小波变换简介.ppt

Subband Coding Algorithm Wavelet: db4 Level: 6 Signal: 0.0-0.4: 20 Hz 0.4-0.7: 10 Hz 0.7-1.0: 2 Hz fH fL Discrete Wavelet Transform: Multilevel Decomposition Inverse Discrete Wavelet Transform: Wavelet Reconstruction The discrete wavelet transform can be used to analyze, or decompose, signals and images. This process is called decomposition or analysis. The other half of the story is how those components can be assembled back into the original signal without loss of information. This process is called reconstruction, or synthesis. The mathematical manipulation that effects synthesis is called the inverse discrete wavelet transform (IDWT). Inverse Discrete Wavelet Transform: Wavelet Reconstruction What How those components can be assembled back into the original signal without loss of information? A Process After decomposition or analysis. Also called synthesis How Reconstruct the signal from the wavelet coefficients Where wavelet analysis involves filtering and downsampling, the wavelet reconstruction process consists of upsampling and filtering Inverse Discrete Wavelet Transform: Wavelet Reconstruction Multistep Decomposition and Reconstruction Wavelet Applications Typical Application Fields Astronomy, acoustics, nuclear engineering, sub-band coding, signal and image processing, neurophysiology, music, magnetic resonance imaging, speech discrimination, optics, fractals, turbulence, earthquake-prediction, radar, human vision, and pure mathematics applications Sample Applications Identifying pure frequencies De-noising signals Detecting discontinuities and breakdown points Detecting self-similarity Compressing images Wavelet Applications: Denoising Highest Frequencies Appear at the Start of The Original Signal Approximations Appear Less and Less Noisy Also Lose Progressively More High-frequency Information. In A5, About the First 20% of the Signal is Truncated Wavelet Applications: Detecting Discontinuities and Breakdown Points The Discontinuous Signal Consist