Application of Geometric Dependency Analysis to the Separation of Convolved Mixtures

Abstract

Abstract. We investigate a generalisation of the structure of frequency domain ICA as applied to the separation of convolved mixtures, and show how a geometric representation of residual dependency can be used both as an aid to visualisation and intuition, and as tool for clustering components into independent subspaces, thus providing a solution to the source separation problem.

An adaptive stereo basis method for convolutive blind audio source separation

“…In a preliminary study [12], we investigated an extension of this technique to stereo signals, applying an ICA algorithm to sequences of stereo time frames.…”

“…As for FD-ICA, we could use a variety of methods to perform this grouping. In earlier work we used a higher-order correlation (F-correlation) between component activities to perform this grouping [12]. However, in Figure 2 we observe that the stereo basis vector pairs tend to be relatively wideband, and exhibit a clear relative time delay between the left and right channels.…”

“…Instead of using a fixed time-frequency transform such as the STFT, applied separately to each observation (microphone) channel, we learn an adaptive transform based on the observed stereo data that is applied to both channels together [12]. Many basis pairs of the resulting transform exhibit properties suggesting that they represent the components of individual sources, together with the filtering process from the sources to the microphone pair.…”

An adaptive orthogonal sparsifying transform for speech signals

“…The most computationally expensive step in the algorithm described in section II is the evaluation of the coefficients of expansion in equation (7). Evaluation of α j (k), for a signal block x k (n) of length k max and an atom a j (n) of length N, is O(N k max ) for each iteration j ∈ {1, .…”

“…It is often difficult to determine a relationship between a class of signals and a particular dictionary, especially for natural signals [6]. This has led researchers to look for learned, rather than fixed dictionaries, using techniques such as independent component analysis (ICA), as the underlying learning algorithm [2], [7], [8]. These methods, however, are computationally very expensive, and often require fairly large datasets in order to learn the dictionary bases.…”