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Source separation is a fundamental signal processing problem, that occurs in a wide range of applications. When a number of sources emit signals that mix together, and only the mixtures can be directly observed, the problem of estimating the original source signals is called a source separation problem.
In contrast to signal decomposition, where the goal is to decompose an observed signal into a sum of simpler signal for mathematical convenience, for signal compression, or other purposes, source separation is concerned with extracting underlying physically plausible signals of interest.
The following examples represent important and difficult source separation problems:
- Neuronal activities in the human brain can be measured non-invasively, for example by recording electrical activities along the scalp. This approach cannot capture the activity of single neurons; rather, the recordings are a mixtures of the activities of thousands or millions of neurons, as well as artifacts that arise from sources other than the brain such as heart beat and eye movements. To identify neuronal activities originating from a localized group of neurons is a source separation problem.
- The condition of an advanced system, such as a wind turbine or a chemical production facility, can be monitored by embedding a number of mechanical, chemical, acoustic, or other sensors. In a complex system, the sensors will in general register mixtures of signals that originate from multiple inter-related processes. To successfully separate these mixtures and ascribe them to physical sources is useful for optimizing system performance or pro-actively detecting faults.
- When audio is recorded in a natural environment, in addition to the signal of interest interfering sounds and background noises are often present. Moreover, the interaction between the different sounds can be very complex due to reverberation and non-stationarities that occur when sound sources move or change. Effective source separation methods that identify and isolate individual sound objects would be a benefit in many audio applications such as mobile phones and hearing aids.
Many different techniques have been developed for source separation problems in these and other application areas, often based on application-specific statistical signal models. The goal of this project is not to develop a practical solutions for a particular source separation problem; rather, we wish to advance the state of the art by developing general models and inference procedures that can be applied in a broad range of applications. General and practical source separation techniques can benefit a range of scientific and industrial applications, both as a technique for analyzing and understanding complex composite signals, and as a pre-processing step to remove noise and interferences before further analysis.
Single channel speech separation is an example of a difficult source separation problem. The voices of two speakers are mixed and recorded by a single microphone, and the task is to separate the two voices. Isolated recordings of the two speakers are used to train the speech separation system.
- Morten Arngren, Mikkel N. Schmidt, and Jan Larsen Unmixing of hyperspectral images using Bayesian nonnegative matrix factorization with volume prior Journal of Signal Processing Systems, 2010
- Morten Mørup and Mikkel N. Schmidt Transformation invariant sparse coding Machine Learning for Signal Processing, IEEE International Workshop on (MLSP), 2011
- Morten Mørup, Mikkel N. Schmidt, and Lars Kai Hansen Infinite multiple membership relational modeling for complex networks Machine Learning for Signal Processing, IEEE International Workshop on (MLSP), 2011
- Mikkel N. Schmidt and Morten Mørup Infinite non-negative matrix factorization European Signal Processing Conference (EUSIPCO), 2010
- Mikkel N. Schmidt Linearly constrained Bayesian matrix factorization for blind source separation Neural Information Processing Systems, Advances in (NIPS), 2009
- Morten Arngren, Mikkel N. Schmidt and Jan Larsen Bayesian nonnegative matrix factorization with volume prior for unmixing of hyperspectral images Machine Learning for Signal Processing, IEEE Workshop on (MLSP), 2009
This project is supported by the The Danish Council for Independent Research | Technology and Production Sciences grant number 274-09-0052.