Agenda

Signal Processing Seminar

Thomas Sherson

Thomas is going to present his recent research.

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Signal Processing Seminar

Electromagnetic 3D anisotropic imaging in the model reduction framework

Jörn Zimmerling
T.U. Delft

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Signal Processing Seminar

Signal Processing on Kernel-based Random Graphs

Matthew Morency

We present the theory of sequences of random graphs and their convergence to limit objects. Sequences of random dense graphs are shown to converge to their limit objects in both their structural properties and their spectra. The limit objects are bounded symmetric functions on $[0,1]^2$. The kernel functions define an equivalence class and thus identify collections of large random graphs who are spectrally and structurally equivalent. As the spectrum of the graph shift operator defines the graph Fourier transform (GFT), the behavior of the spectrum of the underlying graph has a great impact on the design and implementation of graph signal processing operators such as filters. The spectra of several graph limits are derived analytically and verified with numerical examples.

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Signal Processing Seminar

Rethinking Sketching as Sampling: A Graph Signal Processing Approach

Fernando Gama

Sampling of bandlimited graph signals has well-documented merits for dimensionality reduction, affordable storage, and online processing of streaming network data. Most existing sampling methods are designed to minimize the error incurred when reconstructing the original signal from its samples. Oftentimes these parsimonious signals serve as inputs to computationally-intensive linear operator (e.g., graph filters and transforms). Hence, interest shifts from reconstructing the signal itself towards instead approximating the output of the prescribed linear operator efficiently.

In this context, we propose a novel sampling scheme that leverages the bandlimitedness of the input as well as the transformation whose output we wish to approximate. We formulate problems to jointly optimize sample selection and a sketch of the target linear transformation, so when the latter is affordably applied to the sampled input signal the result is close to the desired output. These designs are carried out off line, and several heuristic (sub)optimal solvers are proposed to accommodate high-dimensional problems, especially when computational resources are at a premium.

Similar sketching as sampling ideas are also shown effective in the context of linear inverse problems. The developed sampling plus reduced-complexity processing pipeline is particularly useful for streaming data, where the linear transform has to be applied fast and repeatedly to successive inputs or response signals.

Numerical tests show the effectiveness of the proposed algorithms in classifying handwritten digits from as few as 20 out of 784 pixels in the input images, as well as in accurately estimating the frequency components of bandlimited graph signals sampled at few nodes.

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