Visual Communication Lab Wavelet in Matlab Visual Communication Lab Park Won Bae ‘98.12.3 영상통신연구실 박 원 배

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 영상통신연구실 박 원 배

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 영상통신연구실 박 원 배

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

* 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 ) - STEP3 : Reconstructing the Level 3 Approximation ( wrcoef - type ‘a’ ) - STEP4 : Reconstructing the Level 1,2 and 3 Details (wrcoef - type ‘d’ ) - STEP 5 : Reconstructing the Original from the Level 3 Decomposition ( waverec ) 영상통신연구실 박 원 배

* 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 영상통신연구실 박 원 배

* 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 영상통신연구실 박 원 배

< pwb1.m file 참고 > 영상통신연구실 박 원 배

* 2-D Discrete Wavelet Analysis #1 - dwt2 : Single-level discrete 2-D wavelet transform [cA,cH,cV,cD] = dwt2(X,’wavelet-name’) - idwt2 : Single-level inverse discrete 2-D wavelet transform X = idwt2(cA,cH,cV,cD,’wavelet-name’,S) S : size(X) = 2*size(cA)-lf+2 ( lf : filter lengths) 영상통신연구실 박 원 배

< Original Image > < pwb4.m file 참고 > < Decomposition Image > 영상통신연구실 박 원 배

* 2-D Discrete Wavelet Analysis #2 - wavedec2 : Multi-level 2-D Wavelet decomposition [C,S] = wavedec2(X,N, ‘wavelet-name’) S : bookkeeping matrix - waverec2 :Multi-level 2-D wavelet reconstruction X = waverec2(C,S,’wavelet-name’) 영상통신연구실 박 원 배

* 2-D Discrete Wavelet Analysis #3 - appcoef2 : Extract 2-D approximation coefficients > A = appcoef2(C,S,’wavelet-name’, N) - detcoef2 : Extract 2-D detail coefficients > D = detcoef2(O,C,S,N) O : Direction ‘h’,’v’,’d’ - wrcoef2 : Reconstruct single branch from 2-D wavelet coeff > X = wrcoef2(‘type’, C,S, ‘wavelet-name’, N) type : ‘a’ - approximation ‘h’,’v’,’d’ - reconstruction 영상통신연구실 박 원 배