# A compressive sensing based compressed neural network for sound source localization

TL;DR: A family of new algorithms for compression of NNs is presented based on Compressive Sampling (CS) theory, which makes it possible to find a sparse structure for NNs, and then the designed neural network is compressed by using CS.

Abstract: Microphone arrays are today employed to specify the sound source locations in numerous real time applications such as speech processing in large rooms or acoustic echo cancellation. Signal sources may exist in the near field or far field with respect to the microphones. Current Neural Networks (NNs) based source localization approaches assume far field narrowband sources. One of the important limitations of these NN-based approaches is making balance between computational complexity and the development of NNs; an architecture that is too large or too small will affect the performance in terms of generalization and computational cost. In the previous analysis, saliency subject has been employed to determine the most suitable structure, however, it is time-consuming and the performance is not robust. In this paper, a family of new algorithms for compression of NNs is presented based on Compressive Sampling (CS) theory. The proposed framework makes it possible to find a sparse structure for NNs, and then the designed neural network is compressed by using CS. The key difference between our algorithm and the state-of-the-art techniques is that the mapping is continuously done using the most effective features; therefore, the proposed method has a fast convergence. The empirical work demonstrates that the proposed algorithm is an effective alternative to traditional methods in terms of accuracy and computational complexity.

## Summary (2 min read)

### INTRODUCTION

- In the sound source localization techniques, location of the source has to be estimated automatically by calculating the direction of the received signal [1] .
- Feature extraction is the process of selection of the useful data for estimation of DOA.
- The important key insight is the use of the instantaneous crosspower spectrum at each pair of sensors.
- After this step the authors have compressed the neural network that is designed with these feature vectors.
- The next section presents a review of techniques for sound source localization.

### II. SOUND SOURCE LOCALIZATION

- The assumption of far field sources remains true while the distance between source and reference microphone is larger than [2] fig.
- And D is the microphone array length.
- So, the time delay of the received signal between the reference microphone and the − ℎ microphone would be [15] : EQUATION.
- Therefore, is the amount of time that the signal traverses the distance between any two neighboring microphones, Fig. 1 EQUATION where, r is the distance between source and the first microphone [15] .

### III. FEATURE SELECTION

- The aim of this section is to compute the feature vectors from the array data and use the MLP (Multi Layer Perceptron) approximation property to map the feature vectors to the corresponding DOA, as shown in Fig. 3 [6] .
- The authors summarized their algorithm for computing a real-valued feature vector of length (2( − 1) + 1) , for dominant frequencies and M sensors below: Preprocessing algorithm for computing a real-valued feature vector: 1. Calculate the -point FFT of the signal at each sensor.
- In conclusion, their purpose is to design a neural network with least number of hidden neurons (or weights) that has the minimum increase in error given by‖ − ‖.
- This problem is equivalent to finding which most of its rows are zeros.
- Comparing these equations with (7) the authors can conclude that these minimization problems can be written as CS problems.

### VI. RESULTS AND DISCUSSION

- As mentioned before, assuming that the received speech signals are modeled with 10 dominant frequencies, the authors have trained a two layer Perceptron neural network with 128 neurons in hidden layer and trained it with feature vectors that are obtained with CS from the cross-power spectrum of the received microphone signals.
- After computing network weights the authors tried to compress network with their algorithms.
- With these outputs the authors can infer that CS algorithms are faster than other algorithms and have smaller error in compare with other algorithms.
- This means that, According to the number of Measurement vectors, the algorithm that uses single-measurement vector (SMV) is faster than another algorithm that uses multiple-measurement vector (MMV) but its achieve error is not smaller.

### VII. CONCLUSION

- Particularly, using the pursuit and greedy methods in CS, a compressing methods for NNs has been presented.
- The key difference between their algorithm and previous techniques is that the authors focus on the remaining elements of neural networks; their method has a quick convergence.
- The simulation results, demonstrates that their algorithm is an effective alternative to traditional methods in terms of accuracy and computational complexity.
- Results revealed this fact that the proposed algorithm could decrease the computational complexity while the performance is increased.

Did you find this useful? Give us your feedback

...read more

##### Citations

25 citations

^{1}

14 citations

### Cites background or methods or result from "A compressive sensing based compres..."

...In next step, to evaluate the proposed sound source localization system, we have compared its performance with those for two of the previously-reported CS-based target localization algorithms, namely DTL [8] and CSNN [9]....

[...]

...The Compressive Sensing-based Neural Network (CSNN) method [9] employs a neural network for the calculation of spectral feature vectors in each microphone....

[...]

...In [9], authors have tried to reduce computational complexity by employing a feature extraction process that selects useful data for estimation of DOA....

[...]

...Comparison between the localization performance of the proposed system, CSNN [9] and DTL algorithm [8] in the case of two sound sources and two microphones....

[...]

9 citations

### Cites methods from "A compressive sensing based compres..."

...Localization performance of (a) the proposed scheme, (b) DTL algorithm in [10], and (c) CSNN algorithm in [23], for three patients and six receiver nodes....

[...]

...We compare the performance of the CS-2FFT-based scheme with that of two CS-based target localization algorithms, namely DTL [10] and CS-based neural network (CSNN) [23]....

[...]

...EML algorithms in [10], [23], and [24] in the case of three patients and six receiver nodes....

[...]

...pared to other classical positioning algorithms such as the EML, DTL, and CSNN approaches in [10] and [23]....

[...]

##### References

13,375 citations

[...]

^{1}

3,354 citations

### "A compressive sensing based compres..." refers methods in this paper

...Several iterative algorithms have been proposed to solve this min imization problem (Greedy Algorithms such as Orthogonal Matching Pursuit (OMP) or Matching Pursuit (MP) and Non-convex local optimizat ion like FOCUSS algorithm[16]....

[...]

...All of the traditional algorithms, such as Optimal Brain Damage (OBD)[16], Optimal Brain Surgeon (OBS)[17], and Magnitude-based pruning (MAG)[ 18], Skeletonization (SKEL)[6], non-contributing units (NC)[7] and Extended Fourier Amplitude Sensitiv ity Test (EFAST)[13], are available in SNNS (CSS1 is name of algorithm that uses SMV for sparse representation and CSS2 is another technique that uses MMV for sparserepresentatio n)....

[...]

1,592 citations

### "A compressive sensing based compres..." refers background in this paper

...In the sound source localization techniques, location of the source has to be estimated automatically by calculating the direction of the received signal [1]....

[...]

1,565 citations

### "A compressive sensing based compres..." refers background in this paper

...Neural network based techniques have been proposed to overcome the computational complexity problem by exploiting their massive parallelism [3,4]....

[...]

647 citations