But each of them is applied ineffectively to the local characteristics suitable for the other. Presented in this paper is an improved multiresolution method based on ridgelet theory, that is, quasiridgelet multiresolution analysis method. This method unifies wavelet theory and ridgelet theory, and makes wavelet theory and ridgelet theory to be its two special cases. Meanwhile, it has the discernment of isotropic and isometric singularity object. Thus the transformation method is able to maintain the ridgelet theory possessing superiority on the line characteristic detection, and enhances the point characteristic detection at the same time. By experimental comparison, it is shown that the effects of this method on combining the advantages and evading the disadvantages of wavelet theory and ridgelet theory are quite obvious, having more flexibility in the application of eliminating image noise.