Low-rank Sparse Matrix Decomposition Research Articles

Speech Enhancement Based on Constrained Low-rank Sparse Matrix Decomposition Integrated with Temporal Continuity Regularisation

Speech enhancement in strong noise condition is a challenging problem. Low-rank and sparse matrix decomposition (LSMD) theory has been applied to speech enhancement recently and good performance was obtained. Existing LSMD algorithms consider each frame as an individual observation. However, real-world speeches usually have a temporal structure, and their acoustic characteristics vary slowly as a function of time. In this paper, we propose a temporal continuity constrained low-rank sparse matrix decomposition (TCCLSMD) based speech enhancement method. In this method, speech separation is formulated as a TCCLSMD problem and temporal continuity constraints are imposed in the LSMD process. We develop an alternative optimisation algorithm for noisy spectrogram decomposition. By means of TCCLSMD, the recovery speech spectrogram is more consistent with the structure of the clean speech spectrogram, and it can lead to more stable and reasonable results than the existing LSMD algorithm. Experiments with various types of noises show the proposed algorithm can achieve a better performance than traditional speech enhancement algorithms, in terms of yielding less residual noise and lower speech distortion.

Non-contact heart rate estimation based on singular spectrum component reconstruction using low-rank matrix and autocorrelation.

The remote photoplethysmography (rPPG) based on cameras, a technology for extracting pulse wave from videos, has been proved to be an effective heart rate (HR) monitoring method and has great potential in many fields; such as health monitoring. However, the change of facial color intensity caused by cardiovascular activities is weak. Environmental illumination changes and subjects' facial movements will produce irregular noise in rPPG signals, resulting in distortion of heart rate pulse signals and affecting the accuracy of heart rate measurement. Given the irregular noises such as motion artifacts and illumination changes in rPPG signals, this paper proposed a new method named LA-SSA. It combines low-rank sparse matrix decomposition and autocorrelation function with singular spectrum analysis (SSA). The low-rank sparse matrix decomposition is employed to globally optimize the components of the rPPG signal obtained by SSA, and some irregular noise is removed. Then, the autocorrelation function is used to optimize the global optimization results locally. The periodic components related to the heartbeat signal are selected, and the denoised rPPG signal is obtained by weighted reconstruction with a singular value ratio. The experiment using UBFC-RPPG and PURE database is performed to assess the performance of the method proposed in this paper. The average absolute error was 1.37 bpm, the 95% confidence interval was -7.56 bpm to 6.45 bpm, and the Pearson correlation coefficient was 98%, superior to most existing video-based heart rate extraction methods. Experimental results show that the proposed method can estimate HR effectively.

Acquisition and Enhancement of Remote Human Vocal Signals Based on Doppler Radar

In order to achieve remote voice acquisition, a 9.75-GHz microwave Doppler radar with a high-sensitivity coherent homodyne demodulator is used to detect voice signals. However, the combined noise sources, including background noise and shock noise, are included in the Doppler audio radar-captured voice, which seriously damages the quality of speech. In the current work, a multi-stage enhancement method is used to enhance Doppler audio radar-captured voice. The first stage is dictionary learning, which uses the K-singular value decomposition algorithm to train speech and noise dictionaries. The noise training data come from the Doppler audio radar-captured shock noise signals under the influence of different relative motion modulations. The second stage generates a position mask of the shock noise. The third stage is the removal of background noise and shock noise. The removal of background noise adopts our proposed constrained low-rank sparse matrix decomposition algorithm based on power spectral density. The final speech spectrum with shock noise removed is obtained through sparse restoration using the LARC algorithm. The experimental results show that the 9.75-GHz Doppler audio radar can effectively acquire human voice signals, and the proposed multi-stage enhancement method can effectively remove the background noise and shock noise in the radar speech, thereby improving the quality of the audio radar voice. The obtained results imply the potential to implement practical Doppler audio radar systems for human voice signal acquisition.

Fast and robust motion averaging via angle constraints of multi‐view range scans

The motion averaging problem arises when recovering the motions for a set of scans in three-dimensional (3D) reconstruction. Motion averaging is taken as an optimisation problem, whose solution can be obtained via matrix decomposition in principal component analysis. The latest motion averaging methods utilize the Cauchy kernel function or overlap rate to construct the weighted matrix in the cost function, yielding weighted low-rank sparse matrix decomposition solutions. Nevertheless, the over-reliance on the initial value and high computational complexity remain two major problems. Here, we aim to improve the motion averaging performance via a fast and robust method based on the angle constraints of multiple scans. The additional term representing the angle constraint is added into the original cost function. By doing this, two benefits are facilitated: 1) the iteration times for the optimisation process are reduced; and 2) it effectively mitigates the over-reliance on the initial value and thus caters for outliers and random noise of initial motions. Compared with state-of-the-art motion averaging methods, it is indicated that the proposed method is more efficient and robust for numerical simulations of using both simulated motions and real 3D scanning data, given a large range of angle constraint values.

Adaptive weighted motion averaging with low-rank sparse for robust multi-view registration

Motion averaging has recently been introduced as an effective means to tackle the registration of multi-view range scans. This approach can view parts of pair-wise motions with high reliability as an input to estimate the global motions for a multi-view registration. However, reliable pair-wise motions are not easy to confirm in most practical applications without prior knowledge. In this paper, we propose an adaptive low-rank sparse (LRS) weighted motion averaging method for a robust and accurate multi-view registration, which can directly reconstruct high-quality 3D shape models from a set of unordered range scans. Specifically, we first introduce LRS matrix decomposition to automatically compute the initial global motions. The LRS matrix decomposition can recover the initial global models through the full exploration of a set of pair-wise motions. Subsequently, we extend the motion averaging with an adaptive weight computation by developing an optimization strategy using the Lagrange multiplier method, which can adaptively compute the weights of the reliability for each pair-wise relative motion. Accordingly, the proposed method can recover accurate and robust global motions in a set of iterations through weighted motion averaging. Experimental results on several public datasets demonstrate the excellent performance of the proposed method in comparison with state-of-the-art multi-view registration and 3D scene reconstruction.

Interactive foreground segmentation and shape reconstruction from RGBD images

Three dimensional shape reconstruction of objects in complex scenes has important applications in intelligent transportation systems and medical image processing. This paper aims to segment and locate the foreground object through the interactive segmentation with multiple cues including saliency, depth and color. The desired foreground object is obtained by using the foreground and background information provided by saliency map and heatmap. Then, the multi-view point cloud information of the foreground object is recovered by depth information, and a multi-view point cloud registration algorithm based on color information is proposed. The three-dimensional shape model of the object is reconstructed through a multi-view point cloud registration algorithm combined with motion averaging and low-rank sparse matrix decomposition. The validity of the framework is empirically assessed with comparative experiments.

Multi-View Laser Point Cloud Global Registration for a Single Object.

Global registration is an important step in the three-dimensional reconstruction of multi-view laser point clouds for moving objects, but the severe noise, density variation, and overlap ratio between multi-view laser point clouds present significant challenges to global registration. In this paper, a multi-view laser point cloud global registration method based on low-rank sparse decomposition is proposed. Firstly, the spatial distribution features of point clouds were extracted by spatial rasterization to realize loop-closure detection, and the corresponding weight matrix was established according to the similarities of spatial distribution features. The accuracy of adjacent registration transformation was evaluated, and the robustness of low-rank sparse matrix decomposition was enhanced. Then, the objective function that satisfies the global optimization condition was constructed, which prevented the solution space compression generated by the column-orthogonal hypothesis of the matrix. The objective function was solved by the Augmented Lagrange method, and the iterative termination condition was designed according to the prior conditions of single-object global registration. The simulation analysis shows that the proposed method was robust with a wide range of parameters, and the accuracy of loop-closure detection was over 90%. When the pairwise registration error was below 0.1 rad, the proposed method performed better than the three compared methods, and the global registration accuracy was better than 0.05 rad. Finally, the global registration results of real point cloud experiments further proved the validity and stability of the proposed method.

Regularized sparse decomposition model for speech enhancement via convex distortion measure

An important stage in speech enhancement is to estimate noise signal which is a difficult task in non-stationary and low signal-to-noise conditions. This paper presents an iterative speech enhancement approach which requires no prior knowledge of noise and is based on low-rank sparse matrix decomposition using Gammatone filterbank and convex distortion measure. To estimate noise and speech, the noisy speech is decomposed into low-rank noise and sparse-speech parts by enforcing sparsity regularization. The exact distribution of noise signals and noise estimator is not required in this approach. The experimental results demonstrate that our approach outperforms competing methods and yields better overall speech quality and intelligibility. Moreover, composite objective measure reinforced a better performance in terms of residual noise and speech distortion in adverse noisy conditions. The time-varying spectral analysis validates significant reduction of the background noise.

Exemplar-based low-rank matrix decomposition for data clustering

Today, digital data is accumulated at a faster than ever speed in science, engineering, biomedicine, and real-world sensing. The ubiquitous phenomenon of massive data and sparse information imposes considerable challenges in data mining research. In this paper, we propose a theoretical framework, Exemplar-based low-rank sparse matrix decomposition (EMD), to cluster large-scale datasets. Capitalizing on recent advances in matrix approximation and decomposition, EMD can partition datasets with large dimensions and scalable sizes efficiently. Specifically, given a data matrix, EMD first computes a representative data subspace and a near-optimal low-rank approximation. Then, the cluster centroids and indicators are obtained through matrix decomposition, in which we require that the cluster centroids lie within the representative data subspace. By selecting the representative exemplars, we obtain a compact "sketch"of the data. This makes the clustering highly efficient and robust to noise. In addition, the clustering results are sparse and easy for interpretation. From a theoretical perspective, we prove the correctness and convergence of the EMD algorithm, and provide detailed analysis on its efficiency, including running time and spatial requirements. Through extensive experiments performed on both synthetic and real datasets, we demonstrate the performance of EMD for clustering large-scale data.