The Research On Nonlinear Data Compression And Reconstruction Based On MRA

Wavelet transform is a power-balance linear transform, which can decompose a signal into space and scale level, i.e. time and frequency level .At the same time, it makes the best of different resolution, solving the conflict between time field and frequency field. When met the high-frequency signal, WT changes into wide window using high resolution in low frequency field and low resolution in high frequency field, and when met the low-frequency signal, the situation is converse. Thus it provides the foundation of MRA and is widely used in the digital signal processing field. As an important aspect in signal processing, signal compression needs to express the source signal using data as little as possible to shrink the storage space, transferring time and occupied width. This thesis aims at combining the idea of MR, which comes from MRA in wavelet theory and digital signal compression application. As to the digital curve signals, this thesis designs a nonlinear algorithm to compress them. In the algorithm, interpolation forecasting method is used under the frame of MR. Then an example is presented using the algorithm to compress the perfect smooth and closed curve signal, numerical experiment operated in MATLAB shows the compress-ratio and result is satisfactory. At the same time, because of the character of MR, it is easy to choose the appropriate level of compression in consideration of the request of compression-ratio and losing constriction. So, if set a control in the choosing procedure, this algorithm becomes self-adjust and optimal.Furthermore, in the numerical experiment, the compression using wavelet is also compared with the nonlinear method presented in this thesis. And the results show that this method is efficient and operable.