Signal Representation And Reconstruction Based On Ridge Extraction

Some of the signal characteristics can be better presented in certain transformed domain, so that in order to describe such features, it being necessary to study the character extraction and signal reconstruction algorithms based on information from transformed domain. For those biological signals like echo of bat or whale, as well as man-made system signals like radar or sonar signal, the instantaneous frequency of signal component contains important information and could be used for signal model parameters extraction. So that the proper choose of transformed domain and signal characteristic extraction method is of crucial important.The ridge extraction method used for signal characterization was first proposed in the 1990s, it's based on the study of the phase of the wavelet (or other linear) transform. Stationary phase method shows that by using information along the ridge defined by the phase on transformed domain, original signal could be represented and reconstructed. The ridge characteristic related closely to the instantaneous frequency of the signal. A serial of ridge extraction and signal reconstruction algorithms have been developed using phase or module information of parameters on the ridges. The ridge characteristics of asymptotic signal on continuous wavelet transforms (CWT) field are studied in this dissertation.Firstly, the ridge resolution under multi-component situation is analyzed; a conclusion shows that the resolution is close related with the ratio between component instantaneous frequencies (IF). Generally if this ratio is greater than 2, the ridges could be well separated; when this ratio is less than 2, the interaction between ridges will form a complex ridge image so that it being impossible to locate single ridge. For those multi-component signals like speech signal, such interaction is a common situation. Secondly, a new common ridge method is discussed; a common ridge across the complex ridge image is used instead of several interacted single ridges. Theoretical analysis shows that information contained along one common ridge could be used to represent the interacted ridges, and be used to reconstruct the related components.Thirdly, a common ridge relocation method is presented based on reassignment method that is generally used to improve the energy concentration on certain distribution plane. The relationship between the extracted complex ridge image and the corresponding common ridge is studied; a common ridge relocation method is derived from reassigning the interacted ridges. During this procedure, only the position information of interacted ridges influence the reassigning result, the energy distribution information makes no contribution to the final result. This is the main different of common ridge reassignment method from general reassignment method The fourth part of this dissertation discusses mainly the practical use of ridge extraction method in several fields namely, signal compression, de-noising, component separation. Experimental result shows that for sonant part of speech signal, 3~5 common ridges is enough to describe the main characteristics. Signal compression is achieved by choosing proper way to represent the ridge information and use it to reconstruct the original signal. Signal de-noising could be also achieved by restriction of ridge information in the reconstruction procedure. Under the condition when ridges can be separated and every single component could be reconstructed from the corresponding ridge, components separation using time-frequency characteristics is achieved. Simulation results show that ridge character is especially useful for description of biology signals like the echoes of bat signal. Finally, some still unsolved problems are concluded for further research.