Publication

Reconstruction Of Biomedical Images And Sparse Stochastic Modeling

Michaël Unser, Emrah Bostan, Ulugbek Kamilov
2012
Conference Papers

Abstract

We propose a novel statistical formulation of the image-reconstruction problem from noisy linear measurements. We derive an extended family of MAP estimators based on the theory of continuous-domain sparse stochastic processes. We highlight the crucial roles of the whitening operator and of the Levy exponent of the innovations which controls the sparsity of the model. While our family of estimators includes the traditional methods of Tikhonov and total-variation (TV) regularization as particular cases, it opens the door to a much broader class of potential functions (associated with infinitely divisible priors) that are inherently sparse and typically nonconvex. We also provide an algorithmic scheme-naturally suggested by our framework-that can handle arbitrary potential functions. Further, we consider the reconstruction of simulated MRI data and illustrate that the designed estimators can bring significant improvement in reconstruction performance.

Official source

https://infoscience.epfl.ch/entities/publication/e5da3cff-aeeb-4289-9e14-41e749f4eea0

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Michaël Unser, Emrah Bostan, Ulugbek Kamilov
2012
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/e5da3cff-aeeb-4289-9e14-41e749f4eea0

About this result

Related concepts (19)

Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values.

Bias of an estimator

In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an property of an estimator. Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased; see bias versus consistency for more.

Robust statistics

Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a parametric distribution.

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