• ETRI Journal
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• 제36권1호
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• pp.167-170
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• 2014

In this letter, we propose an unsupervised framework for speech noise reduction based on the recent development of low-rank and sparse matrix decomposition. The proposed framework directly separates the speech signal from noisy speech by decomposing the noisy speech spectrogram into three submatrices: the noise structure matrix, the clean speech structure matrix, and the residual noise matrix. Evaluations on the Noisex-92 dataset show that the proposed method achieves a signal-to-distortion ratio approximately 2.48 dB and 3.23 dB higher than that of the robust principal component analysis method and the non-negative matrix factorization method, respectively, when the input SNR is -5 dB.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권12호
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• pp.6043-6062
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• 2019

Low-rank matrix decomposition has shown its capability in many applications such as image in-painting, de-noising, background reconstruction and defect detection etc. In this paper, we consider the texture background of rail track images and the sparse foreground of the defects to construct a low-rank matrix decomposition model with block sparsity for defect inspection of rail tracks, which jointly minimizes the nuclear norm and the 2-1 norm. Similar to ADM, an alternative method is proposed in this study to solve the optimization problem. After image decomposition, the defect areas in the resulting low-rank image will form dark stripes that horizontally cross the entire image, indicating the preciselocations of the defects. Finally, a two-stage defect extraction method is proposed to locate the defect areas. The experimental results of the two datasets show that our algorithm achieved better performance compared with other methods.

• ETRI Journal
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• 제39권1호
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• pp.21-29
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• 2017

This paper addresses the problem of unsupervised speech separation based on robust non-negative matrix factorization (RNMF) with ${\beta}$-divergence, when neither speech nor noise training data is available beforehand. We propose a robust version of non-negative matrix factorization, inspired by the recently developed sparse and low-rank decomposition, in which the data matrix is decomposed into the sum of a low-rank matrix and a sparse matrix. Efficient multiplicative update rules to minimize the ${\beta}$-divergence-based cost function are derived. A convolutional extension of the proposed algorithm is also proposed, which considers the time dependency of the non-negative noise bases. Experimental speech separation results show that the proposed convolutional RNMF successfully separates the repeating time-varying spectral structures from the magnitude spectrum of the mixture, and does so without any prior training.

• 대한전자공학회논문지SP
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• 제46권5호
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• pp.15-24
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• 2009

Compressed sensing은 소수의 선형 관측으로부터 sparse 신호를 복원하는 문제를 언급하고 있다. 최근 벡터 경우에서의 성공적인 연구 결과가 행렬의 경우로 확장되었다. Low-rank 행렬의 compressed sensing은 ill-posed inverse problem을 low-rank 정보를 이용하여 해결한다. 본 문제는 rank 최소화 혹은 low-rank 근사의 형태로 나타내질 수 있다. 본 논문에서는 최근 제안된 여러 가지 효율적인 알고리즘에 대한 survey를 제공한다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권6호
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• pp.2634-2648
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• 2020

In this paper, an adaptive sparse singular value decomposition (ASSVD) algorithm is proposed to estimate the signal matrix when only one data matrix is observed and there is high dimensional white noise, in which we assume that the signal matrix is low-rank and has sparse singular vectors, i.e. it is a simultaneously low-rank and sparse matrix. It is a structured matrix since the non-zero entries are confined on some small blocks. The proposed algorithm estimates the singular values and vectors separable by exploring the structure of singular vectors, in which the recent developments in Random Matrix Theory known as anisotropic Marchenko-Pastur law are used. And then we prove that when the signal is strong in the sense that the signal to noise ratio is above some threshold, our estimator is consistent and outperforms over many state-of-the-art algorithms. Moreover, our estimator is adaptive to the data set and does not require the variance of the noise to be known or estimated. Numerical simulations indicate that ASSVD still works well when the signal matrix is not very sparse.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권5호
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• pp.2141-2155
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• 2020

In order to meet the requirements of background change, illumination variation, moving shadow interference and high accuracy in object detection of moving camera, and strive for real-time and high efficiency, this paper presents an object detection algorithm based on sparse approximation recursion and sparse coding migration in subspace. First, low-rank sparse decomposition is used to reduce the dimension of the data. Combining with dictionary sparse representation, the computational model is established by the recursive formula of sparse approximation with the video sequences taken as subspace sets. And the moving object is calculated by the background difference method, which effectively reduces the computational complexity and running time. According to the idea of sparse coding migration, the above operations are carried out in the down-sampling space to further reduce the requirements of computational complexity and memory storage, and this will be adapt to multi-scale target objects and overcome the impact of large anomaly areas. Finally, experiments are carried out on VDAO datasets containing 59 sets of videos. The experimental results show that the algorithm can detect moving object effectively in the moving camera with uniform speed, not only in terms of low computational complexity but also in terms of low storage requirements, so that our proposed algorithm is suitable for detection systems with high real-time requirements.