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December 20, 2017


Wednesday, December 20, 2017

Biostatistics Help: Faculty, Staff, Pre-MD and Post Doc Walk-In Clinic
11:00 AM - 12:00 PM

Biostatistics consulting is available to all Johns Hopkins University faculty, staff, pre-MD and post docs conducting clinical and translational research. 11:00 AM – 12:00 PM Wolfe Street Building Room: E3142 Contact Information: Nita James |
Valeriya Naumova "Multi-parameter regularisation for solving unmixing problems in signal processing"
3:00 PM - 4:00 PM


Speaker: Valeriya Naumova, Simula Research Laboratory (Simula) Title: Multi-parameter regularisation for solving unmixing problems in signal processing: theoretical and practical aspects Abstract: Motivated by real-life applications in signal processing and image analysis, where the quantity of interest is generated by several sources to be accurately modelled and separated, as well as by recent advances in sparse regularisation theory and optimisation, we present a theoretical and algorithmic framework for optimal support recovery in inverse problems of unmixing type by means of multi-penalty regularisation. While multi-penalty regularisation is not a novel technique [1], we aim at providing precise reconstruction guarantees and methods for adaptive regularisation parameter choice. We consider and analyse a regularisation functional composed of a data-fidelity term, where signal and noise are additively mixed, a non-smooth, convex, sparsity promoting term, and a convex penalty term to model the noise. We prove not only that the well-established theory for sparse recovery in the single parameter case can be translated to the multi-penalty settings, but we also demonstrate the enhanced properties of multi-penalty regularisation in terms of support identification compared to sole ℓ1-minimisation. Extending the notion of Lasso path algorithm, we additionally propose an efficient procedure for an adaptive parameter choice in multi-penalty regularisation, focusing on the recovery of the correct support of the solution. The approach essentially enables a fast construction of a tiling over the parameter space in such a way that each tile corresponds to a different sparsity pattern of the solution. Finally, we propose an iterative alternating algorithm based on simple iterative thresholding steps to perform the minimisation of the extended multi-penalty functional, containing non-smooth and non-convex sparsity promoting term. To exemplify the robustness and effectiveness of the multi-penalty framework, we provide an extensive numerical analysis of our method and compare it with state-of-the-art single-penalty algorithms for compressed sensing problems. This is joint work with Markus Grasmair [3, 4], Norwegian University of Science and Technology; Timo Klock [4], Simula Research Laboratory, and Johannes Maly and Steffen Peter [2], Technical University of Munich. iscuss a particular interest in medicine — extracting hidden dynamics from a single observed time series composed of multiple oscillatory signals, which could be viewed as a single-channel blind source separation problem. This problem is common nowadays due to the popular mobile health monitoring devices, and is made challenging by the structure of the signal which consists of non-sinusoidal oscillations with time varying amplitude/frequency, and by the heteroscedastic nature of the noise. Inspired by the fetal electrocardiogram (ECG) signal analysis from the single lead maternal abdominal ECG signal, in this talk I will discuss some new data analysis tools, including the cepstrum-based nonlinear-type time-frequency analysis and fiber-bundle based manifold learning technique. In addition to showing the results in fetal ECG analysis, I will also show how the approach could be applied to simultaneously extract the instantaneous heart/respiratory rate from a PPG signal during exercise. If time permits, the clinical trial results will be discussed.Abstract: Some Data Analysis Tools Inspired by Medical Challenges — Fetal ECG as an example

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