Design And Application Of Non-redundant Pyramid And Research On Fast Algorithm Of 2-D Filter

Wavelet transform is the most widely used time-frequency analysis theory,and has been succesfuly applied to the fields such as signal processing,image processing, pattern recongnition,differential equation,and fault diagnosis,etc.Wavelet is a perfect tool for one dimensional(1-D) piecewise smooth signal and it can provide optimal representation for these signals.However,this excentlent characteristic in 1-D case can not be easily extended to 2-D and even higher dimension cases.Natutral images are not the simple combination of 1-D piecewise smooth segments,but instead,contain abundant directional information.Two-dimensional discrete wavelet transform(2-D DWT) generated by a tensor-product of two perpendicular 1-D wavelets is sensitive to horizontal,vertical and diagonal directions only,thus encounters difficulty in effective representation of geometrical structures in images.To overcome the weakness of the wavelet in higher dimensions,the multiscale geometric analysis theory is developed recently and has provided several novel transform methods,such as ridgelet transform, curvelet transform,and contourlet transform and has been a powerful tool for high dimensional signal analysis.Generally speaking,multiscale geometric analysis methods contain two key steps, one is the multiscale decomposition and the other is geometric analysis.Multiscale decomposition aims at characteristic analysis of the signal at different scales,just as the so-called mathematic microscope property of wavelet.While the purpose of geometric analysis is to obtain the geometric information of the image,including direction, contour,edge,and texture,etc.This dissertation focus on these two steps and the main work includes,(1) We studied the design and implementation strategy of Directional Filter Banks (DFB).After a brief review on some conventional 2-D filter design methods such as window function method,frequency sampling method and McClellan transformation method,the concept of Directional Filter Banks and multidimensional sampling theory are introduced.Furthermore,based on study of the method of mapping of 2-D kernels, we extend it to multichannel cases.(2) Based on analysis of the pyramid structure and the Directional Filter Banks (DFB),a non-redundant multi-resolution and multi-directional pyramid structure is proposed according to the maximal decimation theory and the PR condition of two-dimensional two-channel filter banks.First,we discuss the origin of the redundancy in the pyramid structure.Second,we address problems facing the DFB,mainly on the frequency scrambling,energy leakage around DC channels and rectangularization of the output subband coefficients,and then give our solutions.Finally,we suggest a pyramid based non-redundancy structure and combine this with the DFB to form a new system to achieve the multi-resolution and multi-directional features.The results of our experimental work show its superiority over Contourlets and wavelets in the application of nonlinear approximation.(3) We propose a 2-D filter decomposition strategy where 2-D filters are implemented by cascade shorter length filters for efficient 2-D convolution computation. All 2-D filters are classified into three categories,namely completely-separable, semi-separable and non-separable according to whether it can be decomposed to small size fiters whose convolution maintains its frequency response,and then the filter decomposition process is modeled as an unconstrained optimization problem. Experimental results indicate that the proposed scheme can dramatically improve the computation efficiency of 2-D convolution.(4) We propose a fast algorithm for YCbCr to RGB colorspace conversion with precision reduction,which is broadly used in many fixed-point applications,e.g.24 bits YCbCr data is converted to 16 bits RGB data for LCD display.Given the conversion precition requirement,we present the optimal criteria and steps for the selection of converion methods utilizing fixed-point shift and addition operations to take place of the float-point multiplication operation.Time consumption is greatly reduced comparing with other methods as a consenquence,while the image quality maintains.Although this algorithm is proposed based on DSPs but is not restricted to,abundant experimental results carried out on other platforms verify the validity of our algorithm.