Wavelet in Matlab Visual Communication Lab Park Won

Wavelet in Matlab Visual Communication Lab Park Won Bae ‘ 98. 12. 3 1 영상통신연구실 박 원 배

Wavelet Overview #1 - Fourier Analysis > In transforming to the frequency domain, time information is lost - STFT(Short Time Fourier Transform) > Provide some information about both when and at what frequencies a signal event occurs > We can only obtain this information with limited precision - Wavelet Analysis > long time intervals where we want more precise low frequencies information > shorter regions where we want high frequencies information 2 영상통신연구실 박 원 배

Wavelet Overview #2 - Wavelet > a waveform of effectively limited duration that has an average value of zero > the breaking up of a signal into shifted and scaled version of the original(mother) wavelet > low scale = compressed wavelet = rapidly changing details = High freq. > high scale = stretched wavelet = slowly changing, coarse = Low freq > wavelet function and scaling function 3 영상통신연구실 박 원 배

Wavelet Overview #3 - Multi-Step Decomposition and Reconstruction 4 영상통신연구실 박 원 배

Wavelet * Multi-level Wavelet Analysis of a signal #1 - STEP 1 : Performing a Multi-Level Wavelet Decomposition of a signal ( wavedec ) - STEP 2 : Extracting Approximation and detail Coefficients ( appcoef, detcoef ) - STEP 3 : Reconstructing the Level 3 Approximation ( wrcoef - type ‘a’ ) - STEP 4 : Reconstructing the Level 1, 2 and 3 Details (wrcoef - type ‘d’ ) - STEP 5 : Reconstructing the Original from the Level 3 Decomposition ( waverec ) 5 영상통신연구실 박 원 배

Wavelet * Multi-level Wavelet Analysis of a signal #2 - wavedec : Multi-level 1 -D Wavelet decomposition [C, L] = wavedec(X, N, ’wavelet-name’) X : signal , N : level 6 영상통신연구실 박 원 배

Wavelet * Multi-level Wavelet Analysis of a signal #3 - appcoef : Extract 1 -D approximation coefficients > A = appcoef(C, L, ’wavelet-name’, N) - detcoef : Extract 1 -D detail coefficients > D = detcoef(C, L, N) - wrcoef : Reconstruct single branch from 1 -D wavelet coeff > X = wrcoef(‘type’, C, L, ‘wavelet-name’, N) type : ‘a’ - approximation ‘d’ - detail 7 영상통신연구실 박 원 배

Wavelet * 2 -D Discrete Wavelet Analysis #1 - dwt 2 : Single-level discrete 2 -D wavelet transform [c. A, c. H, c. V, c. D] = dwt 2(X, ’wavelet-name’) - idwt 2 : Single-level inverse discrete 2 -D wavelet transform X = idwt 2(c. A, c. H, c. V, c. D, ’wavelet-name’, S) S : size(X) = 2*size(c. A)-lf+2 ( lf : filter lengths) 9 영상통신연구실 박 원 배

Wavelet < Original Image > < pwb 4. m file 참고 > 10 < Decomposition Image > 영상통신연구실 박 원 배

Wavelet * 2 -D Discrete Wavelet Analysis #2 - wavedec 2 : Multi-level 2 -D Wavelet decomposition [C, S] = wavedec 2(X, N, ‘wavelet-name’) S : bookkeeping matrix - waverec 2 : Multi-level 2 -D wavelet reconstruction X = waverec 2(C, S, ’wavelet-name’) 11 영상통신연구실 박 원 배

Wavelet * 2 -D Discrete Wavelet Analysis #3 - appcoef 2 : Extract 2 -D approximation coefficients > A = appcoef 2(C, S, ’wavelet-name’, N) - detcoef 2 : Extract 2 -D detail coefficients > D = detcoef 2(O, C, S, N) O : Direction ‘h’, ’v’, ’d’ - wrcoef 2 : Reconstruct single branch from 2 -D wavelet coeff > X = wrcoef 2(‘type’, C, S, ‘wavelet-name’, N) type : ‘a’ - approximation ‘h’, ’v’, ’d’ - reconstruction 12 영상통신연구실 박 원 배