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We consider the recovery of degraded videos without complete knowledge about the degradation. A spatially shift-invariant but temporally shift-varying video formation model is used. This leads to a simple multiframe degradation model that relates each original video frame with multiple observed frames and point spread functions (PSFs). We propose a variational method that simultaneously reconstructs each video frame and the associated PSFs from the corresponding observed frames. Total variation (TV) regularization is used on both the video frames and the PSFs to further reduce the ill-posedness and to better preserve edges. In order to make TV minimization practical for video sequences, we propose an efficient splitting method that generalizes some recent fast single-image TV minimization methods to the multiframe case. Both synthetic and real videos are used to show the performance of the proposed method. OCIS codes: 100.1455, 100.3020, 110.4155, 150.1135.

A total variation-based model with a non-negativity constraint is used for examining image deblurring problems. Findings reveal the speed, accuracy and effectiveness of the model in solving image deblurring problems.

Density-based clustering has the advantages for 1) allowing arbitrary shape of cluster and 2) hot requiring the number of clusters as input. However, when clusters touch each other, both the cluster centers and cluster boundaries (as the peaks and valleys of the density distribution) become fuzzy and difficult to determine. We introduce the notion of cluster intensity function (CIF) which captures the important characteristics of clusters. When clusters are well-separated, CIFs are similar to density functions. But, when clusters become closed to each other, CIFs still clearly reveal cluster centers, cluster boundaries, and degree of membership of each data point to the cluster that it belongs. Clustering through bump hunting and valley seeking based on these functions are more robust than that based on density functions obtained by kernel density estimation, which are often oscillatory or oversmoothed. These problems of kernel density estimation are resolved using Level Set Methods and related techniques. Comparisons with two existing density-based methods, valley seeking and DBSCAN, are presented which illustrate the advantages of our approach. Index Terms--Dynamic clustering, level set methods, cluster intensity functions, kernel density estimation, duster contours, partial differential equations.

Abstract Background Network methods are increasingly used to represent the interactions of genes and/or proteins. Genes or proteins that are directly linked may have a similar biological function or may be part of the same biological pathway. Since the information on the connection (adjacency) between 2 nodes may be noisy or incomplete, it can be desirable to consider alternative measures of pairwise interconnectedness. Here we study a class of measures that are proportional to the number of neighbors that a pair of nodes share in common. For example, the topological overlap measure by Ravasz et al. 1 can be interpreted as a measure of agreement between the m = 1 step neighborhoods of 2 nodes. Several studies have shown that two proteins having a higher topological overlap are more likely to belong to the same functional class than proteins having a lower topological overlap. Here we address the question whether a measure of topological overlap based on higher-order neighborhoods could give rise to a more robust and sensitive measure of interconnectedness. Results We generalize the topological overlap measure from m = 1 step neighborhoods to m ≥ 2 step neighborhoods. This allows us to define the m-th order generalized topological overlap measure (GTOM) by (i) counting the number of m-step neighbors that a pair of nodes share and (ii) normalizing it to take a value between 0 and 1. Using theoretical arguments, a yeast co-expression network application, and a fly protein network application, we illustrate the usefulness of the proposed measure for module detection and gene neighborhood analysis. Conclusion Topological overlap can serve as an important filter to counter the effects of spurious or missing connections between network nodes. The m-th order topological overlap measure allows one to trade-off sensitivity versus specificity when it comes to defining pairwise interconnectedness and network modules.