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Innovation Modeling

Investigators: Pouya Dehghani Tafti

Introduction

Innovation modeling is a framework for constructing stochastic representations of phenomena, where it is assumed that, at a fundamental level, the phenomenon under investigation is composed of independent atoms of randomness or "innovations" that go through a process of "mixing". In certain cases, the assumption of independence in such models may be derived from physical considerations but, most often, it is based on the level of complexity one is willing or able to incorporate in the model while meeting computational and/or analytical limitations. In any case, this modeling principle can be employed in order to interpret, guide, and inform the design of schemes and algorithms for treating data obtained from observation, with applications in many areas of science and engineering including biomedical imaging and reconstruction.

Goal

The goal of this project is to develop new models for biomedical images in the above-mentioned framework, and to explore and identify their connections with existing image-processing schemes and algorithms as well as their implications for designing improved algorithms for image reconstruction and analysis.

Collaborations: Michael Unser

Period: 2009-ongoing

Major Publications

[1] 

M. Unser, P.D. Tafti, "Stochastic Models for Sparse and Piecewise-Smooth Signals," IEEE Transactions on Signal Processing, vol. 59, no. 3, pp. 989-1006, March 2011.

[2] 

P.D. Tafti, M. Unser, "Fractional Brownian Vector Fields," Multiscale Modeling & Simulation, vol. 8, no. 5, pp. 1645-1670, 2010.

[3] 

P.D. Tafti, D. Van De Ville, M. Unser, "Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes," IEEE Transactions on Image Processing, vol. 18, no. 4, pp. 689-702, April 2009.

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