Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Experimenting with Multidimensional Wavelet Transformations Tarık Arıcı and Buğra Gedik Outline of Project Goals Writing discrete wavelet transformation and inverse transformation wrappers (in Matlab) to handle multidimensional data; possible uses include: 2D Images, 3D turbulence data or multi-attribute sensor readings Using wavelets in some example applications Lossy compression, De-noising for images, Selfsimilarity analysis Studying the phases of the wavelet filters (that delays the wavelet smoothes) and approximately computing the delay amount using DSP methods Using this on Mammogram reconstruction Possible uses of Bayesian? (not done) DWTR / IDWTR wrappers Assume D dimensions Perform D sweeps, one across each dimension, making recursive smoothes calls for each D-1 dimensional slice Top level recursive calls go D-1 levels deep before calling the 1 dimensional wavelet transformation functions 7 detail groups As a result 2^D-1 detail groups and a single smooth group is constructed for each level of transformation smoothes 3 detail groups Example Applications: Lossy Compression Example Applications: De-noising Example Applications: Self-similarity Analysis Calculate the means of the detail squares for each level and plot their log as a function of level If the line is linear, then there is self-similarity Brownian motion is self-similar, Random data (of course) is not Mammogram Reconstruction Original Image after wavelet interpolation after fixing delay problem Assume all details are zero Perform inverse wavelet transformation Possible use of Bayesian Methods: Model missing details using a Bayesian approach DSP Perspective: Problems Related with Non-zero Phase Filtering Filtering in time domain is multiplication in frequency domain X[n] h[n] y[n] Phase(Y(f)) = Phase(H(f))+Phase(X(f)) Non-zero Phase Filtering cos(2pf0t+f) = cos(2pf0(t+f/(2pf0)) = f/(2pf0) td is constant if f is a linear function of frequency td Therefore, wavelet filters should be (approximately) linear phase filters Symmetric filters have linear phase Ex: {1, 1} (Haar), {1, 2, 1} Least Asymmetric (LA) Wavelet Filters Choose filter coefficients: s.t. min |f(f) – 2pfv| v= -L/2+1, if L =8,12,16,20 -L/2, if L =10, 18 -L/2+2, if L =14 LA(8) and LA(12) works best. The End! Thanks!!!