外文翻译---一种新型基于小波图像去噪法

外文翻译---一种新型基于小波图像去噪法内容摘要：

that the functions with different region of support that are used in the transformation process are derived from one main function, or the mother wavelet. In other words, the mother wavelet is a prototype for generating the other window functions. 外文文献原文 The term translation is used in the same sense as it was used in the STFT。 it is related to the location of the window, as the window is shifted through the signal. This term, obviously, corresponds to time information in the transform domain. However, we do not have a frequency parameter, as we had before for the STFT. Instead, we have scale parameter which is defined as $1/frequency$. The term frequency is reserved for the STFT. Scale is described in more detail in the next section. MULTIRESOLUTION ANALYSIS Although the time and frequency resolution problems are results of a physical phenomenon (the Heisenberg uncertainty principle) and exist regardless of the transform used, it is possible to analyze any signal by using an alternative approach called the multiresolution analysis (MRA) . MRA, as implied by its name, analyzes the signal at different frequencies with different resolutions. Every spectral ponent is not resolved equally as was the case in the STFT. MRA is designed to give good time resolution and poor frequency resolution at high frequencies and good frequency resolution and poor time resolution at low frequencies. This approach makes sense especially when the signal at hand has high frequency ponents for short durations and low frequency ponents for long durations. Fortunately, the signals that are encountered in practical applications are often of this type. For example, the following shows a signal of this type. It has a relatively low frequency ponent throughout the entire signal and relatively high frequency ponents for a short duration somewhere around the middle. WAVELE PACKETS Performance of any transform in a particular application is highly dependent on the basis functions chosen. The choice of quadrature mirror filters (QMF) used in a wavelet packet analysis should be taken into consideration in a pression scheme. The choice of appropriate QMF is not only signal dependent, but scale dependent within a given generalization, known as Hybrid Wavelet Packet analysis, which includes the choice of optimal QMF at each level of deposition is explored. Computational results show that optimized hybrid wavelet packet bases provide better pression for a class of signals and indicate methods to develop search strategies to find these optimal bases. The discrete wavelet transform (DWT) can be characterized as a recursive application of the highpass and lowpass filters that form a QMF pair. The calculation of the DWT begins by filtering a signal by the highpass and lowpass filters and then downsampling the output. The putation proceeds by applying the QMF pair to the output of the lowpass recursion, then, is simply just a repeated application of the QMF pair to the lowpass filtered output of the previous level. Wavelet packets are generated by only slightly changing this operation. To calculate a wavelet packet deposition, the procedure begins as before, with the application of the QMF to the data followed by downsampling. However, now the putation proceeds by applying the QMF to not only the owpass output but to the highpass output as well. The recursion is simply to filter and downsample all output of the previous level. The calculation of wavelet packets is often schematically 外文文献原文 characterized by the formation of a binary tree with each branch representing the highpass and lowpass filtered output of a root node. Definition A tableau is a wavelet packet tree. It is a structure for anizing the output of the recursive applications of a single QMF pair in a wavelet packet expansion. HYBRIDWAVELET PACKETS Accepting that the choice of QMF inherently affects the performance of a pression scheme, a simple solution is to perform a best basis analysis for m different QMFs and then choose the “best of the best.” This offers the possibility of improved pression, but this simple approach is merely a superficial use of multiple QMFs. The central concept of this research is that the choice of appropriate QMF is not only signal dependent but scale dependent within a given signal as well. That is, given pression as the ultimate goal, the choice of QMF which yields the best performance may change at different levels within a wavelet packet analysis. (Ⅱ ) COMPLEX RIDGELETS FOR IMAGE DENOISING INTRODUCTION Wavelet transforms have been successfully used in many scientific fields such as image pression, image denoising, signal processing, puter graphics,and pattern recognition, to name only a and his coworkers pioneered a wavelet denoising scheme by using soft thresholding and hard thresholding. This approach appears to be a good choice for a number of applications. This is because a wavelet transform can pact the energy of the image to only a small number of large coefficients and the majority of the wavelet coeficients are very small so that they can be set to zero. The thresholding of the wavelet coeficients can be done at only the detail wavelet deposition subbands. We keep a few low frequency wavelet subbands untouched so that the。