Audio Inpainting

(c) 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Published version: IEEE Transactions on Audio, Speech and Language Processing 20(3): 922-932, Mar 2012. DOI: 10.1090/TASL.2011.2168211

Recovery of Missing Samples Using Sparse Approximation via a Convex Similarity Measure

In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of image signal. This problem is also known as inpainting in the context of image processing and for this purpose, we suggest an iterative sparse recovery algorithm based on constrained $l_1$-norm minimization with a new fidelity metric. The proposed metric called Convex SIMilarity (CSIM) index, is a simplified version of the Structural SIMilarity (SSIM) index, which is convex and error-sensitive. The optimization problem incorporating this criterion, is then solved via Alternating Direction Method of Multipliers (ADMM). Simulation results show the efficiency of the proposed method for missing sample recovery of 1D patch vectors and inpainting of 2D image signals

CS reconstruction of the speech and musical signals

The application of Compressive sensing approach to the speech and musical signals is considered in this paper. Compressive sensing (CS) is a new approach to the signal sampling that allows signal reconstruction from a small set of randomly acquired samples. This method is developed for the signals that exhibit the sparsity in a certain domain. Here we have observed two sparsity domains: discrete Fourier and discrete cosine transform domain. Furthermore, two different types of audio signals are analyzed in terms of sparsity and CS performance - musical and speech signals. Comparative analysis of the CS reconstruction using different number of signal samples is performed in the two domains of sparsity. It is shown that the CS can be successfully applied to both, musical and speech signals, but the speech signals are more demanding in terms of the number of observations. Also, our results show that discrete cosine transform domain allows better reconstruction using lower number of observations, compared to the Fourier transform domain, for both types of signals