Matrix-transformation-based method for underdetermined blind source separation

Abstract

The invention discloses a matrix-transformation-based method for underdetermined blind source separation. The method comprises the following steps of: gradually transforming a mixed matrix to obtain a transformed matrix, then acting the transformed matrix on an observation signal to gradually remove each source signal, and constructing multi-stage binary shielding templates by zero points generated in each observation signal to gradually separate the source signal. By the method, the requirement on sparsity of the source signal is reduced; aliasing of at most M-1 paths of source signals is prevented (wherein M is the number of sensors); source signals for forming each time frequency point can be clearly known; the underdetermined separation problem of music signals and noise signals is solved; the statistical property requirement on the source signal is low; the underdetermined separation problem of Gaussian signals and related signals is solved; processing stages are adjusted according to the requirement of separation precision; when the processing level is more, the separation result is better; the separation process is realized by aid of the matrix transformation; and the complexity is relatively low.

Description

technical field [0001] The invention relates to a method for blindly separating instantaneous mixed signals under the condition of underdetermination. The method can separate sparse, weakly sparse or correlated signals, and can be applied in the fields of signal processing, biomedicine and communication. Background technique [0002] Blind Source Separation (BSS) is a technology to determine a transformation based on the observed mixed data vector to restore the original signal or source. Typically, the observed data vector is the output of a set of sensors, where each sensor receives a different combination of source signals. The term "blind" has two meanings: a. the source signal cannot be observed; b. how the source signal mixes is unknown. When the number of source signals is more than the number of observation signals, it is an underdetermined blind separation (UBSS) problem, which is closer to practical applications, and it is also a technical difficulty of linear in...

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Problems solved by technology

The advantage of this method is that the traditional overdetermined separation technology can be used. The disadvantage is that the separation effect depends on the quality of the newly constructed observation signal. Once the signal is not well constructed, the separation quality will deteriorate.

The two-step method is actually an extension of the basis tracking method. It obtains the optimal solution by solving the linear equation and constraining the solution. Using the sparsity of the signal, it minimizes the 0 norm and then constrains the solution. The 0 norm is very easy to deal with. Inconvenient and especially sensitive to noise

In 1999, D. L. Donoho demonstrated the equivalence of using the smallest norm of 1 and the smallest norm of 0 under certain conditions. The norm of 1 is easier to deal with than the norm of 0. The optimal solution can be easily obtained by using linear programming, and the anti-noise performance Although it is better than the 0-norm criterion, the effect is still unsatisfactory. In addition, the algorithm is based on the sparsity of the signal in the time domain, so the general separation effect is very poor.

The time-frequency masking method was first proposed by Sam T. Roweis in 2000. In 2004, Yilmaz and Rickard combined the DUET algorithm to further develop the time-frequency masking algorithm. However, this type of method strictly requires that the source signal approximately satisfies W-dislocation orthogonality, harsh conditions

In 2005, Abrard proposed the TIFROM algorithm. This method requires that only one source signal exists in the observation signals of several adjacent time-frequency windows. The length of the time-frequency window is difficult to determine, and it is impossible to search for all single-source time-frequency frequency domain

This type of method is based on the sparsity condition of the time-frequency domain of the source signal, and designs a masking template equivalent to a time-frequency filter, and uses the template to extract the time-frequency points of each source signal one by one, thereby achieving separation. The disadvantage is that the requirements for signal sparsity are very strict, and the anti-noise performance is poor

These methods have a common defect that is based on the sparsity of the signal, which greatly limits their application.

In recent years, the problem of underdetermined blind source separation based on weak sparsity has gradually attracted the attention of scholars. In 2007, A. Aissa-El-Bey et al. used the subspace method to realize underdetermined blind source separation under weak sparse conditions , but this method requires a lot of computation and needs to be improved

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