Publication

MAP Estimators for Self-Similar Sparse Stochastic Models

Michaël Unser, Emrah Bostan, Julien René Pierre Fageot, Ulugbek Kamilov
2013
Conference Papers

Abstract

We consider the reconstruction of multi-dimensional signals from noisy samples. The problem is formulated within the framework of the theory of continuous-domain sparse stochastic processes. In particular, we study the fractional Laplacian as the whitening operator specifying the correlation structure of the model. We then derive a class of MAP estimators where the priors are confined to the family of infinitely divisible distributions. Finally, we provide simulations where the derived estimators are compared against total-variation (TV) denoising.

Official source

https://infoscience.epfl.ch/entities/publication/218483a8-fad5-48b9-bbb5-df1dcdabd99e

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Michaël Unser, Emrah Bostan, Julien René Pierre Fageot, Ulugbek Kamilov
2013
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/218483a8-fad5-48b9-bbb5-df1dcdabd99e

About this result

Related concepts (24)

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.

M-estimator

In statistics, M-estimators are a broad class of extremum estimators for which the objective function is a sample average. Both non-linear least squares and maximum likelihood estimation are special cases of M-estimators. The definition of M-estimators was motivated by robust statistics, which contributed new types of M-estimators. However, M-estimators are not inherently robust, as is clear from the fact that they include maximum likelihood estimators, which are in general not robust.

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.

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