G. Abhilash

This paper proposes a learning method to construct an efficient sensing (measurement) matrix, having orthogonal rows, for compressed sensing of a class of signals. The learning scheme identifies the sensing matrix by maximizing the entropy of measurement vectors. The bounds on the entropy of the measurement vector necessary for the unique recovery of a signal are also proposed. A comparison of the performance of the designed sensing matrix and the sensing matrices constructed using other existing methods is also presented. The simulation results on the recovery of synthetic, speech, and image signals, compressively sensed using the sensing matrix identified, shows an improvement in the accuracy of recovery. The reconstruction quality is better, using less number of measurements, than those measured using sensing matrices identified by other methods.

The authors propose entropy minimisation‐based matching pursuit algorithm which has the capability to reject noise even when the noise level is comparable to the signal level. The proposed algorithm can cater to compressible signals and sparse signals with unknown sparsity.

In this article, we discuss a novel greedy algorithm for the recovery of compressive sampled signals under noisy conditions. Most of the greedy recovery algorithms proposed in the literature require sparsity of the signal to be known or they estimate sparsity, for a known representation basis, from the number of measurements. These algorithms recover signals when noise level is significantly low. We propose Entropy minimization based Matching Pursuit (EMP) which has the capability to reject noise even when noise level is comparable to that of signal level. The proposed algorithm can cater to compressible signals and signals for which sparsity is not known in advance. Simulation study of the proposed scheme shows improved robustness to white Gaussian noise in comparison with the conventional greedy recovery algorithms.

This paper contains the application of Unimodular Filterbanks (UMFBs) based on two new structures for audio coding. Two key properties make UMFBs ideal for audio coding applications. Firstly, they have the lowest possible system delay of M _ 1 samples, where M is the number of channels. This property resolves the problem of pre-echoes. Secondly, the presence of nilpotent matrix in the structure furnishes unequal lengths of analysis and synthesis filters to adapt to perceptual limits; long analysis filters for good frequency selectivity and short synthesis filters for noise reduction. The proposed structures ensure perfect reconstruction (PR) and are of minimum delay in the McMillan sense. The number of free parameters is as low as 2M and the optimal set of parameters can be obtained with unconstrained optimization. The low computational overhead makes it suitable for simple and efficient hardware implementation. We have also carried out a brief study of the quantization noise shaping with the proposed structures.