Convolutive Blind Source Separation Methods

In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks

Blind separation of convolutive mixtures based on second order and third order statistics

This paper addresses the problem of blind separation of linear convolutive mixtures. We first reformulate the problem into a blind separation of linear instantaneous mixtures, and then a statistical approach is applied to solve the reformulated problem. From the statistics of the mixtures, two kinds of matrix pencils are constructed to estimate the mixing matrix. The original sources are then separated with the estimated mixing matrix. For the purpose of computational efficiency and robustness, in the matrix pencil, one matrix is constructed from the second order statistics, and the other is constructed from the third order statistics. The proposed novel methods do not require the exact knowledge of the channel order. Simulation results show that the methods are robust and have good performance.published_or_final_versio

Short-time homomorphic wavelet estimation

Successful wavelet estimation is an essential step for seismic methods like impedance inversion, analysis of amplitude variations with offset and full waveform inversion. Homomorphic deconvolution has long intrigued as a potentially elegant solution to the wavelet estimation problem. Yet a successful implementation has proven difficult. Associated disadvantages like phase unwrapping and restrictions of sparsity in the reflectivity function limit its application. We explore short-time homomorphic wavelet estimation as a combination of the classical homomorphic analysis and log-spectral averaging. The introduced method of log-spectral averaging using a short-term Fourier transform increases the number of sample points, thus reducing estimation variances. We apply the developed method on synthetic and real data examples and demonstrate good performance.Comment: 13 pages, 5 figures. 2012 J. Geophys. Eng. 9 67

Extended object reconstruction in adaptive-optics imaging: the multiresolution approach

We propose the application of multiresolution transforms, such as wavelets (WT) and curvelets (CT), to the reconstruction of images of extended objects that have been acquired with adaptive optics (AO) systems. Such multichannel approaches normally make use of probabilistic tools in order to distinguish significant structures from noise and reconstruction residuals. Furthermore, we aim to check the historical assumption that image-reconstruction algorithms using static PSFs are not suitable for AO imaging. We convolve an image of Saturn taken with the Hubble Space Telescope (HST) with AO PSFs from the 5-m Hale telescope at the Palomar Observatory and add both shot and readout noise. Subsequently, we apply different approaches to the blurred and noisy data in order to recover the original object. The approaches include multi-frame blind deconvolution (with the algorithm IDAC), myopic deconvolution with regularization (with MISTRAL) and wavelets- or curvelets-based static PSF deconvolution (AWMLE and ACMLE algorithms). We used the mean squared error (MSE) and the structural similarity index (SSIM) to compare the results. We discuss the strengths and weaknesses of the two metrics. We found that CT produces better results than WT, as measured in terms of MSE and SSIM. Multichannel deconvolution with a static PSF produces results which are generally better than the results obtained with the myopic/blind approaches (for the images we tested) thus showing that the ability of a method to suppress the noise and to track the underlying iterative process is just as critical as the capability of the myopic/blind approaches to update the PSF.Comment: In revision in Astronomy & Astrophysics. 19 pages, 13 figure