A comparative study of wavelets and adaptively learned dictionary in compressive image sensing

The choice of a dictionary for sparse representation is a crucial step in compressive sensing. Wavelets are very commonly used sparse basis, and K-SVD is a dictionary learning algorithm having shown its potential in sparse representation. In this paper, we combine K-SVD and compressive sensing in image sampling, and compare the performance of K-SVD dictionary as sparse basis to Daubechies wavelets. A series of tests are done on clean and noisy images at different sampling rate, results show that K-SVD can sparsely represent images very effectively, and performs much better in compressive image sensing at low sampling rate than Daubechies wavelets do.