Image Denoising | OMP | L0 Problem | Sparse Recovery | DCT Dictionary | python
Color Image Denoising (Sparse iterative Recovery) with OMP (Orthogonal Matching Pursuit) algorithm with a DCT dictionary - an implementation with python
Image Denoising by solving the L0 (pseudonorm) optimization problem min_x ||x||_0 s.t. Ax=b,0 with Greedy sparse approximation algorithm Orthogonal Matching Pursuit (OMP) using DCT Dictionary (256 atoms) with python (since the original problem is NP-hard).
overlapping 8x8 image patches are computed (vectorized as b and stacked into matrix) and for each patch OMP is run to compute a sparse representation of the patch by using at most 10 atoms (to construct matrix A) from the (precomputed fixed) DCT dictionary D (typically overcomplete, containing 256 or 1024 atoms), with residual thresholding as a stopping criterion for the iterative OMP along with sparsity.
OMP iteratively selects the best matching (correlating) atom with a given patch, adds the atom to the set of atoms selected so far in A and projects the patch on A, computes the residual from b, repeats reconstruction of the residual until the stopping criteria reached.
Here a DCT overcomplete dictionary with 256 atoms was used. Different (overcomplete) DCT dictionaries (D) can be used for reconstruction (e.g., with 16^2=256 and 32^2=1024 atoms).
color channels are reconstructed separately.
#imageprocessing #imageprocessingpython #python #computervision #algorithm #machinelearning #optimization #sparse
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