Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace representation by constructing affinity matrix shared among all views. Relying on the importance of both low-rank and sparsity constraints in the construction of the affinity matrix, we introduce the objective that balances between the agreement across different views, while at the same time encourages sparsity and low-rankness of the solution. Related low-rank and sparsity constrained optimization problem is for each view solved using the alternating direction method of multipliers. Furthermore, we extend our approach to cluster data drawn from nonlinear subspaces by solving the corresponding problem in a reproducing kernel Hilbert space. The proposed algorithm outperforms state-of-the-art multi-view subspace clustering algorithms on one synthetic and four real-world datasets.

Abstract-Accurate lung tumor delineation plays an important role in radiotherapy treatment planning. Since the lung tumor has poor boundary in PET images and low contrast in CT images, segmentation of tumor in PET and CT images is a challenging task. In this study, we effectively integrate the two modalities by making fully use of the superior contrast of PET images and superior spatial resolution of CT images. Random walk and graph cut method are integrated to solve the segmentation problem, in which random walk is utilized as an initialization tool to provide object seeds for graph cut segmentation on PET and CT images. The co-segmentation problem is formulated as an energy minimization problem which is solved by max-flow/min-cut method. A graph includes two sub-graphs and a special link is constructed, in which one sub-graph is for PET and another is for CT, and the special link encodes a context term which penalizes the difference of the tumor segmentation on the two modalities. To fully utilize the characteristics of PET and CT images, a novel energy representation is devised. For PET, a downhill cost and a 3D derivative cost is proposed. For CT, a shape penalty cost is integrated into the region and boundary function which helps constrain the tumor location during the segmentation. We validate our algorithm on a dataset which consists of 18 PET-CT images. The experimental results indicate the proposed method is superior to the graph cut method solely using the PET or CT is more accurate compared with the random walk method, random walk co-segmentation method, and non-improved graph-cut method.Index Terms-Image segmentation, interactive segmentation, graph cut, random walks, prior information, lung tumor, positron emission tomography (PET), computed tomography (CT).

No abstract

Sparse Component Analysis (SCA) is demonstrated for blind extraction of three pure component spectra from only two measured mixed spectra in 13 C and 1 H nuclear magnetic resonance (NMR) spectroscopy. This appears to be the first time to report such results and that is the first novelty of the paper. Presented concept is general and directly applicable to experimental scenarios that possibly would require use of more than two mixtures. However, it is important to emphasize that number of required mixtures is always less than number of components present in these mixtures. The second novelty is formulation of blind NMR spectra decomposition exploiting sparseness of the pure components in the wavelet basis defined by either Morlet or Mexican hat wavelet. This enabled accurate estimation of the concentration matrix and number of pure components by means of data clustering algorithm and pure components § Patent pending under the number PCT/HR2008/000037. 2 spectra by means of linear programming with constraints from both 1 H and 13 C NMR experimental data.The third novelty is capability of proposed method to estimate number of pure components in demanding underdetermined blind source separation (uBSS) scenario. This is in contrast to majority of the BSS algorithms that assume this information to be known in advance. Presented results are important for the NMR spectroscopy-associated data analysis in pharmaceutical industry, medicine diagnostics and natural products research.

A single-frame multichannel blind image deconvolution technique has been formulated recently as a blind source separation problem solved by independent component analysis (ICA). The attractive feature of this approach is that neither origin nor size of the spatially invariant blurring kernel has to be known. To enhance the statistical independence among the hidden variables, we employ multiscale analysis implemented by wavelet packets and use mutual information to locate a subband with the least dependent components, where the basis matrix is learned by means of standard ICA. We show that the proposed algorithm is capable of performing blind deconvolution of nonstationary signals that are not independent and identically distributed processes. The image poses these properties. The algorithm is tested on experimental data and compared with state-of-the-art single-frame blind image deconvolution algorithms. Our good experimental results demonstrate the viability of the proposed concept.