Question: have Au E U. Explain why U = WI. 6 (JPEG compression - Example). Consider the Haar Wavelet basis H of R8: NIHSIN NIHOIL I

have Au E U. Explain why U = WI. 6 (JPEG compression - Example). Consider the Haar Wavelet basis H of R8: NIHSIN NIHOIL I NIHNIH O O O NIHOIL Let H be 8 x 8-matrix whose columns are the vectors in H. Let & be the standard basis of R8. (1) What is Ie,H? (2) What is Ine? Let c = 5. Consider the following 8 x 8-grayscale picture: Page 22...--4ma. -ur ..._u'..._..4u._.... a.\" It is represented by the following 8 X 8matrix IT] 255 255 255 255 255 255 255 255 [l 255 255 U [l 255 255 U U 255 255 U [l 255 255 U 255 255 255 255 255 255 255 255 (3) Calculate HTAH! This is a base change. Can you explain why? (4) Divide HTAH by c and round each entry to the nearest integer. Call the resulting matrix B. (Quantization) 0000000 00000000 00000000 00000000 (5) Determine the compression ratio, that is divide the number of non-zero entries of A by the number of nonzero entries of B. (6) Calculate HBHT! Compare this matrix to A. (Recovering the original image)

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