DOI

We consider a deconvolution problem with a random noise. The noise is a product of a Gaussian stationary random process by a weight function εh ∈ L2(R1) with constant ε > 0. We study the asymptotically minimax and Bayes settings (ε → 0). In the minimax model a priori information is given that the solution belongs to a ball in Sobolev space W2β(R1). For such a priori information we find an asymptotically minimax estimator of the solution. In the Bayes setting the noise is the same. The solution is a realization of a random process defined as a product of a Gaussian stationary random process by a weight function h1 ∈ L2(R1). We show that the standard Wiener filters remain asymptotically Bayes estimators for this modification of Wiener filtration. The introduction of weight functions h, h1 ∈ L2(R1) is the main difference from the standard settings. This allows us not to make the traditional assumptions that the powers of noise and solutions are infinite or tend to infinity.

Язык оригиналаанглийский
Страницы (с-по)1339-1359
Число страниц21
ЖурналInverse Problems
Том19
Номер выпуска6
DOI
СостояниеОпубликовано - дек 2003

    Предметные области Scopus

  • Теоретические компьютерные науки
  • Обработка сигналов
  • Математическая физика
  • Прикладные компьютерные науки
  • Прикладная математика

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