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(a) Spectrogram of the original guitar source and spectrogram of the separated guitar source using (b) the first fixed-point algorithm and (c) the second fixed-point algorithm
Source publication
One of the most powerful techniques applied to blind audio source separation is Independent Component Analysis (ICA). For the separation of audio sources recorded in a real environment, we need to model the mixing process as convolutional. Many methods have been introduced for separating convolved mixtures, the most successful of which require work...
Context in source publication
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... is a quite highly correlated mixture as the two guitars are playing notes in unison, making it even difficult for the human ear to separate. However, the results are very good, as presented in figure 4. These highly correlated signals are well separated by the two algorithms, with the second fixed-point being a little bit more robust this time, with negligible crosstalk in the background. ...
Similar publications
Recent advances in separation of convolutive mixtures of audio signals have shown that the problem can be successfully solved in time-domain in a multistep procedure including an application of some method of instantaneous independent component analysis (ICA) or independent subspace analysis (ISA), as one of the steps. In this paper we propose a te...
To increase the efficiency of the independent component analysis (ICA) and reduce the computational complexity of the system, this paper proposes a methodology based on the compressive sampling with minimum measurements. This allows compressing and modifying the Gaussian characteristics of audio signals. ICA is one of the most widely used schemes f...
Citations
... Several methods have been proposed to unmix convolutive mixtures in time domain [7,15], but these methods were limited and computationally expensive [16]. Other methods were dedicated to solving the problem in the frequency domain [17][18][19]. Motivated by these works, Ciaramella et al. proposed a novel approach in which the fixed-point ICA algorithm in complex domain is combined with Short-Time Fourier Transform (STFT) [20]. ...
This paper describes a new multi-resolution approach for the blind separation of convolutive image mixtures in transform domain. The proposed method uses an Adaptive Vectorial case of Quincunx Lifting Scheme (AVQLS), based on wavelet decomposition, and a geometric unmixing algorithm. It proceeds in three steps: first, the mixed images are decomposed by AVQLS. Then, the unmixing algorithm is applied to the more relevant component to get a transformed estimate of the original images. An inverse transform is, thereafter, applied to obtain an estimate of the original images. Experiments carried out on medical images showed that the proposed method yields better separation results than many widely used blind source separation algorithms.
... Several methods have been proposed to unmix convolutive mixtures in time domain [4,9], but these methods were limited and computationally expensive [10]. Other methods were dedicated to solving the problem in the frequency domain [11][12][13]. Motivated by these works, Ciaramella et al proposed a novel approach in which the fixed-point ICA algorithm in complex domain is combined with Short-Time Fourier Transform (STFT) [14]. ...
This paper describes a new multilevel decomposition method for the
separation of convolutive image mixtures. The proposed method uses an
Adaptive Quincunx Lifting Scheme (AQLS) based on wavelet decompo-
sition to preprocess the input data, followed by a Non-Negative Matrix
Factorization whose role is to unmix the decomposed images. The un-
mixed images are, thereafter, reconstructed using the inverse of AQLS
transform.
Experiments carried out on images from various origins showed that
the proposed method yields better results than many widely used blind
source separation algorithms.
... , P . Several methods have been proposed to solve the problem of unmixing convolutive mixtures in the frequency domain [25] [26] [27] using the Short-Time Fourier Transform (STFT). We choose to solve this problem in the frequency domain using an efficient wavelet transform as described in [28]. ...
We propose a robust autofocus method for reconstructing digital holograms and twin-image removal based on blind source separation approach. The method is made up of two components: an efficient quincunx lifting scheme based on wavelet packet transform, whose role is to maximize a sharpness metric related to the sparseness of the input holograms, and a geometric unmixing algorithm, which achieves the separation task. Experimental results confirm the ability of sparse blind source separation to discard the unwanted twin-image from in-line digital holograms of particles.
... Such filtered sums of different sources are called convolutive mixtures.In [4] and [7], authors have been proposed to unmixing convolutive mixtures in time domain , but these methods are limited [8] and computationally expensive. Other methods proposed to solve this problem in the frequency domain [9] [10] [11] using the Short-Time Fourier Transform (STFT).In [12], the author discussed why the separation performance of frequency domain BSS using FFT is poor when there is long reverberation and it is not good to be constrained by the condition T ≥ P , where T is the frame size of the FFT and P is the length of a room impulse response. ...
This paper describes a new multi-resolution approach for the blind source separation of convolutive image mixtures in transform domain. The proposed method uses an Adaptive Quincunx Lifting Scheme based on wavelet decomposition and a Complex ICA unmixing algorithm. It proceeds in three steps: first, the mixed signals are decomposed by an adaptive lifting scheme. Then, the unmixing algorithm is applied to the more relevant component. The unmixed signals are, thereafter, reconstructed using an inverse transform. Experiments carried out on images from various origins showed that the proposed method yields better results than many widely used blind source separation algorithms.
... Several methods have been proposed to solve the problem of unmixing convolutive mixtures in time domain [4] [7], but these methods are limited [8] and computationally expensive. Other methods proposed to solve this problem in the frequency domain [9] [10] [11] using the Short-Time Fourier Transform (STFT). ...
This paper describes a new multilevel-decomposition method for the blind source separation of convolutive image mixture. The proposed method uses an Adaptive Quincunx Lifting Scheme based on wavelet decomposition and a geometric unmixing algorithm. It proceeds in three steps. In the first step, the mixed signals are decomposed by an adaptive lifting scheme. The unmixing algorithm therefore applied to the most relevant component. The unmixed signals are, thereafter, reconstructed using an inverse transform. Experiments carried out on images from various origins showed that the proposed method yields better results than many widely used blind source separation algorithms.
... Unlike the gradient descent method, there is no need for the adjustment of learning steps or other adjustable parameters and the rate of convergence is therefore fixed without regard to the changing environment. Fixed-point algorithms also tend to be much more stable than other algorithms [40]. Like all fixed-point algorithms we have a two-step approachprewhitening and rotation of the observation vector. ...
The information theoretic concept of mutual information provides a general framework to evaluate dependencies between variables. Its estimation however using B-Spline has not been used before in creating an approach for Independent Component Analysis. In this paper we present a B-Spline estimator for mutual information to find the independent components in mixed signals. Tested using electroencephalography (EEG) signals the resulting BMICA (B-Spline Mutual Information Independent Component Analysis) exhibits better performance than the standard Independent Component Analysis algorithms of FastICA, JADE, SOBI and EFICA in similar simulations. BMICA was found to be also more reliable than the "renown" FastICA. .
... In the particular case of evaluating BSS algorithms, many different alternatives have been used, generally derived from other areas of signal processing. Those methods can be classified into two main areas: subjective assessment, where some appreciation is used regarding subjective perceived quality of resulting sound [9,10], or visual differences between waveforms of separated signal and original ones [10,11,12], or visual differences of spectrograms of separated signals and original ones [9]; and objective evaluation, where some numerical quantity directly associated to separation quality is used, permitting an objective comparison between different algorithms. ...
... In the particular case of evaluating BSS algorithms, many different alternatives have been used, generally derived from other areas of signal processing. Those methods can be classified into two main areas: subjective assessment, where some appreciation is used regarding subjective perceived quality of resulting sound [9,10], or visual differences between waveforms of separated signal and original ones [10,11,12], or visual differences of spectrograms of separated signals and original ones [9]; and objective evaluation, where some numerical quantity directly associated to separation quality is used, permitting an objective comparison between different algorithms. ...
The determination of quality of the signals obtained by blind source separation is a very important subject for development and evaluation of such algorithms. When this approach is used as a pre-processing stage for automatic speech recognition, the quality measure of separation applied for assessment should be related to the recognition rates of the system. Many measures have been used for quality evaluation, but in general these have been applied without prior research of their capabilities as quality measures in the context of blind source separation, and often they require experimentation in unrealistic conditions. Moreover, these measures just try to evaluate the amount of separation, and this value could not be directly related to recognition rates. Presented in this work is a study of several objective quality measures evaluated as predictors of recognition rate of a continuous speech recognizer. Correlation between quality measures and recognition rates is analyzed for a separation algorithm applied to signals recorded in a real room with different reverberation times and different kinds and levels of noise. A very good correlation between weighted spectral slope measure and the recognition rate has been verified from the results of this analysis. Furthermore, a good performance of total relative distortion and cepstral measures for rooms with relatively long reverberation time has been observed.
... Numerous methods have been used in the published literature to indicate separation performance. The list includes MSE [20], [21] bit/symbol error rate [22], [23], Frobenius distance [24], multi-channel row and multi-channel column ISI [25], plot of global mixing filter responses [26], [27], [28], SNR [29], [30], [31], ISR [19], SIR [32], [33], [34], [35], [36], [37], [38], one-at-a-time SIR [8], ISI [39], [40], [41], bias and standard deviation of filter coefficients [42], [43], plot of estimated sources in the time or frequency domain [44], [45], [46], hand-segmented SIR [47], automatic speech recognition rate [48], [33], [34], and the mean opinion score [18]. Several of these are not ideal for comparisons because they are either subjective, such as the plots and the mean opinion score, or require knowledge of the mixing filters, which makes them inapplicable for real mixtures. ...
An important problem in the field of blind source separation (BSS) of real convolutive mixtures is the determination of the role of the demixing filter structure and the criterion/optimization method in limiting separation performance. This issue requires the knowledge of the optimal performance for a given structure, which is unknown for real mixtures. Herein, the authors introduce an experimental upper bound on the separation performance for a class of convolutive blind source separation structures, which can be used to approximate the optimal performance. As opposed to a theoretical upper bound, the experimental upper bound produces an estimate of the optimal separating parameters for each dataset in addition to specifying an upper bound on separation performance. Estimation of the upper bound involves the application of a supervised learning method to the set of observations found by recording the sources one at a time. Using the upper bound, it is demonstrated that structures other than the finite-impulse-response (FIR) structure should be considered for real (convolutive) mixtures, there is still much room for improvement in current convolutive BSS algorithms, and the separation performance of these algorithms is not necessarily limited by local minima.
... Some authors have used second-order statistics and decorrelation procedures [6,7,8]. Others have proposed the use of fixed-point algorithms derived from FastICA algorithm [9,10,11] . Some information theory derived algorithms based on minimization of mutual information [12], information maximization (InfoMax) [13] or Kullback-Leibler divergency [14], combined with Natural Gradient [4] have been also successfully used. ...
Blind source separation for convolutive mixtures of sound sources is a complex task, mainly because the mixing filters are long and non-minimum phase. One approach to solve this problem is frequency domain blind source separation, in which the separation is calculated for each frequency bin in the time-frequency domain. Although there are several methods for this task, separation quality is degraded by many factors. This paper presents a method for separation in time-frequency domain, that combines the advantages of other two separation methods and uses a time-frequency Wiener filter as post-processing to increase separation quality. The algorithm has been evaluated over a database of Spanish speech recorded in a reverberant room using two active sound sources and two microphones. Speech recognition results show an incre-ment in recognition rate of the separated speech in the order of 70% from the noisy case.
... In real world situations, we observe convolutive mixtures of the sources and not instantaneous mixtures. Several methods have been proposed to solve the problem of separation of convolutive mixtures in time domain [3] [25] or in frequency domain [22], [16], [8]. The methods in time domain are limited [14] and computationally expensive. ...
In this paper, a novel approach to solve the permutation indeterminacy
in the separation of convolved mixtures in frequency domain is
proposed. A fixed-point algorithm in complex domain is used to separate
the signals in each frequency bin. These are obtained applying
a Short Time Fourier Transform on a set of fixed frames. To solve
the ambiguity of the amplitude dilation, a simple method is proposed.
The permutation indeterminacy is solved using an approach based on
the Hungarian algorithm that solves an Assignment Problem and an
algorithm of Dynamic Programming. To obtain the distances in the
Assignment Problem, a Kullback-Leibler divergence is adopted. The
results of the experiments, performed using both synthetic and benchmark
data, allows us to conclude that the approach presents a good
performance and permits to obtain a clear separation of the signals also
when they are more than two.
