Vitiligo lesion identification is essential for quantifying disease severity, monitoring disease progression and assessing treatment response, particularly for objective quantification. However, segmenting vitiligo lesions from clinical images is challenging due to indistinct borders, complex backgrounds, and image artifacts. The difficulty increases when handling small and sparse lesions in global-view photographs. Fully supervised segmentation models require extensively annotated datasets, making the labelling process time-consuming and costly. To address these challenges, we propose GloW-VSNet, a scribble-guided weakly supervised segmentation method for global-view vitiligo detection. Our approach integrates differentiable feature clustering with a spatial attention mechanism based on physician-provided scribble annotations, enabling the model to focus on relevant spatial features and improve segmentation accuracy despite background noise and artifacts. Additionally, we introduce spatial continuity optimization to preserve the natural distribution of vitiligo, enhancing segmentation consistency while reducing computational demands. Extensive experiments on two public vitiligo datasets and two private datasets demonstrate that GloW-VSNet achieves state-of-the-art performance. To our knowledge, this is the first study to explore weakly supervised global-view vitiligo segmentation, addressing a critical research gap. Our method enhances the assessment of disease severity and monitoring of treatment response through an objective assessment for real-world applications. Our code is publicly available at https://github.com/YuhanZheng0327/Weakly-Supervised-Vitiligo-Lesion-Segmentation.

Compound bearing fault diagnosis is an essentially challenging task due to the mutual interference among multiple fault components. The state-of-the-art methods usually take the potential fault characteristic frequencies as the prior knowledge and then try to recover every fault component by exploiting the impulse signal sparsity. However, they inevitably suffer from algorithmic degradation caused by energy leakage,$l_{1}$-norm approximation, and/or improper parameter selection. To handle these shortcomings, in this article, we propose a novel sparse Bayesian learning (SBL)-based method for the compound bearing fault diagnosis. We first present a new categorical probabilistic model to efficiently capture the truly-occurred fault components with a truncated feasible domain, which can greatly reduce the energy leakage effect. Then, we devise a more general SBL framework to recover the compound sparse impulse signal under the new categorical probabilistic model. The newly proposed method successfully avoids the$l_{1}$-norm approximation and manual parameter selection; thus, it can yield much higher accuracy and robustness. Both simulations and experiments demonstrate the superiority of the developed method.

The performance of sparse signal recovery (SSR) can be enhanced by exploiting rich temporal correlation in the multiple snapshots of signal of interest. However, existing methods need to transform the temporally correlated multiple measurements SSR problem into its vectorization form, imposing huge computational cost for algorithmic realization. To overcome this drawback, we propose a novel formulation to model the temporal correlation so that variational Bayesian inference (VBI) can be applied to simplify the inference and a novel uncoupling trick is also proposed to reduce the computation. Theoretical and simulation results indicate that our method can bring a considerable computational complexity reduction and achieve a performance improvement for the temporally correlated SSR problem compared to the state of arts time-varying sparse Bayesian learning (TSBL) method.

This paper addresses the problem of massive multiple-input multiple-output (MIMO) channel estimation in the presence of impulsive noise. In the literature, a sparse Bayesian learning (SBL) approach for outlier-resistant direction-of-arrival (DOA) estimation can be tailored to handle this problem. However, it suffers from two major shortcomings: first, it takes the impulsive noise as a part of the unknown signal-of-interest, which brings a high computational complexity due to the larger size of the problem; and second, the assumption that both the signal-of-interest and the impulsive noise have a common sparsity level is not always valid, which could cause a performance loss. To deal with these shortcomings, we resort to the variational Bayesian inference (VBI) methodology to separate effects from the signal-of-interest and the impulsive noise. Then, we introduce an improved two-stage hierarchical prior to enforce sparsity while guarantee a denser impulsive noise over the signal-of-interest simultaneously. Due to adopting the VBI separation and the new sparsity prior, our method can bring a considerable computational complexity reduction and achieve better channel estimation accuracy. Simulation results reveal substantial performance improvement over the existing methods.

The performance of the existing sparse Bayesian learning (SBL) methods for off-grid direction-of-arrival (DOA) estimation is dependent on the tradeoff between the accuracy and the computational workload. To speed up the off-grid SBL method while remain a reasonable accuracy, this letter describes a computationally efficient root SBL method for off-grid DOA estimation, which adopts a coarse grid and considers the sampled locations in the coarse grid as the adjustable parameters. We utilize an expectation-maximization algorithm to iteratively refine this coarse grid and illustrate that each updated grid point can be simply achieved by the root of a certain polynomial. Simulation results demonstrate that the computational complexity is significantly reduced, and the modeling error can be almost eliminated.

Underdetermined direction-of-arrival (DOA) estimation for wideband signals by sparse arrays is discussed in the framework of sparse Bayesian learning (SBL). The problem is transformed to recovering multiple nonnegative sparse vectors, which share the same sparse support but correspond to distinct overcomplete basis matrices, from their noise contaminated linear combination vectors. A two-layer Bayesian model is established, and a hyperparameter vector, which reveals the true DOAs, is set to control this common sparsity in the model. The expectation-maximization algorithm is employed to realize this joint nonnegative SBL procedure, which can give the DOA estimation in a few iterations. The proposed method manifests mild computational complexity, and numerical simulation results show that compared with the existing underdetermined DOA estimation methods, it yields superior estimation accuracy, without the prior knowledge of number of sources.

This paper proposes a novel approach to handle the singularity problem in the Homotopy algorithm. Following a state‐of‐art ridge‐adding‐based method, the authors introduce a random ridge term to each element of the measure matrix to avoid the occurrence of singularities. Then, the authors give the sufficient condition of avoiding singularities, and prove that adding random ridge is greatly useful to deal with the singularity problem, even the random ridge tends to zero. Although the main procedures in the method coincide with the state‐of‐art method, all the derivations and theoretical analyses are different because of distinct forms of optimisation problems. Thus, this work is by no means a trivial task. Moreover, the authors note that the most computationally expensive step in the proposed method is the inversion of active matrices, whose time complexity relative to that of other required operations is proportional to the active set's cardinality. This motivates us to develop an efficient QR update algorithm based on the new ridge‐adding‐based method, which is incorporated in Givens QR factorisation and Gaussian elimination. It turns out that, with such new QR update algorithm, the previous ratio of time complexities can be reduced to a constant order. As a consequence, the new method can eliminate the bottleneck of matrix inversion in the improved Homotopy algorithm.

This paper proposes a novel ridge-adding-based approach for handling singularities that are frequently encountered in the powerful SVMpath algorithm. Unlike the existing method that performs linear programming as an additional step to track the optimality condition path in a multidimensional feasible space, our new approach provides a simpler and computationally more efficient implementation, which needs no extra time-consuming procedures other than introducing a random ridge term to each data point. Contrary to the existing ridge-adding method, which fails to avoid singularities as the ridge terms tend to zero, our novel approach, for any small random ridge terms, guarantees the existence of the inverse matrix by ensuring that only one index is added into or removed from the active set. The performance of the proposed algorithm, in terms of both computational complexity and the ability of singularity avoidance, is manifested by rigorous mathematical analyses as well as experimental results.

This work studies the reconstruction of gene regulatory networks by the means of network component analysis (NCA). We will expound a family of convex optimization-based methods for estimating the transcription factor control strengths and the transcription factor activities (TFAs). The approach taken in this work is to decompose the problem into a network connectivity strength estimation phase and a transcription factor activity estimation phase. In the control strength estimation phase, we formulate a new subspace-based method incorporating a choice of multiple error metrics. For the source estimation phase we propose a total least squares (TLS) formulation that generalizes many existing methods. Both estimation procedures are noniterative and yield the optimal estimates according to various proposed error metrics. We test the performance of the proposed algorithms on simulated data and experimental gene expression data for the yeast Saccharomyces cerevisiae and demonstrate that the proposed algorithms have superior effectiveness in comparison with both Bayesian Decomposition (BD) and our previous FastNCA approach, while the computational complexity is still orders of magnitude less than BD.

This paper considers linear precoder optimization problems for multiple-input multiple-output (MIMO) systems. In addition to the conventionally used sum-power constraint, maximum eigenvalue constraint on the precoding matrix is also considered so as to account for power limitations imposed on each antenna by the linearity of its own power amplifier in practical implementations. A framework employing directional derivative is developed to obtain optimal precoder designs for different criteria including maximizing the information rate and minimizing the sum of mean-square error (MSE). It turns out that power allocations in such situations are piecewise linear in sum-power space. The piecewise linear property allows us to generate the entire path of solution through finding out a finite number of breakpoints. A Homotopy-type algorithm is then proposed to obtain the solution for an arbitrary sum-power constraint. The number of breakpoints to be determined in our exact piecewise linear solution is in fact only about two times of the number of transmit antennas, so that our method is super fast and outperforms existing approximate solutions in the literature in both effectiveness and efficiency. Simulated experiments are performed to verify our theoretical analysis.

Recently a network-constraint regression model[1] is proposed to incorporate the prior biological knowledge to perform regression and variable selection. In their method, a l1-norm of the coefficients is defined to impose sparse, meanwhile a Laplacian operation on the biological graph is designed to encourage smoothness of the coefficients along the network. However the grouping effect of their Laplacian smoothness operation only exits when the two connected genes both have positive or negative effects on the response. To overcome this problem, we proposed to apply the Laplacian operation on the absolute values of the coefficients to take account of the positive and negative effects. Here, we call the presented method as graph-based elastic net (GENet) because the proposed method has similar grouping effect with elastic net(ENet)[2] except the smoothness of two coefficients are specified by the network in GENet. Further, an efficient algorithm which has same spirit with LARS [3] is developed to solve our optimization problem. Simulation studies showed that the proposed method has better performance than network-constrained regularization without absolute values. Application to Alzheimer's disease(AD) microarray gene-expression dataset identified several subnetworks on Kyoto Encyclopedia of Genes and Genomes(KEGG) transcriptional pathways that are related to progression of AD. Many of those findings are confirmed by published literatures.

Network component analysis (NCA) has been established as a promising tool for reconstructing gene regulatory networks from microarray data. NCA is a method that can resolve the problem of blind source separation when the mixing matrix instead has a known sparse structure despite the correlation among the source signals. The original NCA algorithm relies on alternating least squares (ALS) and suffers from local convergence as well as slow convergence. In this paper, we develop new and more robust NCA algorithms by incorporating additional signal constraints. In particular, we introduce the biologically sound constraints that all nonzero entries in the connectivity network are positive. Our new approach formulates a convex optimization problem which can be solved efficiently and effectively by fast convex programming algorithms. We verify the effectiveness and robustness of our new approach using simulations and gene regulatory network reconstruction from experimental yeast cell cycle microarray data.

An improved direction-of-arrivals (DOAs) estimation via phase information of sparse solution is presented in this paper. Unlike the conventional sparse source localization approach using the amplitude of sparse solutions only, through a special partition of the receiving data of the sensors, the phase information of the available sparse solutions is also extracted to estimate DOAs. For the true DOAs exactly on the grids which are used to generate the over-complete dictionary, the performance of our method is close to the conventional sparse source localization method. For the true DOAs that are not on the grids, our method is far superior to the conventional method, as demonstrated by several simulation results.

In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M-1), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible.

MOTIVATION: Recently developed network component analysis (NCA) approach is promising for gene regulatory network reconstruction from microarray data. The existing NCA algorithm is an iterative method which has two potential limitations: computational instability and multiple local solutions. The subsequently developed NCA-r algorithm with Tikhonov regularization can help solve the first issue but cannot completely handle the second one. Here we develop a novel Fast Network Component Analysis (FastNCA) algorithm which has an analytical solution that is much faster and does not have the above limitations. RESULTS: Firstly FastNCA is compared to NCA and NCA-r using synthetic data. The reconstruction of FastNCA is more accurate than that of NCA-r and comparable to that of properly converged NCA. FastNCA is not sensitive to the correlation among the input signals, while its performance does degrade a little but not as dramatically as that of NCA. Like NCA, FastNCA is not very sensitive to small inaccuracies in a priori information on the network topology. FastNCA is about several tens times faster than NCA and several hundreds times faster than NCA-r. Then, the method is applied to real yeast cell-cycle microarray data. The activities of the estimated cell-cycle regulators by FastNCA and NCA-r are compared to the semi-quantitative results obtained independently by Lee et al. (2002). It is shown here that there is a greater agreement between the results of FastNCA and Lee's, which is represented by the ratio 23/33, than that between the results of NCA-r and Lee's, which is 14/33. AVAILABILITY: Software and supplementary materials are available from http://www.eee.hku.hk/~cqchang/FastNCA.htm

BACKGROUND: Currently, clustering with some form of correlation coefficient as the gene similarity metric has become a popular method for profiling genomic data. The Pearson correlation coefficient and the standard deviation (SD)-weighted correlation coefficient are the two most widely-used correlations as the similarity metrics in clustering microarray data. However, these two correlations are not optimal for analyzing replicated microarray data generated by most laboratories. An effective correlation coefficient is needed to provide statistically sufficient analysis of replicated microarray data. RESULTS: In this study, we describe a novel correlation coefficient, shrinkage correlation coefficient (SCC), that fully exploits the similarity between the replicated microarray experimental samples. The methodology considers both the number of replicates and the variance within each experimental group in clustering expression data, and provides a robust statistical estimation of the error of replicated microarray data. The value of SCC is revealed by its comparison with two other correlation coefficients that are currently the most widely-used (Pearson correlation coefficient and SD-weighted correlation coefficient) using statistical measures on both synthetic expression data as well as real gene expression data from Saccharomyces cerevisiae. Two leading clustering methods, hierarchical and k-means clustering were applied for the comparison. The comparison indicated that using SCC achieves better clustering performance. Applying SCC-based hierarchical clustering to the replicated microarray data obtained from germinating spores of the fern Ceratopteris richardii, we discovered two clusters of genes with shared expression patterns during spore germination. Functional analysis suggested that some of the genetic mechanisms that control germination in such diverse plant lineages as mosses and angiosperms are also conserved among ferns. CONCLUSION: This study shows that SCC is an alternative to the Pearson correlation coefficient and the SD-weighted correlation coefficient, and is particularly useful for clustering replicated microarray data. This computational approach should be generally useful for proteomic data or other high-throughput analysis methodology.

In this paper we propose a novel and fast nonlinear association measure based on order statistics and rearrangement inequality. We employ one episode of heart signal, one episode of EEG signal and 1000 white Gaussian noises in our study. Extensive statistical analysis are performed based on one linear model and one nonlinear model. Comparative studies with three other prominent methods are presented. Theoretical derivations and experimental results suggest that our new method has small biasedness, high sensitivity to changes in association, fast computational speed, and robustness under monotone nonlinear transformations.

This paper addresses the problem of blind separation of linear convolutive mixtures. We first reformulate the problem into a blind separation of linear instantaneous mixtures, and then a statistical approach is applied to solve the reformulated problem. From the statistics of the mixtures, two kinds of matrix pencils are constructed to estimate the mixing matrix. The original sources are then separated with the estimated mixing matrix. For the purpose of computational efficiency and robustness, in the matrix pencil, one matrix is constructed from the second order statistics, and the other is constructed from the third order statistics. The proposed novel methods do not require the exact knowledge of the channel order. Simulation results show that the methods are robust and have good performance.

The problem of blind source separation in additive white noise is an important problem in speech, array and acoustic signal processing. In general this problem requires the use of higher order statistics of the received signals. However for many signal sources, such as speech with distinct non-white power spectral densities, second order statistics of the received signal mixture can be exploited for signal separation. While previous approaches often assume that additive noise is absent or that the noise correlation matrix is known, we propose a simple and yet effective signal extraction method for signal source separation under unknown white noise. This new and unbiased signal extractor is derived from the matrix pencil formed between output auto-correlation matrices at different delays. Simulation examples are presented.