arXiv subjects

Ronny Ramlau

Publications and source records attributed to Ronny Ramlau.

At least 37 records · Page 2Linked to original sources

arXiv2024

Regularization of linear inverse problems with irregular noise using embedding operators

In this paper, we investigate regularization of linear inverse problems with irregular noise. In particular, we consider the case that the noise can be preprocessed by certain adjoint embedding operators. By introducing the consequent preprocessed problem, we provide convergence analysis for general regularization schemes under standard assumptions. Furthermore, for a special case of Tikhonov regularization in Computerized Tomography, we show that our approach leads to a novel (Fourier-based) filtered backprojection algorithm. Numerical examples with different parameter choice rules verify the efficiency of our proposed algorithm.

math.NA↗

arXiv2023

Characterizations of Adjoint Sobolev Embedding Operators with Applications in Inverse Problems

We consider the Sobolev embedding operator $E_s : H^s(Ω) \to L_2(Ω)$ and its role in the solution of inverse problems. In particular, we collect various properties and investigate different characterizations of its adjoint operator $E_s^*$, which is a common component in both iterative and variational regularization methods. These include variational representations and connections to boundary value problems, Fourier and wavelet representations, as well as connections to spatial filters. Moreover, we consider characterizations in terms of Fourier series, singular value decompositions and frame decompositions, as well as representations in finite dimensional settings. While many of these results are already known to researchers from different fields, a detailed and general overview or reference work containing rigorous mathematical proofs is still missing. Hence, in this paper we aim to fill this gap by collecting, introducing and generalizing a large number of characterizations of $E_s^*$ and discuss their use in regularization methods for solving inverse problems. The resulting compilation can serve both as a reference as well as a useful guide for its efficient numerical implementation in practice.

math.NA↗

arXiv2023

Off-axis Point Spread Function Reconstruction for Single Conjugate Adaptive Optics

Modern Giant Segmented Mirror Telescopes (GSMTs) like the Extremely Large Telescope, which is currently under construction, depend heavily on Adaptive Optics (AO) systems to correct for atmospheric distortions. However, a residual blur always remains in the astronomical images corrected by Single Conjugate AO (SCAO) systems due to fitting and bandwidth errors, which can mathematically be described by a convolution of the true image with a point spread function (PSF). Due to the nature of the turbulent atmosphere and its correction, the PSF is spatially varying, which is known as aniosplanatic effect. The PSF serves, e.g., as a quality measure for the science images and therefore needs to be known as accurately as possible. In this paper, we present an algorithm for PSF reconstruction in directions apart from the guide star direction in an SCAO system adapted to the needs of GSMTs focused on estimating the contribution of the anisoplanatic and generalized fitting error to the PSF. In particular, the PSF reconstruction algorithm for Single Conjugate Adaptive Optics from (Wagner, 2018) is combined with an algorithm for time-dependent atmospheric tomography from (Niebsch, 2021) to obtain a direction dependent reconstruction of the post-AO PSF. Results obtained in an end-to-end simulation tool show a qualitatively good reconstruction of the PSF compared to the PSF calculated directly from the simulated incoming wavefront as well as a stable performance with respect to imprecise knowledge of atmospheric parameters.

astro-ph.IM↗

arXiv2023

Subaperture-based Digital Aberration Correction for OCT: A Novel Mathematical Approach

In this paper, we consider subaperture-based approaches for the digital aberration correction (DAC) of optical coherence tomography (OCT) images. In particular, we introduce a mathematical framework for describing this class of approaches, leading to new insights for the subaperture-correlation method. Furthermore, we propose a novel DAC approach requiring only minimal statistical assumptions on the spectral phase of the scanned object. Finally, we demonstrate the applicability of our novel DAC approach via numerical examples based on both simulated and experimental OCT data.

physics.optics↗

arXiv2023

VISIONS: The VISTA Star Formation Atlas -- I. Survey overview

VISIONS is an ESO public survey of five nearby (d < 500 pc) star-forming molecular cloud complexes that are canonically associated with the constellations of Chamaeleon, Corona Australis, Lupus, Ophiuchus, and Orion. The survey was carried out with VISTA, using VIRCAM, and collected data in the near-infrared passbands J, H, and Ks. With a total on-sky exposure time of 49.4 h VISIONS covers an area of 650 deg$^2$, and it was designed to build an infrared legacy archive similar to that of 2MASS. Taking place between April 2017 and March 2022, the observations yielded approximately 1.15 million images, which comprise 19 TB of raw data. The observations are grouped into three different subsurveys: The wide subsurvey comprises shallow, large-scale observations and has visited the star-forming complexes six times over the course of its execution. The deep subsurvey of dedicated high-sensitivity observations has collected data on the areas with the largest amounts of dust extinction. The control subsurvey includes observations of areas of low-to-negligible dust extinction. Using this strategy, the VISIONS survey offers multi-epoch position measurements, is able to access deeply embedded objects, and provides a baseline for statistical comparisons and sample completeness. In particular, VISIONS is designed to measure the proper motions of point sources with a precision of 1 mas/yr or better, when complemented with data from VHS. Hence, VISIONS can provide proper motions for sources inaccessible to Gaia. VISIONS will enable addressing a range of topics, including the 3D distribution and motion of embedded stars and the nearby interstellar medium, the identification and characterization of young stellar objects, the formation and evolution of embedded stellar clusters and their initial mass function, as well as the characteristics of interstellar dust and the reddening law.

astro-ph.GA↗

arXiv2022

Localization of fixed dipoles at high precision by accounting for sample drift during illumination

Single molecule localization microscopy relies on the precise quantification of the position of single dye emitters in a sample. This precision is improved by the number of photons that can be detected from each molecule. It is therefore recommendable to increase illumination times for the recording process. Particularly recording at cryogenic temperatures dramatically reduces photobleaching and thereby allows a massive increase in illumination times to several seconds. As a downside, microscope instabilities may well introduce jitter during such long illuminations, deteriorating the localization precision. In this paper, we theoretically demonstrate that a parallel recording of fiducial marker beads together with a novel fitting approach accounting for the full drift trajectory allows for largely eliminating drift effects for drift magnitudes of several hundred nanometers per frame.

physics.optics↗

arXiv2022

On Regularization via Frame Decompositions with Applications in Tomography

In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class of continuous regularization methods and derive convergence rates under both a-priori and a-posteriori parameter choice rules. Furthermore, we apply our derived results to a standard tomography problem based on the Radon transform.

math.NA↗

arXiv2022

A projected Nesterov-Kaczmarz approach to stellar population-kinematic distribution reconstruction in Extragalactic Archaeology

In this paper, we consider the problem of reconstructing a galaxy's stellar population-kinematic distribution function from optical integral field unit measurements. These quantities are connected via a high-dimensional integral equation. To solve this problem, we propose a projected Nesterov-Kaczmarz reconstruction (PNKR) method, which efficiently leverages the problem structure and incorporates physical prior information such as smoothness and non-negativity constraints. To test the performance of our reconstruction approach, we apply it to a dataset simulated from a known ground truth density, and validate it by comparing our recoveries to those obtained by the widely used pPXF software.

math.NA↗

arXiv2022

LBT SOUL data as a science test bench for MICADO PSF-R tool

Current state-of-the-art adaptive optics (AO) provides ground-based, diffraction-limited observations with high Strehl ratios (SR). However, a detailed knowledge of the point spread function (PSF) is required to fully exploit the scientific potential of these data. This is even more crucial for the next generation AO instruments that will equip 30-meter class telescopes, as the characterization of the PSF will be mandatory to fulfill the planned scientific requirements. For this reason, there is a growing interest in developing tools that accurately reconstruct the observed PSF of AO systems, the so-called PSF reconstruction. In this context, a PSF-R service is a planned deliverable for the MICADO@ELT instrument and our group is in charge of its development. In the case of MICADO, a blind PSF-R approach is being pursued to have the widest applicability to science cases. This means that the PSF is reconstructed without extracting information from the science data, relying only on telemetry and calibrations. While our PSF-R algorithm is currently being developed, its implementation is mature enough to test performances with actual observations. In this presentation we will discuss the reliability of our reconstructed PSFs and the uncertainties introduced in the measurements of scientific quantities for bright, on-axis observations taken with the SOUL+LUCI instrument of the LBT. This is the first application of our algorithm to real data. It demonstrates its readiness level and paves the way to further testing. Our PSF-R algorithm is able to reconstruct the SR and full-width at half maximum of the observed PSFs with errors smaller than 2% and 4.5%, respectively. We carried out the scientific evaluation of the obtained reconstructed PSFs thanks to a dedicated set of simulated observations of an ideal science case.

astro-ph.IM↗

arXiv2022

Point spread function reconstruction for SOUL+LUCI LBT data

This paper presents the status of an ongoing project aimed at developing a PSF reconstruction software for adaptive optics (AO) observations. In particular, we test for the first time the implementation of pyramid wave-front sensor data on our algorithms. As a first step in assessing its reliability, we applied the software to bright, on-axis, point-like sources using two independent sets of observations, acquired with the single-conjugated AO upgrade for the Large Binocular Telescope. Using only telemetry data, we reconstructed the PSF by carefully calibrating the instrument response. The accuracy of the results has been first evaluated using the classical metric: specifically, the reconstructed PSFs differ from the observed ones by less than 2% in Strehl ratio and 4.5% in full-width at half maximum. Moreover, the recovered encircled energy associated with the PSF core is accurate at 4% level in the worst case. The accuracy of the reconstructed PSFs has then been evaluated by considering an idealized scientific test-case consisting in the measurements of the morphological parameters of a compact galaxy. In the future, our project will include the analysis of anisoplanatism, low SNR regimes, and the application to multi-conjugated AO observations.

astro-ph.IM↗

arXiv2022

Performance of an iterative wavelet reconstructor for the Multi-conjugate Adaptive Optics RelaY of ESO's ELT

The Multi-conjugate Adaptive Optics RelaY (MAORY) is one of the key Adaptive Optics (AO) systems on the European Southern Observatory's Extremely Large Telescope. MAORY aims to achieve a good wavefront correction over a large field of view, which involves a tomographic estimation of the 3D atmospheric wavefront disturbance. Mathematically, the reconstruction of turbulent layers in the atmosphere is severely ill-posed, hence, limits the achievable reconstruction accuracy. Moreover, the reconstruction has to be performed in real-time at a few hundred to one thousand Hertz frame rates. Huge amounts of data have to be processed and thousands of actuators of the deformable mirrors have to be controlled by elaborated algorithms. Even with extensive parallelization and pipelining, direct solvers, such as the Matrix Vector Multiplication (MVM) method, are extremely demanding. Thus, research in the last years shifted into the direction of iterative methods. In this paper we focus on the iterative Finite Element Wavelet Hybrid Algorithm (FEWHA). The key feature of FEWHA is a matrix-free representation of all operators involved, which makes the algorithm fast and enables on the fly system updates whenever parameters at the telescope or in the atmosphere change. We provide a performance analysis of the method regarding quality and run-time for the MAORY instrument using the AO software package COMPASS.

astro-ph.IM↗

arXiv2021

Direction dependent Point spread function reconstruction for Multi-Conjugate Adaptive Optics on Giant Segmented Mirror Telescopes

Modern Giant Segmented Mirror Telescopes (GSMT) like the Extremely Large Telescope (ELT), currently under construction depend heavily on Adaptive Optics (AO) systems to correct for atmospheric turbulence. To be able to correct wider fields of view (FoV), Multi-Conjugate Adaptive Optics (MCAO) systems were introduced, which use multiple guide stars to obtain an almost uniform correction over the FoV. However, a residual blur remains in the astronmical images due to the time delay stemming from the wavefront sensor (WFS) integration time and temporal response of the deformable mirror(s) (DM). This results in a blur which can be mathematically described by a convolution of the true image with the point spread function (PSF). Due to the nature of the atmosphere and its correction, the PSF is spatially varying. In this paper, we present an algorithm for MCAO PSF reconstruction adapted to the needs of GSMTs in a storage efficient way. In particular, the PSF reconstruction algorithm for Single Conjugate Adaptive Optics (SCAO) from [40] is combined with an algorithm for atmospheric tomography from [33] to obtain a direction dependent reconstruction of the post-AO PSF. Results obtained in an end-to-end simulation tool show qualitatively good reconstruction of the PSF compared to the PSF calculated directly from the simulated incoming wavefront. Furthermore, the used algorithm has a reasonable runtime and memory consumption.

astro-ph.IM↗

arXiv2021

Adaptive optics imaging with a pyramid wavefront sensor for visual science

The pyramid wavefront sensor (P-WFS) has replaced the Shack-Hartmann (SH-) WFS as sensor of choice for high performance adaptive optics (AO) systems in astronomy because of its flexibility in pupil sampling, its dynamic range, and its improved sensitivity in closed-loop application. Usually, a P-WFS requires modulation and high precision optics that lead to high complexity and costs of the sensor. These factors limit the competitiveness of the P-WFS with respect to other WFS devices for AO correction in visual science. Here, we present a cost effective realization of AO correction with a non-modulated PWFS and apply this technique to human retinal in vivo imaging using optical coherence tomography (OCT). P-WFS based high quality AO imaging was, to the best of our knowledge for the first time, successfully performed in 5 healthy subjects and benchmarked against the performance of conventional SH-WFS based AO. Smallest retinal cells such as central foveal cone photoreceptors are visualized and we observed a better quality of the images recorded with the P-WFS. The robustness and versatility of the sensor is demonstrated in the model eye under various conditions and in vivo by high-resolution imaging of other structures in the retina using standard and extended fields of view.

physics.med-ph↗

arXiv2021

Subspace Recycling-based Regularization Methods

Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known algorithm with a fixed subspace of vectors which are ``useful'' for solving the problem. Often, this has the effect of inducing a projected version of the original linear system to which the known iterative method is then applied, and this projection can act as a deflation preconditioner, accelerating convergence. Most often, these methods have been applied for the solution of well-posed problems. However, they have also begun to be considered for the solution of ill-posed problems. In this paper, we consider subspace augmentation-type iterative schemes applied to linear ill-posed problems in a continuous Hilbert space setting, based on a recently developed framework describing these methods. We show that under suitable assumptions, a recycling method satisfies the formal definition of a regularization, as long as the underlying scheme is itself a regularization. We then develop an augmented subspace version of the gradient descent method and demonstrate its effectiveness, both on an academic Gaussian blur model and on problems arising from the adaptive optics community for the resolution of large sky images by ground-based extremely large telescopes.

math.NA↗

arXiv2021

Phase-contrast THz-CT for non-destructive testing

A new approach for image reconstruction in THz computed tomography (THz-CT) is presented. Based on a geometrical optics model containing the THz signal amplitude and phase, a novel algorithm for extracting an average phase from the measured THz signals is derived. Applying the algorithm results in a phase-contrast sinogram, which is further used for image reconstruction. For experimental validation, a fast THz time-domain spectrometer (THz-TDS) in transmission geometry is employed, enabling CT measurements within several minutes. Quantitative evaluation of reconstructed 3D printed plastic profiles reveals the potential of our approach in non-destructive testing of plastic profiles.

physics.app-ph↗

arXiv2021

Robust and bias-free localization of individual fixed dipole emitters achieving the Cramér Rao bound

Single molecule localization microscopy has the potential to resolve structural details of biological samples at the nanometer length scale. However, to fully exploit the resolution it is crucial to account for the anisotropic emission characteristics of fluorescence dipole emitters. In case of slight residual defocus, localization estimates may well be biased by tens of nanometers. We show here that astigmatic imaging in combination with information about the dipole orientation allows to extract the position of the dipole emitters without localization bias and down to a precision of ~1nm, thereby reaching the corresponding Cramér Rao bound. The approach is showcased with simulated data for various dipole orientations, and parameter settings realistic for real life experiments.

physics.optics↗

arXiv2021

Frame Decompositions of Bounded Linear Operators in Hilbert Spaces with Applications in Tomography

We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and ill-posedness of the problem and can be used as the basis for the design and implementation of efficient numerical solution methods. In contrast to the singular-value decomposition, the presented frame decompositions can be derived explicitly for a wide class of operators, in particular for those satisfying a certain stability condition. In order to show the usefulness of this approach, we consider different examples from the field of tomography.

math.NA↗

arXiv2020

Estimating solution smoothness and data noise with Tikhonov regularization

A main drawback of classical Tikhonov regularization is that often the parameters required to apply theoretical results, e.g., the smoothness of the sought-after solution and the noise level, are unknown in practice. In this paper we investigate in new detail the residuals in Tikhonov regularization viewed as functions of the regularization parameter. We show that the residual carries, with some restrictions, the information on both the unknown solution and the noise level. By calculating approximate solutions for a large range of regularization parameters, we can extract both parameters from the residual given only one set of noisy data and the forward operator. The smoothness in the residual allows to revisit parameter choice rules and relate a-priori, a-posteriori, and heuristic rules in a novel way that blurs the lines between the classical division of the parameter choice rules. All results are accompanied by numerical experiments.

math.NA↗