Your task will be to code a simulation of image compression based on the approximate low rank structure of the set of image patches. You will write functions .code = my block compress(I, B, nz); .I = my block reconstruct(code, B,m,n);

The function my block compress takes as input an m×n image grayscale I, extracts all the distinct 8 × 8 blocks from the image using the matlab command im2col, and finds the representation of each block in the (64× 64) orthogonal basis B, and then discards all but the nz largest magnitude coefficients over all the blocks in the image. The output code is a nz × 3 array which gives the nz most valuable coefficients for reconstructing all the patches, and the locations. It should be structured as follows: each entry of the first column of the variable code contains a coefficient. Each entry in the second column specifies which block that coefficient belongs to. Each entry in the third column specifies which basis element the coefficient belongs to1.

The function my block reconstructs takes as input a coded array code, a 64 × 64 basis B, and output size parameters m and n. It outputs an m× n image I reconstructed from the coefficients in code; you may use the function col2im if you find it convenient.

For example, suppose I is a 24×24 image. We can write I in block form:
I =0@
I1 I4 I7
I2 I5 I8
I3 I6 I9
1A
,
where Ik is a 8×8 matrix for k 2 {1, 2, ..., 9}. Using im2col on I, we obtain
J = (J1 J2 J3 J4 J5 J6 J7 J8 J9) = im2col(I, [8 8], 'distinct'),