nips nips2009 nips2009-17 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Paris Smaragdis, Madhusudana Shashanka, Bhiksha Raj
Abstract: In this paper we present an algorithm for separating mixed sounds from a monophonic recording. Our approach makes use of training data which allows us to learn representations of the types of sounds that compose the mixture. In contrast to popular methods that attempt to extract compact generalizable models for each sound from training data, we employ the training data itself as a representation of the sources in the mixture. We show that mixtures of known sounds can be described as sparse combinations of the training data itself, and in doing so produce significantly better separation results as compared to similar systems based on compact statistical models. Keywords: Example-Based Representation, Signal Separation, Sparse Models. 1
Reference: text
sentIndex sentText sentNum sentScore
1 edu Abstract In this paper we present an algorithm for separating mixed sounds from a monophonic recording. [sent-8, score-0.166]
2 Our approach makes use of training data which allows us to learn representations of the types of sounds that compose the mixture. [sent-9, score-0.164]
3 In contrast to popular methods that attempt to extract compact generalizable models for each sound from training data, we employ the training data itself as a representation of the sources in the mixture. [sent-10, score-0.454]
4 We show that mixtures of known sounds can be described as sparse combinations of the training data itself, and in doing so produce significantly better separation results as compared to similar systems based on compact statistical models. [sent-11, score-0.394]
5 1 Introduction This paper deals with the problem of single-channel signal separation – separating out signals from individual sources in a mixed recording. [sent-13, score-0.451]
6 As of recently, a popular statistical approach has been to obtain compact characterizations of individual sources and employ them to identify and extract their counterpart components from mixture signals. [sent-14, score-0.404]
7 Statistical characterizations may include codebooks [1], Gaussian mixture densities [2], HMMs [3], independent components [4, 5], sparse dictionaries [6], non-negative decompositions [7–9] and latent variable models [10, 11]. [sent-15, score-0.372]
8 Separation is achieved by abstracting components from the mixed signal that conform to the statistical characterizations of the individual sources. [sent-17, score-0.163]
9 The key here is the specific statistical model employed – the more effectively it captures the specific characteristics of the signal sources, the better the separation that may be achieved. [sent-18, score-0.235]
10 This has been the basis of several example-based characterizations of a data source, such as nearest-neighbor, K-nearest neighbor, Parzen-window based models of source distributions etc. [sent-20, score-0.536]
11 Here, we use the same idea to develop a monaural source-separation algorithm that directly uses samples from the training data to represent the sources in a mixture. [sent-21, score-0.233]
12 Identifying the proper samples from the training data that best approximate a sample of the mixture is of course a hard combinatorial problem, which can be computationally demanding. [sent-23, score-0.27]
13 We additionally show that this approach results in 1 source estimates which are guaranteed to lie on the source manifold, as opposed to trainedbasis approaches which can produce arbitrary outputs that will not necessarily be plausible source estimates. [sent-25, score-1.541]
14 Experimental evaluations show that this approach results in separated signals that exhibit significantly higher performance metrics as compared to conceptually similar techniques which are based on various types of combinations of generalizable bases representing the sources. [sent-26, score-0.401]
15 1 The Basic Model Given a magnitude spectrogram of a single source, each spectral frame is modeled as a histogram of repeated draws from a multinomial distribution over the frequency bins. [sent-29, score-0.344]
16 At a given time frame t, consider a random process characterized by the probability Pt (f ) of drawing frequency f in a given draw. [sent-30, score-0.15]
17 The model assumes that Pt (f ) is comprised of bases indexed by a latent variable z. [sent-32, score-0.266]
18 We use this model to learn the source-specific bases given by Pt (f |z) as done in [10, 11]. [sent-35, score-0.226]
19 Now let the matrix VF ×T of entries vf t represent the magnitude spectrogram of the mixture sound and vt represent time frame t (the t-th column vector of matrix V). [sent-37, score-0.665]
20 Each mixture spectral frame is again modeled as a histogram of repeated draws, from the multinomial distributions corresponding to every source. [sent-38, score-0.337]
21 We can assume that for each source in the mixture we have an already trained model in the form of basis vectors Ps (f |z). [sent-40, score-0.657]
22 These bases will represent a dictionary of spectra that best describe each source. [sent-41, score-0.334]
23 Armed with this knowledge we can decompose a new mixture of these known sources in terms of the contributions of the dictionaries for each source. [sent-42, score-0.368]
24 The triangles denote the position of basis functions for two source classes. [sent-44, score-0.476]
25 The square is an instance of a mixture of the two sources. [sent-45, score-0.181]
26 The mixture point is not within the convex hull which covers either source, but it is within the convex hull defined by all the bases combined. [sent-46, score-0.783]
27 These reconstructions will approximate the magnitude spectrogram of each source in the mixture. [sent-47, score-0.634]
28 Once we obtain these reconstructions we can use them to modulate the original phase spectrogram of the mixture and obtain the time-series representation of the sources. [sent-48, score-0.381]
29 Each basis vector and the mixture input will lie in a F − 1 dimensional simplex (due to the fact that these quantities are normalized to sum to unity). [sent-50, score-0.302]
30 Each source’s basis set will define a convex hull within which any point can be approximated using these bases. [sent-51, score-0.249]
31 Assuming that the training data is accurate, all potential inputs from that source should lie in that area. [sent-52, score-0.602]
32 The union of all the source bases will define a larger space in which a mixture input will be inside. [sent-53, score-0.841]
33 Any mixture point can then be approximated as a weighted sum of multiple bases from both sources. [sent-54, score-0.426]
34 2 Using Training Data Directly as a Dictionary In this paper, we would like to explain the mixture frame from the training spectral frames instead of using a smaller set of learned bases. [sent-57, score-0.499]
35 The secondary rationale behind this operation is based on the observation that the points defined by the convex hull of a source’s model, do not necessarily all fall on that source’s manifold. [sent-61, score-0.188]
36 In both of these plots the sources exhibit a clear structure. [sent-63, score-0.195]
37 In the left plot both sources appear in a circular pattern, and in the right plot in a spiral form. [sent-64, score-0.247]
38 As shown in [12], learning a set of bases that explains these sources results in defining a convex hull that surrounds the training data. [sent-65, score-0.647]
39 Under this model potential source estimates can now lie anywhere inside these hulls. [sent-66, score-0.541]
40 Using trainedbasis models, if we decompose the mixture points in these figures we obtain two source estimates which do not lie in the same manifold as the original sources. [sent-67, score-0.804]
41 Although the input was adequately approximated, there is no guarantee that the extracted sources are indeed appropriate outcomes for their sound class. [sent-68, score-0.212]
42 In order to address this problem and to also provide a richer dictionary for the source reconstructions, we will make direct use of the training data in order to explain the mixture, and bypass the basis representation as an abstraction. [sent-69, score-0.673]
43 To do so we will use each frame of the (s) spectrograms of the training sequences as the bases Ps (f |z). [sent-70, score-0.494]
44 More specifically, let WF ×T (s) (s) be the training spectrogram from source s and let wt represent the time frame t from the spectrogram. [sent-71, score-0.79]
45 In this case, the latent variable z for source s takes T (s) values, and the z-th basis function will be given by the (normalized) z-th column vector of W(s) . [sent-72, score-0.516]
46 In both plots the training data for each source are denoted by △ and ▽, and the mixture sample by . [sent-74, score-0.734]
47 The learned bases of each source are the vertices of the two dashed convex hulls that enclose each class. [sent-75, score-0.699]
48 The source estimates and the approximation of the mixture are denoted by ×, + and . [sent-76, score-0.664]
49 In the left case the two sources lie on two overlapping circular areas, the source estimates however lie outside these areas. [sent-77, score-0.787]
50 The recovered sources lie very closely on the competing source’s area, thereby providing a highly inappropriate decomposition. [sent-79, score-0.223]
51 Although the mixture was well approximated in both cases, the estimated sources were poor representations of their classes. [sent-80, score-0.344]
52 With the above model we would ideally want to use one dictionary element per source at any point in time. [sent-81, score-0.542]
53 Doing so will ensure that the outputs would lie on the source manifold, and also offset any issues of potential overcompleteness. [sent-82, score-0.513]
54 One way to ensure this is to perform a reconstruction such that we only use one element of each source at any time, much akin to a nearest-neighbor model, albeit in an additive setting. [sent-83, score-0.472]
55 The intuition is that at any given point in time, the mixture frame is explained by very few active elements from the training data. [sent-85, score-0.42]
56 In other words, we need the mixture weight distributions and the speaker priors to be sparse at every time instant. [sent-86, score-0.364]
57 We would like to minimize the entropies of both the speaker dependent mixture weight distributions (given by Pt (z|s)) and the source priors (given by Pt (s)) at every frame. [sent-91, score-0.77]
58 Thus, reducing the entropy of the joint distribution Pt (z, s) is equivalent to reducing the conditional entropy of the source dependent mixture weights and the entropy of the source priors. [sent-94, score-1.186]
59 Since the dictionary is already known and is given by the normalized spectral frames from source training spectrograms, the parameter to be estimated is given by Pt (z, s). [sent-95, score-0.733]
60 We impose an entropic prior distribution on Pt (z, s) 4 Source A Source B Mixture Estimate for A Estimate for B Approximation of mixture Source A Source B Mixture Estimate for A Estimate for B Approximation of mixture Figure 3: Using a sparse reconstruction on the data in figure 2. [sent-100, score-0.528]
61 Note how in contrast to that figure the source estimates are now identified as training data points, and are thus plausible solutions. [sent-101, score-0.601]
62 The approximation of the mixture is the nearest point of the line connecting the two source estimates, to the actual mixture input. [sent-102, score-0.837]
63 Note that the proper solution is the one that results in such a line that is as close as possible to the mixture point, and not one that is defined by two training points close to the mixture. [sent-103, score-0.27]
64 Once Pt (z, s) is estimated, the reconstruction of source s can be computed as z∈{zs } (s) vf t = ˆ s Ps (f |z)Pt (z, s) z∈{zs } Ps (f |z)Pt (z, s) vf t Now let us consider how this problem resolves the issues presented in figure 2. [sent-110, score-0.805]
65 In both plots we see that the source reconstructions lie on a training point, thereby being a plausible source estimate. [sent-114, score-1.176]
66 The approximation of the mixture is not as exact as before, since now it has to lie on the line connecting the two active source elements. [sent-115, score-0.738]
67 This is not however an issue of concern since in practice the approximation is always good enough, and the guarantee of a plausible source estimate is more valuable than the exact approximation of the mixture. [sent-116, score-0.568]
68 In these approaches the priors are imposed on the mixture weights and thus are not as effective for this particular task since they still suffer from the symptoms of learned-basis models. [sent-118, score-0.207]
69 The top plots show the input waveforms, and the bottom plots shows the estimated weights multiplied with the source priors. [sent-121, score-0.494]
70 The sources were sampled as 16 kHz, we used 64 ms windows for the spectrogram computation, and an overlap of 32 ms. [sent-125, score-0.284]
71 The training data was around 25 sec worth of speech for each speaker, and the testing mixture was about 3 sec long. [sent-127, score-0.445]
72 We evaluated the separation performance using the metrics provided in [17]. [sent-128, score-0.225]
73 The first is a measure of how well we suppress the interfering speaker, whereas the other two provide us with a sense of how much the extracted source is corrupted due to the separation process. [sent-130, score-0.597]
74 The first experiment we perform is on a mixture for which the training data includes its isolated constituent sentences. [sent-137, score-0.27]
75 The primary observation from this experiment is that the more bases we use the better the results get. [sent-146, score-0.226]
76 01 β 0 5 10 20 40 80 Train 320 160 Bases Figure 5: Average separation performance metrics for oracle cases, as dependent on the choice of different number of elements in the speaker’s dictionary, and different choices of the entropic prior parameter β. [sent-166, score-0.388]
77 The basis row labeled as “Train” is the case where we use all the training data as a basis set. [sent-168, score-0.173]
78 01 β 0 5 10 20 40 80 Train 320 160 Bases Figure 6: Average separation performance metrics for real-world cases, as dependent on the choice of different number of elements in the speaker’s dictionary, and different choices of the entropic prior parameter β. [sent-187, score-0.325]
79 2 Results on Realistic Situations Let us now consider the more realistic case where the mixture data is different from the training set. [sent-191, score-0.292]
80 The input mixture has to be reconstructed using approximate samples. [sent-193, score-0.181]
81 We do not obtain such high numbers in performance as in the oracle case, but we also see a stronger trend in favor of sparsity and the use of all the training data as a dictionary. [sent-195, score-0.228]
82 We can clearly see that in all metrics using all the training data significantly outperforms trained-basis models. [sent-197, score-0.151]
83 The use of sparsity ensures that the output is a plausible speech signal devoid of artifacts like distortion and musical noise. [sent-204, score-0.368]
84 dB 15 10 5 SDR 0 0% SIR 20% SAR 40% 60% 70% 80% Percentage of discarded training frames 90% 95% Figure 8: Effect of discarding low energy training frames. [sent-214, score-0.323]
85 The horizontal axis denotes the percentage of training frames that have been discarded. [sent-215, score-0.162]
86 In order to address this concern we show that the size of the training data can be easily pruned down to a size comparable to trainedbasis models and still outperform them. [sent-219, score-0.17]
87 Since sound signals, especially speech, tend to have a considerable amount of short-term pauses and regions of silence, we can use an energy threshold to in order to select the loudest frames of the training spectrogram as bases. [sent-220, score-0.406]
88 In figure 8 we show how the separation performance metrics are influenced as we increasingly remove bases which lie under various energy percentiles. [sent-221, score-0.566]
89 It is clear that even after discarding up to at least 70% of the lowest energy training frames the performance is still approximately the same. [sent-222, score-0.234]
90 Overall computations for a single mixture took roughly 4 sec when not using the sparsity prior, 14 sec when using the sparsity prior (primarily due to slow computation of Lambert’s function), and dropped down to 5 sec when using the 30% highest energy frames from the training data. [sent-227, score-0.684]
91 4 Conclusion In this paper we present a new approach to solving the monophonic source separation problem. [sent-228, score-0.637]
92 In order to do so we present a sparse learning algorithm which can efficiently solve this problem, and also guarantees that the returned source estimates are plausible given the training data. [sent-230, score-0.649]
93 We provide experiments that show how this approach is influenced by the use of varying sparsity constraints and training data selection. [sent-231, score-0.165]
94 Roweis, One microphone source separation, in Advances in Neural Information Processing Systems, 2001. [sent-235, score-0.434]
95 Gopinath, Super-human multitalker speech recognition: The IBM 2006 speech separation challenge system, in International Conference on Spoken Language Processing (INTERSPEECH), 2006, pp. [sent-246, score-0.309]
96 Separation of mixed audio sources by independent subspace analysis, in Proceedings of the International Conference of Computer Music, 2000. [sent-254, score-0.207]
97 Gribonval, Non negative sparse representation for wiener based source separation with a single sensor, in Acoustics, Speech, and Signal Processing, IEEE International Conference on, 2003, pp. [sent-272, score-0.645]
98 Olsson, Single-channel speech separation using sparse nonnegative matrix factorization, in International Conference on Spoken Language Processing (INTERSPEECH), 2006. [sent-278, score-0.284]
99 Virtanen, Sound source separation using sparse coding with temporal continuity objective, in International Computer Music Conference, ICMC, 2003. [sent-280, score-0.645]
100 Using unsupervised learning of a finite Dirichlet mixture model to improve pattern recognition applications, Pattern Recognition Letters, Volume 26, Issue 12, September 2005. [sent-324, score-0.181]
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