Recent dictionary training algorithms for sparse representation like K-SVD, MOD, and their variation are reminiscent of K-means clustering, and this letter investigates such algorithms from that viewpoint. It shows: though K-SVD is sequential like K-means, it fails to simplify to K-means by destroying the structure in the sparse coefficients. In contrast,… (More)
—In this paper, we advance the concept of warped discrete-Fourier transform (WDFT), which is the evaluation of frequency samples of the-transform of a finite-length sequence at nonuniformly spaced points on the unit circle obtained by a frequency transformation using an allpass warping function. By factorizing the WDFT matrix, we propose an exact… (More)
This letter presents a variant of Orthogonal Matching Pursuit (OMP) method, called Backtracking-based Adaptive OMP (BAOMP), for compressive sensing and sparse signal reconstruction. As an extension of the OMP algorithm, the BAOMP method incorporates a simple backtracking technique to detect the previous chosen atoms' reliability and then deletes the… (More)
The decoding of a class of discrete cosine transform (DCT) and discrete sine transform (DST) codes that are maximum distance separable codes (MDS) is considered in this paper. These class of codes are considered for error correction over real fields. All the existing algebraic decoding algorithms are capable of decoding only a subclass of these codes [which… (More)
Existing image denoising frameworks via sparse representation using learned dictionaries have an weakness that the dictionary, trained from noisy image, suffers from noise incursion. This paper analyzes this noise incursion, explicitly derives the noise component in the dictionary update step, and provides a simple remedy for a desired signal to noise… (More)
We propose a fragile watermarking with self-embedding for recovery of tampered image that does not use authentication bits. We use a robust spread spectrum based watermarking scheme using block based embedding, DCT based compression, and other improvements. Simulation results showing recovery performance are presented.