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- TAPIO HELIN
- 2009

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 Mkn = AkUn+Ek is discussed.… (More)

- M. Yudytskiy, T. Helin, R. Ramlau, Mykhaylo Yudytskiy1a, Tapio Helin2b, Ronny Ramlau3c
- 2014

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 Telescope, this problem becomes overly complex and an efficient algorithm is needed to reduce numerical costs. Recently, a… (More)

- Tapio Helin, Matti Lassas
- 2009

The Bayesian methods for linear inverse problems is studied using hierarchical Gaussian 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)

- Tapio Helin, TEKNILLINEN KORKEAKOULU, TEKNISKA HÖGSKOLAN, Olavi Nevanlinna
- 2010

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 Bayesian methods for solving ill-posed signal processing problems in edge-preserving manner are… (More)

- Tapio Helin, Matti Lassas, Samuli Siltanen
- Journal of Mathematical Imaging and Vision
- 2009

A new mathematical image model is introduced using the photographic process as the starting point. Images are represented as infinite sequences of photons allowing analysis at arbitrarily high resolution and leading to novel computational methods for processing, representation, transmission and storage of images. The resulting space of infinite photographs… (More)

- Daniela Saxenhuber, Günter Auzinger, Miska Le Louarn, Tapio Helin
- Applied optics
- 2017

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)

- Roland Wagner, Tapio Helin, Andreas Obereder, Ronny Ramlau
- Applied optics
- 2016

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)

- Mykhaylo Yudytskiy, Tapio Helin, Ronny Ramlau
- Journal of the Optical Society of America. A…
- 2014

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)

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