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.. (לתיקייה המכילה) | |
Question #1, section (1) | |
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The multi-resolution property is an example of a successive refinement procedure. Here it means that if you use a larger set of orthonormal functions, then a subset of the coefficients corresponds (i.e., equal) also to a (smaller) set of the correponding orthonormal functions in the corresponding lower resolution. Accordingly, this property may be utilized for a successive refinement procedure. In this question you need to calculate the representation-coefficients for the set of 8 Walsh-Hadamard functions, while considering the coefficients obtained in the tutorial for the set of 4 Walsh-Hadamard functions. This question also addresses the multi-resolution property that exists between these two function-sets. |
Matlab part section 3.c.iii (English version). | |
| A minor typo was fixed in the Matlab part section 3.c.iii (English version). |
Matlab Part | |
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Please note that you need to create the Walsh-Hadamard matrix by yourselves. Also note the difference between Walsh-Hadamard and Hadamard matrices. |
Matlab Part: Resolution-Reduction in the Walsh-Hadamard Domain | |
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While the resolution-reduction in the standard basis is done by averaging, the resolution-reduction in the Walsh-Hadamard basis should be applied differently as follows: In subsection 3c: Since WH supports the multi-resolution property (in dimensions that are powers of 2) you can reduce the resolution by zeroing the coefficients that correspond to the high-resolution basis-vectors, then quantizing the kept coefficients, and finally reconstruct the image by transforming-back to the standard basis. In subsection 3d: Here you still need to zero coefficients, however, these are determined by their absolute values. The results in the Walsh-Hadamard section are extensively affected by row-order in the WH matrix, i.e., it is important to use the Walsh-Hadamard matrix and not just the Hadamard matrix. |
Matlab Part: Quantization | |
| As already specified in the assignment, the quantization in the Matlab part should be uniform and may use more than 8 bits. |
Matlab Part: 2D Walsh-Hadamard Transform | |
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Here, the 2D Walsh-Hadamard transform should be in the separable form. |