Signal Singularity Detection And Image Edge Detection Based On Interpolation Wavelet

The singularity of signal is an important object in signal processing and contains many important information of signal.Since wavelet transform is an effective method to analyze signals in time-frequency,it can effectively describe sharp changes in localization of images.Hence,this has make wavelets become an important method for signal processing.When classic wavelet theory is applied to detect singularities of signal,discrete integral formula is often used to replace continuous integral to obtain wavelet coefficients.Since discrete integral is approximate expression of continuous integral,great numerical errors often cannot avoided in calculations.This has leaded up to the fact that accurate result cannot be detected.To solve the above-mentioned problem,a new algorithm is proposed in this paper.By applying interpolation wavelets to signal singularity detection and image edge detection,this algorithm can avoid numerical integral formula for obtaining wavelet coefficients,hence a better detect result can be obtained.The main work of this paper is as follows:(1)Studied characteristics of interpolation wavelets and a construction method of interpolation dual filter.Based on above,interpolation filters corresponding to six-order B-spline wavelet was constructed and applied to subsequent simulation experiment.(2)Analyzed a relationship between resolution of image edge detection and solving accuracy of wavelet coefficients in the classic wavelet algorithm.Defects in the classic wavelet algorithm is proposed on the basis of simulation results and theoretical analysis.Further on an optimization direction of the algorithm is pointed out.(3)A new algorithm is proposed to detect signal singularity with sparse representation of interpolation wavelets.In this approach,by utilizing the special property that signal sampling values can be considered as interpolation wavelet coefficients,interpolation dual filter is combined with Mallat pyramidal algorithm.Thus the calculation of wavelet coefficients can be simplified and the accuracy of wavelet coefficients can be improved.(4)According to a mathematical model of images,the process of combining interpolation wavelets and interpolation filters with the two-dimensional Mallat pyrami-dal algorithm is further studied.Further on a new image edge detection algorithm is proposed.With this arithmetic,wavelet coefficients can be get directly from image pixels,thus image edges can be detected simply and accurately.(5)In the experiment,our algorithm is compared with other detect algorithm.It is shown that the new algorithm can obtain clearer and more intact detection results.This implies that our algorithm is more effective and accurate than others.In this paper,the application research of interpolation wavelets in signal singularity detection and image edge detection was completed,which has certain reference value for signal processing and image processing.