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multimedia Telecommunications
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1. Find the lifting steps representation of the following lters: haar, db4, cdf3.1; 2. Write the corresponding polyphase matricesP (z^-1)and and P (z); 3. Display the corresponding analysis and synthesis lters; 4. For all the considered lters perform the DWT on the images einstein.jpg, mandrill.tif, Flowers.003.tif with J = 4 (four decomposition levels) using (i) the classical implementation; and (ii) the lifting steps implementation; 5. Verify that (a) The two decompositions are equivalent; (b) Perfect reconstruction holds in both cases. 6. Quantize the wavelet coe cients of all the subbands uniformly with quantization step for Q = 4. Reconstruct the image and display the result. 7. For the lter cdf3.1: (a) Exchange the analysis and synthesis lters and perform the decomposition on the image einsten. Are the resulting subbands di erent from those previously obtained? Why? (b) Quantize the wavelet coe cients
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For each of the following images: einstein.jpg, mandrill.tif, Flowers.003.tif 1. Convert the images to grayscale and save them; 2. Perform the Discrete Wavelet transform with the parameters listed in the Table: Number of levels J=4 Filters haar, biorthogonal 2.2, biorthogonal 2.4, Daubechies' 4 (db4) 3. Choose one wavelet and set J = 3. Perform the following operations on the subband coefficients: (a) Successively set to zero the di erent subband coe cients ( rst subband by subband and then level by level); (b) Keep the absolute value of the coe cients (change each negative sign to positive); (c) Keep the signs of the coe cients while setting the absolute value of each coefcient equal to radq(2)^j , where j represents the level; (d) Quantize the coe cients by rounding to the nearest integer; Then, for each case, perform the inverse transform to reconstruct the image. Save the corresponding image and comment the
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