Bilateral Filter: Graph Spectral Interpretation and Extensions

In this paper we study the bilateral filter proposed by Tomasi and Manduchi, as a spectral domain transform defined on a weighted graph. The nodes of this graph represent the pixels in the image and a graph signal defined on the nodes represents the intensity values. Edge weights in the graph correspond to the bilateral filter coefficients and hence are data adaptive. Spectrum of a graph is defined in terms of the eigenvalues and eigenvectors of the graph Laplacian matrix. We use this spectral interpretation to generalize the bilateral filter and propose more flexible and application specific spectral designs of bilateral-like filters. We show that these spectral filters can be implemented with k-iterative bilateral filtering operations and do not require expensive diagonalization of the Laplacian matrix

Perfect Reconstruction Two-Channel Wavelet Filter-Banks for Graph Structured Data

In this work we propose the construction of two-channel wavelet filterbanks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph. These graph based functions are referred to as graph-signals as we build a framework in which many concepts from the classical signal processing domain, such as Fourier decomposition, signal filtering and downsampling can be extended to graph domain. Especially, we observe a spectral folding phenomenon in bipartite graphs which occurs during downsampling of these graphs and produces aliasing in graph signals. This property of bipartite graphs, allows us to design critically sampled two-channel filterbanks, and we propose quadrature mirror filters (referred to as graph-QMF) for bipartite graph which cancel aliasing and lead to perfect reconstruction. For arbitrary graphs we present a bipartite subgraph decomposition which produces an edge-disjoint collection of bipartite subgraphs. Graph-QMFs are then constructed on each bipartite subgraph leading to "multi-dimensional" separable wavelet filterbanks on graphs. Our proposed filterbanks are critically sampled and we state necessary and sufficient conditions for orthogonality, aliasing cancellation and perfect reconstruction. The filterbanks are realized by Chebychev polynomial approximations.Comment: 32 pages double spaced 12 Figures, to appear in IEEE Transactions of Signal Processin

Multi-dimensional separable critically sampled wavelet filterbanks on arbitrary graphs

In our previous work, we observed an “aliasing ” phenomenon for functions defined on bipartite graphs which is analogous to aliasing occurring in the downsampling of regular 1-dimensional signals. We exploited these concepts to design critically sampled two-channel wavelet filterbanks for any bipartite graph. For arbitrary graphs, we proposed a bipartite subgraph decomposition scheme to decompose the graph into edge-disjoint bipartite subgraphs and apply filtering and downsampling separately on each subgraph. This leads to the design of multi-dimensional separable filterbanks on graphs. In this paper, we study these bipartite decompositions in more detail. In par-ticular, we describe the meaning of dimensionality in the subgraph decomposition of arbitrary graphs and define some graph based met-rics based on this understanding. Subsequently, we propose a heuris-tics based algorithm for bipartite subgraph decomposition and com-pare it with other non-optimized algorithms. The results show both qualitative and quantitative improvements in the decomposed bipar-tite subgraphs with the proposed heuristics. Index Terms—Nyquist theorem, bipartite graphs, subsampling 1

Distributed Transforms for Efficient Data Gathering in Sensor Networks

Devices, systems, and techniques for data collecting network such as wireless sensors are disclosed. A described technique includes detecting one or more remote nodes included in the wireless sensor network using a local power level that controls a radio range of the local node. The technique includes transmitting a local outdegree. The local outdegree can be based on a quantity of the one or more remote nodes. The technique includes receiving one or more remote outdegrees from the one or more remote nodes. The technique includes determining a local node type of the local node based on detecting a node type of the one or more remote nodes, using the one or more remote outdegrees, and using the local outdegree. The technique includes adjusting characteristics, including an energy usage characteristic and a data compression characteristic, of the wireless sensor network by selectively modifying the local power level and selectively changing the local node type

Ruptured tubal pregnancy in an undiagnosed heterotopic pregnancy

Heterotopic pregnancy is rare obstetrical emergency the diagnosis of which is usually delayed. A high degree of suspicion is required to diagnose to reduce maternal morbidity and mortality. At the same time salvage of the intrauterine pregnancy can be done

ECMO: a lifesaving modality in ARDS during puerperium

Acute respiratory distress syndrome (ARDS) is an uncommon condition encountered in pregnancy. The incidence of ARDS in pregnancy has been reported to be 1 in 6229 deliveries with mortality rates to range from 24% to 39% in pregnant patients. An essential component in management of ARDS involves good communication between the obstetrics team and critical care specialist and a fundamental understanding of mechanical ventilatory support. In critically ill patients where both cardiorespiratory support is required, Extracorporeal Membrane Oxygenation (ECMO) can be used to help maintain the vital functions. ECMO is a temporary cardio respiratory or respiratory support in critically ill patients who are unresponsive to conventional management.  In present case a young female with post-partum ARDS was successfully managed with extra corporeal membrane oxygenation (ECMO)

Lifting Based Wavelet Transforms on Graphs

We present a novel method to implement lifting based wavelet transforms on general graphs. The detail and approximation coefficients computed from this graph transform can be interpreted similarly to their counterparts in standard signal processing process. Our approach is based on partitioning all nodes in the graph into two sets, containing "even" and "odd" nodes, respectively. Then, as in standard lifting, nodes of one parity are used to predict/update those of the other. We discuss the even-odd assignment problem on the graph and provide a solution that is well suited to construct the transform. As an example we discuss how our transform could be used in a denoising application.APSIPA ASC 2009: Asia-Pacific Signal and Information Processing Association, 2009 Annual Summit and Conference. 4-7 October 2009. Sapporo, Japan. Poster session: Signal Processing Theory and Methods I (6 October 2009)