ksvd-sparse-dictionary

Sparse dictionary using the iterative K-SVD algorithm. Useful for compressive sensing applications. Sensing and reconstruction done using Orthogonal Matching Pursuit (OMP).

Example Result:

Example generated using randomly generated sinusoids. See test.py.

• Dictionary size : 60
• Max sparsity : 15
• Signal length : 50
• (Random) Samples : 25
• Compression ratio: 2:1

Example Usage:

from ksvd import ksvd
from sparseRep import random_sensor, sense, reconstruct

# learn dictionary D from data
dictionary,_,_ = ksvd(data, dictionary_size, max_sparsity, maxiter=max_iter)

# sense test data using sensing matrix
representation = sense(test_data, sensing_matrix)

# sparse reconstruction using learned dictionary
reconstruction = reconstruct(representation, sensing_matrix, dictionary, max_sparsity)

References:

• M. Aharon, M. Elad and A. Bruckstein, "K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation," in IEEE Transactions on Signal Processing, vol. 54, no. 11, pp. 4311-4322, Nov. 2006.

• Rubinstein, R., Zibulevsky, M. and Elad, M., "Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit Technical Report" - CS Technion, April 2008.