Learning parametric dictionaries for graph signals

In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary. In this work, we propose a parametric dictionary learning algorithm to design data-adapted, structured dictionaries that sparsely represent graph signals. In particular, we model graph signals as combinations of overlapping local patterns. We impose the constraint that each dictionary is a concatenation of subdictionaries, with each subdictionary being a polynomial of the graph Laplacian matrix, representing a single pattern translated to different areas of the graph. The learning algorithm adapts the patterns to a training set of graph signals. Experimental results on both synthetic and real datasets demonstrate that the dictionaries learned by the proposed algorithm are competitive with and often better than unstructured dictionaries learned by state-of-the-art numerical learning algorithms in terms of sparse approximation of graph signals. In contrast to the unstructured dictionaries, however, the dictionaries learned by the proposed algorithm feature localized atoms and can be implemented in a computationally efficient manner in signal processing tasks such as compression, denoising, and classification

Chebyshev Polynomial Approximation for Distributed Signal Processing

Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals collected by sensor networks. The proposed method features approximations of the graph Fourier multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We demonstrate how the proposed method can be used in a distributed denoising task, and show that the communication requirements of the method scale gracefully with the size of the network.Comment: 8 pages, 5 figures, to appear in the Proceedings of the IEEE International Conference on Distributed Computing in Sensor Systems (DCOSS), June, 2011, Barcelona, Spai

Energy-Efficient Transmission Scheduling with Strict Underflow Constraints

We consider a single source transmitting data to one or more receivers/users over a shared wireless channel. Due to random fading, the wireless channel conditions vary with time and from user to user. Each user has a buffer to store received packets before they are drained. At each time step, the source determines how much power to use for transmission to each user. The source's objective is to allocate power in a manner that minimizes an expected cost measure, while satisfying strict buffer underflow constraints and a total power constraint in each slot. The expected cost measure is composed of costs associated with power consumption from transmission and packet holding costs. The primary application motivating this problem is wireless media streaming. For this application, the buffer underflow constraints prevent the user buffers from emptying, so as to maintain playout quality. In the case of a single user with linear power-rate curves, we show that a modified base-stock policy is optimal under the finite horizon, infinite horizon discounted, and infinite horizon average expected cost criteria. For a single user with piecewise-linear convex power-rate curves, we show that a finite generalized base-stock policy is optimal under all three expected cost criteria. We also present the sequences of critical numbers that complete the characterization of the optimal control laws in each of these cases when some additional technical conditions are satisfied. We then analyze the structure of the optimal policy for the case of two users. We conclude with a discussion of methods to identify implementable near-optimal policies for the most general case of M users.Comment: 109 pages, 11 pdf figures, template.tex is main file. We have significantly revised the paper from version 1. Additions include the case of a single receiver with piecewise-linear convex power-rate curves, the case of two receivers, and the infinite horizon average expected cost proble

A Multiscale Pyramid Transform for Graph Signals

Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric structure of the underlying graph data domain. In this paper, we adapt the Laplacian pyramid transform for signals on Euclidean domains so that it can be used to analyze high-dimensional data residing on the vertices of a weighted graph. Our approach is to study existing methods and develop new methods for the four fundamental operations of graph downsampling, graph reduction, and filtering and interpolation of signals on graphs. Equipped with appropriate notions of these operations, we leverage the basic multiscale constructs and intuitions from classical signal processing to generate a transform that yields both a multiresolution of graphs and an associated multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure

Effect of cell density on thrombin binding to a specific site on bovine vascular endothelial cells.

We studied thrombin binding to proliferating and confluent endothelial cells derived from bovine vascular endothelium. [125]thrombin was incubated with nonconfluent or confluent endothelial cells and both the total amount bound and the amount linked in a 77,000-dalton thrombin-cell complex were determined. Approximately 230,000 molecules of thrombin bound per cell in nonconfluent cultures compared to 12,800 molecules per cell in confluent cultures. Approximately 67,7000 thrombin molecules were bound in an apparently covalent complex, Mr = 77,000, with each cell in sparse cultures, whereas only 4,600 thrombin molecules per cell were bound in this complex with confluent cultures. Similar studies with [125I]thrombin and endothelial cells derived from bovine cornea revealed no difference either in the total amount of thrombin bound or in the amount bound in the 77,000-dalton complex using sparse or confluent cultures. When confluent vascular endothelial cultures were wounded, additional cellular binding sites for the 77,000-dalton complex with thrombin appeared within 24 h. A 237% increase in the amount of thrombin bound to these sites was induced by a wound which resulted in a 20% decrease in cell number in the monolayer. There was no significant increase in thrombin binding to other cellular sites at 24 h. These experiments provide evidence that the first change in thrombin binding after injury is an increase in the cellular sites involved in the 77,000-dalton complex, and suggest that thrombin binding to endothelial cells may be important in the vascular response to injury

Concert recording 2018-03-13

[Track 1]. The rovin\u27 gambler [Track 2].Gambler, don\u27t you lose your place The gambler\u27s lament / John Jacob Niles -- [Track 3]. Immortality [Track 4]. Serenity Religion / Charles Ives -- [Track 5]. Old American songs, first set. 1. The boatman\u27s dance (Minstrel song - 1843) [Track 6]. 2. The dodger (Campaign song) [Track 7]. 3. Long time ago (Ballad) [Track 8]. 4. Simple gifts (Shaker song) [Track 9]. 5. I bought me a cat (Children\u27s song) / Aaron Copland -- [Track 10]. Three songs, op. 45. 1. Now have I fed and eaten up the rose (James Joyce) [Track 11]. 2. A green lowland of pianos (Czeslaw Milosz) [Track 12]. 3. O boundless, boundless evening (Christopher Middleton) / Samuel Barber -- [Track 13]. Five Walt Whitman poems. O you whom I often and silently come [Track 14]. Sometimes with one I love [Track 15]. Gliding o\u27er all [Track 16]. Look down, fair moon [Track 17]. Gods / Ned Rorem -- [Track 18]. Four encore songs. 1. Tobacco (Graham Lee Hemingher) [Track 19]. 2. A flea and a fly (Anonymous) [Track 20]. 3. Come, come , said Tom\u27s father (Thomas Moore) [Track 21]. 4. Song of the open road (Ogden Nash) / Florence B. Price

Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames

We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph wavelet constructions are only adapted to the length of the spectrum, the filters proposed in this paper are adapted to the distribution of graph Laplacian eigenvalues, and therefore lead to atoms with better discriminatory power. Our approach is to first characterize a family of systems of uniformly translated kernels in the graph spectral domain that give rise to tight frames of atoms generated via generalized translation on the graph. We then warp the uniform translates with a function that approximates the cumulative spectral density function of the graph Laplacian eigenvalues. We use this approach to construct computationally efficient, spectrum-adapted, tight vertex-frequency and graph wavelet frames. We give numerous examples of the resulting spectrum-adapted graph filters, and also present an illustrative example of vertex-frequency analysis using the proposed construction

Families of spectral sets for Bernoulli convolutions

In this paper, we study the harmonic analysis of Bernoulli measures. We show a variety of orthonormal Fourier bases for the L^2 Hilbert spaces corresponding to certain Bernoulli measures, making use of contractive transfer operators. For other cases, we exhibit maximal Fourier families that are not orthonormal bases.Comment: 25 pages, same result