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The application of sparse approximation techniques faces two main problems: (i) algorithms for performing sparse decomposition and their performance analysis and (ii) dictionary composition methods.
To the best of our knowledge, the application of sparse VSS-NLMS to simultaneously exploit the channel sparsity and control the step size has not been reported in the literature.
Although there are some pioneering studies carried out in the late nineties, e.g., [20, 21], the application of sparse representation to direction finding has gained noticeable interest during the last decade.
The proposed approach greatly improves the imaging quality as compared to Fourier-based reconstruction, whereas it exhibits significant reduction of the computational complexity when compared to direct application of sparse reconstruction techniques.
The successful application of sparse representation-based classification (SRC) in image recognition inspires us to use SRC on the weighted dictionary and test image to perform the final identification.
Performance analysis and simulation results reveal that the proposed method has a much lower computational complexity and a similar statistical performance compared with the well-known l 1-SVD algorithm, which has several advantages over conventional direction finding techniques due to the application of sparse signal reconstruction.
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Many of the articles in this special issue are related to applications of sparse signal processing.
As such, this tutorial has provided a route for new applications of sparse signal processing to emerge, which can potentially reduce computational complexity and improve performance quality.
Other applications of sparse signal processing in the speaker recognition area include a study of GMM mean shifted supervectors using learned and discriminatively learned dictionaries [44] and a study employing feature vectors as the base elements in the dictionary [45].
In fact, the multiple measurement vectors (MMV) problem is encountered in many applications of sparse signal representation such as array processing [1, 6 11], magne-toencephalography [1], nonparametric spectrum analysis of time series [17], equalization of sparse communication channels [18] and so on.
The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, component analysis, and multipath channel estimation.
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