Single-Channel Sparse Non-Negative Blind Source Separation Method for Automatic 3-D Delineation of Lung Tumor in PET Images

In this paper, we propose a novel method for single-channel blind separation of nonoverlapped sources and, to the best of our knowledge, apply it for the first time to automatic segmentation of lung tumors in positron emission tomography (PET) images. Our approach first converts a 3-D PET image into a pseudo-multichannel image. Afterward, regularization free sparseness constrained non-negative matrix factorization is used to separate tumor from other tissues. By using complexity based criterion, we select tumor component as the one with minimal complexity. We have compared the proposed method with threshold based on 40% and 50% maximum standardized uptake value (SUV), graph cuts (GC), random walks (RW), and affinity propagation (AP) algorithms on 18 nonsmall cell lung cancer datasets with respect to ground truth (GT) provided by two radiologists. Dice similarity coefficient averaged with respect to two GTs is: 0.78 ± 0.12 by the proposed algorithm, 0.78 ± 0.1 by GC, 0.77 ± 0.13 by AP, 0.77 ± 0.07 by RW, and 0.75 ± 0.13 by 50% maximum SUV threshold. Since the proposed method achieved performance comparable with interactive methods, considering the unique challenges of lung tumor segmentation from PET images, our findings support possibility of using our fully automated method in routine clinics. The source codes will be available at www.mipav.net/English/research/research.html.

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title: Automated Delineation of Lung Tumors in PET Images Based on Monotonicity and a Tumor-Customized Criterion
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title: Optimal Co-Segmentation of Tumor in PET-CT Images With Context Information
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title: Joint segmentation of anatomical and functional images: Applications in quantification of lesions from PET, PET-CT, MRI-PET, and MRI-PET-CT images
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title: A review on segmentation of positron emission tomography images
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title: Random Walk and Graph Cut for Co-Segmentation of Lung Tumor on PET-CT Images
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title: Random Walks for Image Segmentation
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title: Fast approximate energy minimization via graph cuts
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title: Robust segmentation and accurate target definition for positron emission tomography images using Affinity Propagation
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title: Segmentation of PET Images for Computer-Aided Functional Quantification of Tuberculosis in Small Animal Models
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title: Observer variation in contouring gross tumor volume in patients with poorly defined non-small-cell lung tumors on CT: the impact of 18FDG-hybrid PET fusion.
abstract: To quantify interobserver variation in gross tumor volume (GTV) localization using CT images for patients with non-small-cell lung carcinoma and poorly defined tumors on CT and to determine whether variability would be reduced if coregistered 2-[18F]fluoro-2-deoxy-d-glucose (FDG)-hybrid positron emission tomography (PET) with CT images were used.



Prospectively, 30 patients with non-small-cell lung carcinoma had CT and FDG-hybrid PET examinations in radiation treatment position on the same day. Images were coregistered using eight fiducial markers. Guidelines were established for contouring GTVs. Three radiation oncologists performed localization independently. The coefficient of variation was used to assess interobserver variability.



The size of the GTV defined showed great variation among observers. The mean ratios of largest to smallest GTV were 2.31 and 1.56 for CT only and for CT/FDG coregistered data, respectively. The addition of PET reduced this ratio in 23 of 30 cases and increased it in 7. The mean coefficient of variation for GTV based on the combined modalities was significantly smaller (p < 0.01) than that for CT data only.



High observer variability in CT-based definition of the GTV can occur. A more consistent definition of the GTV can often be obtained if coregistered FDG-hybrid PET images are used.

title: Radiotherapy treatment planning for patients with non-small cell lung cancer using positron emission tomography (PET).
abstract: Many patients with non-small cell lung cancer (NSCLC) receive external beam radiation therapy as part of their treatment. Three-dimensional conformal radiation therapy (3DCRT) commonly uses computed tomography (CT) to accurately delineate the target lesion and normal tissues. Clinical studies, however, indicate that positron emission tomography (PET) has higher sensitivity than CT in detecting and staging of mediastinal metastases. Imaging with fluoro-2-deoxyglucose (FDG) PET in conjunction with CT, therefore, can improve the accuracy of lesion definition. In this pilot study, we investigated the potential benefits of incorporating PET data into the conventional treatment planning of NSCLC. Case-by-case, we prospectively analyzed planning target volume (PTV) and lung toxicity changes for a cohort of patients.



We have included 11 patients in this study. They were immobilized in the treatment position and CT simulation was performed. Following CT simulation, PET scanning was performed in the treatment position using the same body cast that was produced for CT simulation and treatment. The PTV, along with the gross target volume (GTV) and normal organs, was first delineated using the CT data set. The CT and PET transmission images were then registered in the treatment planning system using either manual or automated methods, leading to consequent registration of the CT and emission images. The PTV was then modified using the registered PET emission images. The modified PTV is seen simultaneously on both CT and PET images, allowing the physician to define the PTV utilizing the information from both data sets. Dose-volume histograms (DVHs) for lesion and normal organs were generated using both CT-based and PET+CT-based treatment plans.



For all patients, there was a change in PTV outline based on CT images versus CT/PET fused images. In seven out of 11 cases, we found an increase in PTV volume (average increase of 19%) to incorporate distant nodal disease. Among these patients, the highest normal-tissue complication probability (NTCP) for lung was 22% with combined PET/CT plan and 21% with CT-only plan. In other four patients PTV was decreased an average of 18%. The reduction of PTV in two of these patients was due to excluding atelectasis and trimming the target volume to avoid delivering higher radiation doses to nearby spinal cord or heart.



The incorporation of PET data improves definition of the primary lesion by including positive lymph nodes into the PTV. Thus, the PET data reduces the likelihood of geographic misses and hopefully improves the chance of achieving local control.

title: 18F-deoxyglucose positron emission tomography (FDG-PET) for the planning of radiotherapy in lung cancer: high impact in patients with atelectasis.
abstract: 18F-deoxyglucose positron emission tomography (FDG-PET) is increasingly applied in the staging of lung cancer (LC). This study analyzes the potential contribution of PET in radiotherapy planning for LC with special respect to tumor-associated atelectasis.



Thirty-four patients with histologically confirmed LC, who had been examined by PET during pretreatment staging, were included. All were irradiated after CT-based therapy planning with anterior/posterior (AP) portals encompassing the primary tumor and the mediastinum (CT portals, CP). The result of the PET examination was unknown in treatment planning. In retrospect, a PET portal (PP) was delineated and compared with the CP.



In 12/34 cases, the shape and/or size of the portals were changed, primarily (n = 10) the size of the fields was reduced. The median area of CP was 182 cm2 versus 167 cm2 of PP. Seventeen of 34 patients had dys- or atelectasis caused by a central primary tumor. In these cases, differences between CP and PP were significantly more frequent than in the other patients (8/17 vs. 3/17, p = 0.03).



In this retrospective analysis, the information provided by FDG-PET would have contributed to a substantial reduction of the size of radiotherapy portals. This applies particularly for patients with tumor-associated dys- or atelectasis.

title: Thresholding in PET images of static and moving targets.
abstract: Continued therapeutic gain in the treatment of non-small-cell lung cancer (NSCLC) will depend upon our ability to escalate the dose to the primary tumour while minimizing normal tissue toxicity. Both these objectives are facilitated by the accurate definition of a target volume that is as small as possible. To this end, both tumour immobilizations via deep inspiratory breath-hold, along with positron emission tomography (PET), have emerged as two promising approaches. Though PET is an excellent means of defining the general location of a tumour focus, its ability to define exactly the geometric extent of such a focus strongly depends upon selection of an appropriate image threshold. However, in clinical practice, the image threshold is typically not chosen according to consistent, well-established criteria. This study explores the relationship between image threshold and the resultant PET-defined volume using a series of F-18 radiotracer-filled hollow spheres of known internal volumes, both static and under oscillatory motion. The effects of both image threshold and tumour motion on the resultant PET image are examined. Imaging data are further collected from a series of simulated gated PET acquisitions in order to test the feasibility of a patient-controlled gating mechanism during deep inspiratory breath-hold. This study illustrates quantitatively considerable variability in resultant PET-defined tumour volumes depending upon numerous factors, including image threshold, size of the lesion, the presence of tumour motion and the scanning protocol. In this regard, when using PET in treatment planning for NSCLC, the radiation oncologist must select the image threshold very carefully to avoid either under-dosing the tumour or overdosing normal tissues.

title: Tri-dimensional automatic segmentation of PET volumes based on measured source-to-background ratios: influence of reconstruction algorithms.
abstract: A method for automatic volume segmentation of functional imaging based on a relationship between source-to-background ratio and the iso-activity level to be used is described. Such method, which has been established with radioactive spheres in a phantom, is independent of the a priori knowledge of the lesion of interest and is valid for small (>2 ml) and/or poorly contrasted (S/B>1.5) lesions. Accuracy varies slightly with the image reconstruction algorithm used.

title: Segmentation of PET volumes by iterative image thresholding.
abstract: The segmentation of metastatic volumes in PET is usually performed by thresholding methods. In a clinical application, the optimum threshold obtained from the adaptive thresholding method requires a priori estimation of the lesion volume from anatomic images such as CT. We describe an iterative thresholding method (ITM) used to estimate the PET volumes without anatomic a priori knowledge and its application to clinical images.



The ITM is based on threshold-volume curves at varying source-to-background (S/B) ratio acquired from a body phantom. The spheres and background were filled either with (18)F-FDG or Na(124)I ((124)I). These calibrated S/B-threshold-volume curves were used in estimating the volume by applying an iterative procedure. The ITM was validated with a PET phantom containing spheres and with 39 PET tumors that were discernable on CT by using whole-body (18)F-FDG (15 patients) and (124)I PET/CT (9 patients): The measured S/B ratios of the lesions were estimated from PET images, and their volumes were iteratively calculated using the calibrated S/B-threshold-volume curves. The resulting PET volumes were then compared with the known sphere inner volume and CT volumes of tumors that served as gold standards.



Phantom data analysis showed that the S/B-threshold-volume curves of (18)F-FDG and (124)I were similar. The average absolute deviation (expressed as a percentage of the expected volume) obtained in the PET validation phantom was 10% for volumes larger than 1.0 mL; sphere volumes of 0.5 mL showed a significantly larger deviation. For patients, the average absolute deviation for volumes between 0.8 and 7.5 mL was about 9% (31 lesions), whereas volumes larger than 7.5 mL showed an average volume mismatch of 15% (8 lesions).



The ITM sufficiently estimated the clinical volumes in the range of 0.8-7.5 mL; volumes larger than 7.5 mL showed greater deviations that were still acceptable. These findings are associated with the limitation of the ITM. The ITM is especially useful for lesions that are only visible on PET. As a consequence, the lesion dosimetry is feasible with sufficient accuracy using PET images only.

title: A Gaussian mixture model for definition of lung tumor volumes in positron emission tomography.
abstract: The increased interest in 18F-fluorodeoxyglucose (FDG) positron emission tomography (PET) in radiation treatment planning in the past five years necessitated the independent and accurate segmentation of gross tumor volume (GTV) from FDG-PET scans. In some studies the radiation oncologist contours the GTV based on a computed tomography scan, while incorporating pertinent data from the PET images. Alternatively, a simple threshold, typically 40% of the maximum intensity, has been employed to differentiate tumor from normal tissue, while other researchers have developed algorithms to aid the PET based GTV definition. None of these methods, however, results in reliable PET tumor segmentation that can be used for more sophisticated treatment plans. For this reason, we developed a Gaussian mixture model (GMM) based segmentation technique on selected PET tumor regions from non-small cell lung cancer patients. The purpose of this study was to investigate the feasibility of using a GMM-based tumor volume definition in a robust, reliable and reproducible way. A GMM relies on the idea that any distribution, in our case a distribution of image intensities, can be expressed as a mixture of Gaussian densities representing different classes. According to our implementation, each class belongs to one of three regions in the image; the background (B), the uncertain (U) and the target (T), and from these regions we can obtain the tumor volume. User interaction in the implementation is required, but is limited to the initialization of the model parameters and the selection of an "analysis region" to which the modeling is restricted. The segmentation was developed on three and tested on another four clinical cases to ensure robustness against differences observed in the clinic. It also compared favorably with thresholding at 40% of the maximum intensity and a threshold determination function based on tumor to background image intensities proposed in a recent paper. The parts of the method that are user dependent were evaluated and resulted in initial estimates of the method's precision, which is in the order of +/-10% of the average tumor volume estimate. With this work we have established the applicability of the GMM-based segmentation on clinical studies and we have made an initial assessment of the method's precision with respect to tumor volume segmentation.

title: A Fuzzy Locally Adaptive Bayesian Segmentation Approach for Volume Determination in PET
abstract: Accurate volume estimation in positron emission tomography (PET) is crucial for different oncology applications. The objective of our study was to develop a new fuzzy locally adaptive Bayesian (FLAB) segmentation for automatic lesion volume delineation. FLAB was compared with a threshold approach as well as the previously proposed fuzzy hidden Markov chains (FHMC) and the fuzzy C-Means (FCM) algorithms. The performance of the algorithms was assessed on acquired datasets of the IEC phantom, covering a range of spherical lesion sizes (10-37 mm), contrast ratios (4:1 and 8:1), noise levels (1, 2, and 5 min acquisitions), and voxel sizes (8 and 64 mm3). In addition, the performance of the FLAB model was assessed on realistic nonuniform and nonspherical volumes simulated from patient lesions. Results show that FLAB performs better than the other methodologies, particularly for smaller objects. The volume error was 5%-15% for the different sphere sizes (down to 13 mm), contrast and image qualities considered, with a high reproducibility (variation < 4%). By comparison, the thresholding results were greatly dependent on image contrast and noise, whereas FCM results were less dependent on noise but consistently failed to segment lesions < 2 cm. In addition, FLAB performed consistently better for lesions < 2 cm in comparison to the FHMC algorithm. Finally the FLAB model provided errors less than 10% for nonspherical lesions with inhomogeneous activity distributions. Future developments will concentrate on an extension of FLAB in order to allow the segmentation of separate activity distribution regions within the same functional volume as well as a robustness study with respect to different scanners and reconstruction algorithms.

title: Segmentation of Lung Tumours in Positron Emission Tomography Scans: A Machine Learning Approach
abstract: Lung cancer represents the most deadly type of malignancy. In this work we propose a machine learning approach to segmenting lung tumours in Positron Emission Tomography (PET) scans in order to provide a radiation therapist with a "second reader" opinion about the tumour location. For each PET slice, our system extracts a set of attributes, passes them to a trained Support Vector Machine (SVM), and returns the optimal threshold value for distinguishing tumour from healthy voxels in that particular slice. We use this technique to analyse four different PET/CT 3D studies. The system produced fairly accurate segmentation, with Jaccard and Dice's similarity coefficients between 0.82 and 0.98 (the areas outlined by the returned thresholds vs. the ones outlined by the reference thresholds). Besides the high level of geometric similarity, a significant correlation between the returned and the reference thresholds also indicates that during the training phase, the learning algorithm effectively acquired the dependency between the extracted attributes and optimal thresholds.

title: Delineation of FDG-PET tumors from heterogeneous background using spectral clustering.
abstract: This paper explored the feasibility of using spectral clustering to segment FDG-PET tumor in the presence of heterogeneous background. Spectral clustering refers to a class of clustering methods which employ the eigenstructure of a similarity matrix to partition image voxels into disjoint clusters. The similarity between two voxels was measured with the intensity distance scaled by voxel-varying factors capturing local statistics and the number of clusters was inferred based on rotating the eigenvector matrix for the maximally sparse representation. Metrics used to evaluate the segmentation accuracy included: Dice coefficient, Jaccard coefficient, false positive dice, false negative dice, symmetric mean absolute surface distance, and absolute volumetric difference. Comparison of segmentation results between the presented method and the adaptive thresholding method on the simulated PET data shows the former attains an overall better detection accuracy. Applying the presented method on patient data gave segmentation results in fairly good agreement with physician manual annotations. These results indicate that the presented method have the potential to accurately delineate complex shaped FDG-PET tumors containing inhomogeneous activities in the presence of heterogeneous background.

title: Principal Component Analysis
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title: Independent Component Analysis
abstract: Independent Component Analysis (ICA) is a computational technique for revealing hidden factors that underlie sets of measurements or signals. ICA assumes a statistical model whereby the observed multivariate data, typically given as a large database of samples, are assumed to be linear or nonlinear mixtures of some unknown latent variables. The mixing coefficients are also unknown. The latent variables are nongaussian and mutually independent, and they are called the independent components of the observed data. By ICA, these independent components, also called sources or factors, can be found. Thus ICA can be seen as an extension to Principal Component Analysis and Factor Analysis. ICA is a much richer technique, however, capable of finding the sources when these classical methods fail completely. In many cases, the measurements are given as a set of parallel signals or time series. Typical examples are mixtures of simultaneous sounds or human voices that have been picked up by several microphones, brain signal measurements from multiple EEG sensors, several radio signals arriving at a portable phone, or multiple parallel time series obtained from some industrial process. The term blind source separation is used to characterize this problem. The lecture will first cover the basic idea of demixing in the case of a linear mixing model and then take a look at the recent nonlinear demixing approaches. Although ICA was originally developed for digital signal processing applications, it has recently been found that it may be a powerful tool for analyzing text document data as well, if the documents are presented in a suitable numerical form. A case study on analyzing dynamically evolving text is covered in the talk.

title: Non-negative and sparse spectral clustering
abstract: Spectral clustering aims to partition a data set into several groups by using the Laplacian of the graph such that data points in the same group are similar while data points in different groups are dissimilar to each other. Spectral clustering is very simple to implement and has many advantages over the traditional clustering algorithms such as k-means. Non-negative matrix factorization (NMF) factorizes a non-negative data matrix into a product of two non-negative (lower rank) matrices so as to achieve dimension reduction and part-based data representation. In this work, we proved that the spectral clustering under some conditions is equivalent to NMF. Unlike the previous work, we formulate the spectral clustering as a factorization of data matrix (or scaled data matrix) rather than the symmetrical factorization of the symmetrical pairwise similarity matrix as the previous study did. Under the NMF framework, where regularization can be easily incorporated into the spectral clustering, we propose several non-negative and sparse spectral clustering algorithms. Empirical studies on real world data show much better clustering accuracy of the proposed algorithms than some state-of-the-art methods such as ratio cut and normalized cut spectral clustering and non-negative Laplacian embedding. HighlightsWe proved that the spectral clustering is equivalent to NMF.Under the NMF framework, we propose nonnegative sparse spectral clustering model.We propose several algorithms to solve the proposed models.Experiment results on real world data show much better performance.

title: Estimation of number of spectrally distinct signal sources in hyperspectral imagery
abstract: With very high spectral resolution, hyperspectral sensors can now uncover many unknown signal sources which cannot be identified by visual inspection or a priori. In order to account for such unknown signal sources, we introduce a new definition, referred to as virtual dimensionality (VD) in this paper. It is defined as the minimum number of spectrally distinct signal sources that characterize the hyperspectral data from the perspective view of target detection and classification. It is different from the commonly used intrinsic dimensionality (ID) in the sense that the signal sources are determined by the proposed VD based only on their distinct spectral properties. These signal sources may include unknown interfering sources, which cannot be identified by prior knowledge. With this new definition, three Neyman-Pearson detection theory-based thresholding methods are developed to determine the VD of hyperspectral imagery, where eigenvalues are used to measure signal energies in a detection model. In order to evaluate the performance of the proposed methods, two information criteria, an information criterion (AIC) and minimum description length (MDL), and the factor analysis-based method proposed by Malinowski, are considered for comparative analysis. As demonstrated in computer simulations, all the methods and criteria studied in this paper may work effectively when noise is independent identically distributed. This is, unfortunately, not true when some of them are applied to real image data. Experiments show that all the three eigenthresholding based methods (i.e., the Harsanyi-Farrand-Chang (HFC), the noise-whitened HFC (NWHFC), and the noise subspace projection (NSP) methods) produce more reliable estimates of VD compared to the AIC, MDL, and Malinowski's empirical indicator function, which generally overestimate VD significantly. In summary, three contributions are made in this paper, 1) an introduction of the new definition of VD, 2) three Neyman-Pearson detection theory-based thresholding methods, HFC, NWHFC, and NSP derived for VD estimation, and 3) experiments that show the AIC and MDL commonly used in passive array processing and the second-order statistic-based Malinowski's method are not effective measures in VD estimation.

title: Blind Decomposition of Transmission Light Microscopic Hyperspectral Cube Using Sparse Representation
abstract: In this paper, we address the problem of fully automated decomposition of hyperspectral images for transmission light microscopy. The hyperspectral images are decomposed into spectrally homogeneous compounds. The resulting compounds are described by their spectral characteristics and optical density. We present the multiplicative physical model of image formation in transmission light microscopy, justify reduction of a hyperspectral image decomposition problem to a blind source separation problem, and provide method for hyperspectral restoration of separated compounds. In our approach, dimensionality reduction using principal component analysis (PCA) is followed by a blind source separation (BSS) algorithm. The BSS method is based on sparsifying transformation of observed images and relative Newton optimization procedure. The presented method was verified on hyperspectral images of biological tissues. The method was compared to the existing approach based on nonnegative matrix factorization. Experiments showed that the presented method is faster and better separates the biological compounds from imaging artifacts. The results obtained in this work may be used for improving automatic microscope hardware calibration and computer-aided diagnostics.

title: Application of independent component analysis to magnetic resonance imaging for enhancing the contrast of gray and white matter
abstract: An application of independent component analysis (ICA) was attempted to develop a method of processing magnetic resonance (MR) images to extract physiologically independent components representing tissue relaxation times and achieve improved visualization of normal and pathologic structures. Anatomical T1-weighted, T2-weighted and proton density images were obtained from 10 normal subjects, 3 patients with brain tumors and 1 patient with multiple sclerosis. The data sets were analyzed using ICA based on the learning rule of Bell and Sejnowski after prewhitening operations. The three independent components obtained from the three original data sets corresponded to (1) short T1 components representing myelin of white matter and lipids, (2) relatively short T1 components representing gray matter and (3) long T2 components representing free water. The involvement of gray or white matter in brain tumor cases and the demyelination in the case of multiple sclerosis were enhanced and visualized in independent component images. ICA can potentially achieve separation of tissues with different relaxation characteristics and generate new contrast images of gray and white matter. With the proper choice of contrast for the original images, ICA may be useful not only for extracting subtle or hidden changes but also for preprocessing transformation before clustering and segmenting the structure of the human brain.

title: Independent Component Analysis of Four-Phase Abdominal CT Images
abstract: This paper presents a new analysis result of two-dimensional four-phase abdominal CT images using variational Bayesian mixture of ICA. The four-phase CT images are modeled as being produced by a mixture of data generators, where each data generator consists of a set of independent components and is responsible for generating a particular cluster. ICA results show that the CT images could be divided into a set of clinically and anatomically meaningful components. Initial analysis of the independent components shows its promising prospect in medical image processing and computer-aided diagnosis.

title: Applying ICA Mixture Analysis for Segmenting Liver from Multi-phase Abdominal CT Images
abstract: Liver segmentation is an important task in the development of computer-aided multi-phase CT diagnosis system of liver. This paper presents a new approach for segmenting liver from multi-phase abdominal CT images using ICA mixture analysis. In particular, we use the variational Bayesian mixture of ICA method  to analyze three-dimensional four-phase abdominal CT images. The analysis results show that the CT images could be divided into a set of clinically and anatomically meaningful components. As to our concern, the organs that surround the liver and have similar intensities, such as stomach, kidney, are nearly completely separated from the liver, which makes the segmentation become much easier than on the original CT images.

title: Robust demarcation of basal cell carcinoma by dependent component analysis-based segmentation of multi-spectral fluorescence images.
abstract: This study was designed to demonstrate robust performance of the novel dependent component analysis (DCA)-based approach to demarcation of the basal cell carcinoma (BCC) through unsupervised decomposition of the red-green-blue (RGB) fluorescent image of the BCC. Robustness to intensity fluctuation is due to the scale invariance property of DCA algorithms, which exploit spectral and spatial diversities between the BCC and the surrounding tissue. Used filtering-based DCA approach represents an extension of the independent component analysis (ICA) and is necessary in order to account for statistical dependence that is induced by spectral similarity between the BCC and surrounding tissue. This generates weak edges what represents a challenge for other segmentation methods as well. By comparative performance analysis with state-of-the-art image segmentation methods such as active contours (level set), K-means clustering, non-negative matrix factorization, ICA and ratio imaging we experimentally demonstrate good performance of DCA-based BCC demarcation in two demanding scenarios where intensity of the fluorescent image has been varied almost two orders of magnitude.

title: Independent component analysis, A new concept?
abstract: The independent component analysis (ICA) of a random vector consists of searching for a linear transformation that minimizes the statistical dependence between its components. In order to define suitable search criteria, the expansion of mutual information is utilized as a function of cumulants of increasing orders. An efficient algorithm is proposed, which allows the computation of the ICA of a data matrix within a polynomial time. The concept of ICA may actually be seen as an extension of the principal component analysis (PCA), which can only impose independence up to the second order and, consequently, defines directions that are orthogonal. Potential applications of ICA include data analysis and compression, Bayesian detection, localization of sources, and blind identification and deconvolution.

title: Analysis of Sparse Representation and Blind Source Separation
abstract: In this letter, we analyze a two-stage cluster-then-l1-optimization approach for sparse representation of a data matrix, which is also a promising approach for blind source separation (BSS) in which fewer sensors than sources are present. First, sparse representation (factorization) of a data matrix is discussed. For a given overcomplete basis matrix, the corresponding sparse solution (coefficient matrix) with minimum l1 norm is unique with probability one, which can be obtained using a standard linear programming algorithm. The equivalence of the l1norm solution and the l0norm solution is also analyzed according to a probabilistic framework. If the obtained l1norm solution is sufficiently sparse, then it is equal to the l0norm solution with a high probability. Furthermore, the l1norm solution is robust to noise, but the l0norm solution is not, showing that the l1norm is a good sparsity measure. These results can be used as a recoverability analysis of BSS, as discussed. The basis matrix in this article is estimated using a clustering algorithm followed by normalization, in which the matrix columns are the cluster centers of normalized data column vectors. Zibulevsky, Pearlmutter, Boll, and Kisilev (2000) used this kind of two-stage approach in underdetermined BSS. Our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed

title: Blind decomposition of low‐dimensional multi‐spectral image by sparse component analysis
abstract: A multilayer hierarchical alternating least square nonnegative matrix factorization approach has been applied to blind decomposition of low‐dimensional multi‐spectral image. The method performs blind decomposition exploiting spectral diversity and spatial sparsity between materials present in the image and, unlike many blind source separation methods, is invariant with respect to statistical (in)dependence among spatial distributions of the materials. As opposed to many existing blind source separation algorithms, the method is capable of estimating the unknown number of materials present in the image. This number can be less than, equal to, or greater than the number of spectral bands. The method is validated on underdetermined blind source separation problems associated with blind decomposition of experimental red‐green‐blue images composed of four materials. Achieved performance has been superior when compared against methods based on minimization of the ℓ1‐norm: linear programming and interior‐point methods. In addition to tumor demarcation, as demonstrated in the paper, other areas that can also benefit from the proposed method include cell, chemical, and tissue imaging.

title: Learning the parts of objects by non-negative matrix factorization
abstract: Is perception of the whole based on perception of its parts? There is psychological and physiological evidence for parts-based representations in the brain, and certain computational theories of object recognition rely on such representations. But little is known about how brains or computers might learn the parts of objects. Here we demonstrate an algorithm for non-negative matrix factorization that is able to learn parts of faces and semantic features of text. This is in contrast to other methods, such as principal components analysis and vector quantization, that learn holistic, not parts-based, representations. Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. When non-negative matrix factorization is implemented as a neural network, parts-based representations emerge by virtue of two properties: the firing rates of neurons are never negative and synaptic strengths do not change sign.

title: Algorithms and applications for approximate nonnegative matrix factorization
abstract: The development and use of low-rank approximate nonnegative matrix factorization (NMF) algorithms for feature extraction and identification in the fields of text mining and spectral data analysis are presented. The evolution and convergence properties of hybrid methods based on both sparsity and smoothness constraints for the resulting nonnegative matrix factors are discussed. The interpretability of NMF outputs in specific contexts are provided along with opportunities for future work in the modification of NMF algorithms for large-scale and time-varying data sets.

title: Using underapproximations for sparse nonnegative matrix factorization
abstract: Nonnegative matrix factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g., text mining, image processing, microarray data analysis, collaborative filtering, etc. We introduce a novel approach to solve NMF problems, based on the use of an underapproximation technique, and show its effectiveness to obtain sparse solutions. This approach, based on Lagrangian relaxation, allows the resolution of NMF problems in a recursive fashion. We also prove that the underapproximation problem is NP-hard for any fixed factorization rank, using a reduction of the maximum edge biclique problem in bipartite graphs. We test two variants of our underapproximation approach on several standard image datasets and show that they provide sparse part-based representations with low reconstruction error. Our results are comparable and sometimes superior to those obtained by two standard sparse nonnegative matrix factorization techniques.

title: Nonlinear mixture‐wise expansion approach to underdetermined blind separation of nonnegative dependent sources
abstract: Underdetermined blind separation of nonnegative dependent sources consists in decomposing a set of observed mixed signals into greater number of original nonnegative and dependent component (source) signals. That is an important problem for which very few algorithms exist. It is also practically relevant for contemporary metabolic profiling of biological samples, such as biomarker identification studies, where sources (a.k.a. pure components or analytes) are aimed to be extracted from mass spectra of complex multicomponent mixtures. This paper presents a method for underdetermined blind separation of nonnegative dependent sources. The method performs nonlinear mixture‐wise mapping of observed data in high‐dimensional reproducible kernel Hilbert space (RKHS) of functions and sparseness‐constrained nonnegative matrix factorization (NMF) therein. Thus, the original problem is converted into new one with increased number of mixtures, increased number of dependent sources, and higher‐order (error) terms generated by nonlinear mapping. Provided that amplitudes of original components are sparsely distributed, which is the case for mass spectra of analytes, sparseness‐constrained NMF in RKHS yields, with significant probability, improved accuracy relative to the case when the same NMF algorithm is performed on the original problem. The method is exemplified on numerical and experimental examples related respectively to extraction of 10 dependent components from five mixtures and to extraction of 10 dependent analytes from mass spectra of two to five mixtures. Thereby, analytes mimic complexity of components expected to be found in biological samples.

title: Source separation using single channel ICA
abstract: Many researchers have recently used independent component analysis (ICA) to generate codebooks or features for a single channel of data. We examine the nature of these codebooks and identify when such features can be used to extract independent components from a stationary scalar time series. This question is motivated by empirical work that suggests that single channel ICA can sometimes be used to separate out important components from a time series. Here we show that as long as the sources are reasonably spectrally disjoint then we can identify and approximately separate out individual sources. However, the linear nature of the separation equations means that when the sources have substantially overlapping spectra both identification using standard ICA and linear separation are no longer possible.

title: A novel blind source separation method for single-channel signal
abstract: The blind separation of single-channel signal is one of the most important aspects in many fields. Our research is carried out to develop a blind separation method of single-channel signal, in which the singular spectrum analysis (SSA) and blind source separation (BSS) techniques are jointly used, i.e. the single-channel signal is firstly changed into pseudo-MIMO (multi-input and multi-output) mode, and then each source signal is separated via a fast BSS algorithm. A signal preprocessing procedure, which is mainly focused on testing the nonstationarity of single-channel signal, is conducted before the operations of mixed signal transform and separation. In this research, the approach of heuristic segmentation of a nonstationary time-series is proposed. Throughout the experiment, the effectiveness of the proposed method is validated with a data set taken from a digital wideband receiver in an outdoor test. Then, a comparison is made between the proposed method and the Hilbert-Huang transform (HHT)-based signal separation method. The advantage of the proposed method is exhibited.

title: Source Separation From Single-Channel Recordings by Combining Empirical-Mode Decomposition and Independent Component Analysis
abstract: In biomedical signal processing, it is often the case that many sources are mixed into the measured signal. The goal is usually to analyze one or several of them separately. In the case of multichannel measurements, several blind source separation techniques are available for decomposing the signal into its components [e.g., independent component analysis (ICA)]. However, only a few techniques have been reported for analyses of single-channel recordings. Examples are single-channel ICA (SCICA) and wavelet-ICA (WICA), which all have certain limitations. In this paper, we propose a new method for a single-channel signal decomposition. This method combines empirical-mode decomposition with ICA. We compare the separation performance of our algorithm with SCICA and WICA through simulations, and we show that our method outperforms the other two, especially for high noise-to-signal ratios. The performance of the new algorithm was also demonstrated in two real-life applications.

title: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the ‘empirical mode decomposition’ method with which any complicated data set can be decomposed into a finite and often small number of ‘intrinsic mode functions’ that admit well-behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and non-stationary processes. With the Hilbert transform, the ‘instrinic mode functions’ yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert spectrum. In this method, the main conceptual innovations are the introduction of ‘intrinsic mode functions’ based on local properties of the signal, which make the instantaneous frequency meaningful; and the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need for spurious harmonics to represent nonlinear and non-stationary signals. Examples from the numerical results of the classical nonlinear equation systems and data representing natural phenomena are given to demonstrate the power of this new method. Classical nonlinear system data are especially interesting, for they serve to illustrate the roles played by the nonlinear and non-stationary effects in the energy-frequency-time distribution.

title: Fault feature separation using wavelet-ICA filter
abstract: Independent component analysis (ICA) is a new effective technique for separation of statistically independent sources. Generally, ICA requires that the number of sensors must be no less than the number of independent sources to ensure enough information for separation of all sources. In some practical applications, this requirement of ICA is not met and we are interested in separation of only one source. A new method called wavelet-ICA filter is proposed in this paper that attempts to extract the independent feature by only using one transducer. The method employs ICA to regularize the wavelet decompositions of a signal to find the independent feature. Morlet wavelet is employed in this application for its nonorthogonality. The analysis of the feasibility of the method is shown in this paper. The effectiveness of this method is demonstrated by applying it to both simulated signals and vibration signals collected from a gearbox for periodic impulse detection. PCA is also used for the same purpose as comparisons. The results show that the proposed method using ICA is much better than PCA for separation of an independent feature.

title: Separating mixed multi-component signal with an application in mechanical watch movement
abstract: This paper presents a method to combine signal decomposition with blind signal separation for separating one-dimensional mixed multi-component signal of mechanical watch movement. The method consists of three steps. First, a multi-component signal is decomposed into a set of redundant signals, called pseudo multi-channel mixtures, using the continuous wavelet transform (CWT). Then, independent component analysis (ICA) is used to acquire the independent components. Finally, a correlation criterion is applied to automatically select the source components. The new method can effectively separate a multi-component signal into a series of independent components corresponding to different sources. The effectiveness of this method is demonstrated by means of a computer simulation example. And the proposed method is applied for analyzing and diagnosing mechanical watch movements. It is found that the separated source components effectively reveal the insight of the mechanical watch movement, and can be used for fault diagnosis.

title: Iterative Phase Estimation for the Synthesis of Separated Sources From Single-Channel Mixtures
abstract: In this letter, we propose a novel method of refining the time-domain synthesis of individual source estimates from a single channel mixture. Employing a closed-loop architecture, the algorithm refines the synthesis of each source by iteratively estimating the phase of the sources, given the estimates of the source magnitude spectra and a single channel time-domain mixture. The performance of the algorithm is evaluated for harmonic musical mixtures, and considerable improvements to the synthesized estimates are obtained relative to phase binary masking, given accurate source magnitude spectra.

title: OneMicr ophoneSourceSeparation SamT
abstract: Sourceseparation, or computationalauditorysceneanalysis,attemptsto extract individual acousticobjectsfrom input which containsa mixtureof soundsfrom different sources,alteredby the acousticenvironment. Unmixing algorithms suchasICA andits extensionsrecover sourcesby reweightingmultiple obser vationsequences, andthuscannotoperatewhenonly a singleobservationsignal is available. I presenta techniquecalled refiltering which recoverssourcesby a nonstationaryreweighting(“masking”) of frequency sub-bandsfrom a single recording,andarguefor theapplicationof statisticalalgorithmsto learningthis maskingfunction. I presentresultsof a simple factorial HMM systemwhich learnsonrecordingsof singlespeakersandcanthenseparatemixturesusingonly oneobservationsignalby computingthemaskingfunctionandthenrefiltering. 1 Learning fr om data in computational auditory sceneanalysis Imaginelisteningto many pianosbeingplayedsimultaneously . If eachpianistwerestriking keys randomlyit would be very difficult to tell which notecamefrom which piano. But if eachwere playing a coherentsong,separationwould be much easierbecauseof the structureof music. Now imagineteachinga computerto do theseparationby showing it many musicalscoresas“training data”. Typical auditoryperceptual input containsa mixtureof soundsfrom differentsources,alteredby theacousticenvironment.Any biological or artificial hearingsystemmust extract individual acousticobjectsor streamsin order to do successfulocalization,denoisingandrecognition. calledthis process auditorysceneanalysisin analogyto vision. Sourceseparation, or computationalauditory sceneanalysis(CASA) is the practicalrealizationof this problemvia computeranalysis of microphonerecordingsandis very similar to the musicaltaskdescribedabove. It has beeninvestigatedby researchgroupswith differentemphases. TheCASA communityhave focusedon bothmultiple andsinglemicrophonesourceseparationproblemsunderhighly realistic acousticconditions,but have usedalmost exclusively hand designedsystems which includesubstantial knowledgeof thehumanauditorysystemandits psychophysical characteristics(e.g.[2,3]). Unfortunately, it is difficult to incorporatelarge amountsof detailedstatisticalknowledgeabout the problem into suchan approach. On the other hand,machinelearningresearchers, especiallythoseworking on independent components analysis(ICA) andrelatedalgorithms,have focusedon thecaseof multiple microphones in simplified mixing environmentsandhave usedpowerful “blind” statisticaltechniques. These“unmixing” algorithms(even thosewhich attemptto recover more sourcesthan signals)cannotoperateonsinglerecordings.Furthermore, sincethey oftendependonly on thejoint amplitudehistogramof theobservationsthey canbeverysensiti veto thedetailsof filtering andreverberationin theenvironment.Thegoalof thispaperis to bringtogetherthe robust representations of CASA andmethodswhich learnfrom datato solve a restricted versionof the sourceseparationproblem– isolatingacousticobjectsfrom only a single microphonerecording. 2 Refiltering vs. unmixing Unmixingalgorithmsreweightmultiplesimultaneousrecordings (genericallycalled microphones)to form anew sourceobject :

title: Automatic extraction and forecast of time series cyclic components within the framework of SSA
abstract: Application of Singular Spectrum Analysis (SSA) for the purpose of extracting and forecasting time series cyclic components is considered. Automatic methods of identiflcation are applied within the framework of SSA. Their suitability for the class of exponentially modulated harmonic components is numerically investigated.

title: Fast QR factorization of Vandermonde matrices
abstract: We introduce a fast algorithm for computing the QR factors of a complex column Vandermonde matrix V . The complexity of the algorithm is 5 mn +7 n 2 /2+ O ( m ), where m is the number of rows in V and n is the number of columns (we assume that m > n ). The matrices Q and R may be computed independently if desired. Two special cases for the row Vandermonde matrix (with real elements, or unit magnitude elements) are also studied, and similar results are obtained.

title: Blind Source Separation Using Temporal Predictability
abstract: A measure of temporal predictability is defined and used to separate linear mixtures of signals. Given any set of statistically independent source signals, it is conjectured here that a linear mixture of those signals has the following property: the temporal predictability of any signal mixture is less than (or equal to) that of any of its component source signals. It is shown that this property can be used to recover source signals from a set of linear mixtures of those signals by finding an un-mixing matrix that maximizes a measure of temporal predictability for each recovered signal. This matrix is obtained as the solution to a generalized eigenvalue problem; such problems have scaling characteristics of O (N3), where N is the number of signal mixtures. In contrast to independent component analysis, the temporal predictability method requires minimal assumptions regarding the probability density functions of source signals. It is demonstrated that the method can separate signal mixtures in which each mixture is a linear combination of source signals with supergaussian, sub-gaussian, and gaussian probability density functions and on mixtures of voices and music.

title: Unsupervised decomposition of low-intensity low-dimensional multi-spectral fluorescent images for tumour demarcation
abstract: Unsupervised decomposition of static linear mixture model (SLMM) with ill-conditioned basis matrix and statistically dependent sources is considered. Such situation arises when low-dimensional low-intensity multi-spectral image of the tumour in the early stage of development is represented by the SLMM, wherein tumour is spectrally similar to the surrounding tissue. The original contribution of this paper is in proposing an algorithm for unsupervised decomposition of low-dimensional multi-spectral image for high-contrast tumour visualisation. It combines nonlinear band generation (NBG) and dependent component analysis (DCA) that itself combines linear pre-processing transform and independent component analysis (ICA). NBG is necessary to improve conditioning of the extended mixing matrix in the SLMM, while DCA is necessary to increase statistical independence between spectrally similar sources. We demonstrate good performance of the method on both computational model and experimental low-intensity red-green-blue fluorescent image of the surface tumour (basal cell carcinoma). We believe that presented method can be of use in other multi-channel medical imaging systems.

title: Non-negative Matrix Factorization with Sparseness Constraints
abstract: Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in parts-based representations. In this paper, we show how explicitly incorporating the notion of 'sparseness' improves the found decompositions. Additionally, we provide complete MATLAB code both for standard NMF and for our extension. Our hope is that this will further the application of these methods to solving novel data-analysis problems.

title: Sparse nonnegative matrix factorization with ℓ0-constraints
abstract: Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the ℓ1-norm of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the ℓ0-pseudo-norm. In this paper, we propose a framework for approximate NMF which constrains the ℓ0-norm of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches.

title: Unsupervised segmentation of low-contrast multichannel images: discrimination of tissue components in microscopic images of unstained specimens
abstract: Low-contrast images, such as color microscopic images of unstained histological specimens, are composed of objects with highly correlated spectral profiles. Such images are very hard to segment. Here, we present a method that nonlinearly maps low-contrast color image into an image with an increased number of non-physical channels and a decreased correlation between spectral profiles. The method is a proof-of-concept validated on the unsupervised segmentation of color images of unstained specimens, in which case the tissue components appear colorless when viewed under the light microscope. Specimens of human hepatocellular carcinoma, human liver with metastasis from colon and gastric cancer and mouse fatty liver were used for validation. The average correlation between the spectral profiles of the tissue components was greater than 0.9985, and the worst case correlation was greater than 0.9997. The proposed method can potentially be applied to the segmentation of low-contrast multichannel images with high spatial resolution that arise in other imaging modalities.