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In this article, the solution of a statistical inverse problem M = AU + E by the Bayesian approach is studied where U is a function on the unit circle T, i.e., a periodic signal. The mapping A is a smoothing linear operator and E a Gaussian noise. The connection to the solution of a finite-dimensional computational model M kn = A k Un +E k is discussed.(More)
The Bayesian methods for linear inverse problems is studied using hierarchical Gaus-sian models. The problems are considered with different discretizations, and we analyze the phenomena which appear when the discretization becomes finer. A hierarchical solution method for signal restoration problems is introduced and studied with arbitrarily fine(More)
A frequency dependent preconditioned wavelet method for atmospheric tomography Powered by TCPDF (www.tcpdf.org) Abstract. Atmospheric tomography, i.e. the reconstruction of the turbulence in the atmosphere, is a main task for the adaptive optics systems of the next generation telescopes. For extremely large telescopes , such as the European Extremely Large(More)
Tapio Helin: Discretization and Bayesian modeling in inverse problems and imaging ; Abstract: In this thesis the Bayesian modeling and discretization are studied in inverse problems related to imaging. The treatise consists of four articles which focus on the phenomena that appear when more detailed data or a priori information become available. Novel(More)
Reconstruction of the refractive index fluctuations in the atmosphere, or atmospheric tomography, is an underlying problem of many next generation adaptive optics (AO) systems, such as the multiconjugate adaptive optics or multiobject adaptive optics (MOAO). The dimension of the problem for the extremely large telescopes, such as the European Extremely(More)
For the new generation of extremely large telescopes (ELTs), the computational effort for adaptive optics (AO) systems is demanding even for fast reconstruction algorithms. In wide-field AO, atmospheric tomography, i.e., the reconstruction of turbulent atmospheric layers from wavefront sensor data in several directions of view, is the crucial step for an(More)
The imaging quality of modern ground-based telescopes such as the planned European Extremely Large Telescope is affected by atmospheric turbulence. In consequence, they heavily depend on stable and high-performance adaptive optics (AO) systems. Using measurements of incoming light from guide stars, an AO system compensates for the effects of turbulence by(More)
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