Point Spread Function (PSF)

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Tensor-Factorization-Based 3D Single Image Super-Resolution with Semi-Blind Point Spread Function Estimation

Tensor-Factorization-Based 3D Single Image Super-Resolution with Semi-Blind Point Spread Function Estimation

Faculty of Information Technology and Bionics Institute de Recherche en Informatique de Toulouse 50/a Pr´ater utca, H-1083 Budapest 118 r. de Narbonne, F-31062 Toulouse ABSTRACT A volumetric non-blind single image super-resolution tech- nique using tensor factorization has been recently introduced by our group. That method allowed a 2-order-of-magnitude faster high-resolution image reconstruction with equivalent image quality compared to state-of-the-art algorithms. In this work a joint alternating recovery of the high-resolution im- age and of the unknown point spread function parameters is proposed. The method is evaluated on dental computed to- mography images. The algorithm was compared to an ex- isting 3D super-resolution method using low-rank and total variation regularization, combined with the same alternating PSF-optimization. The two algorithms have shown similar improvement in PSNR, but our method converged roughly 40 times faster, under 6 minutes both in simulation and on exper- imental dental computed tomography data.
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Subpixel Point Spread Function Estimation from Two Photographs at Different Distances

Subpixel Point Spread Function Estimation from Two Photographs at Different Distances

In most digital cameras, and even in high-end digital single lens re- flex cameras, the acquired images are sampled at rates below the Nyquist critical rate, causing aliasing effects. This work introduces an algorithm for the subpixel estimation of the point spread function of a digital cam- era from aliased photographs. The numerical procedure simply uses two fronto-parallel photographs of any planar textured scene at different dis- tances. The mathematical theory developed herein proves that the camera psf can be derived from these two images, under reasonable conditions. Mathematical proofs supplemented by experimental evidence show the well-posedness of the problem and the convergence of the proposed al- gorithm to the camera in-focus psf. An experimental comparison of the resulting psf estimates shows that the proposed algorithm reaches the accuracy levels of the best non-blind state-of-the-art methods.
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Joint Bayesian Deconvolution And Point Spread  Function Estimation For Ultrasound Imaging

Joint Bayesian Deconvolution And Point Spread Function Estimation For Ultrasound Imaging

3 T´eSA Laboratory, 14-16 Port Saint-Etienne, 31000 Toulouse, France {nzhao, jean-yves.tourneret}@enseeiht.fr, {adrian.basarab, denis.kouame}@irit.fr ABSTRACT This paper addresses the problem of blind deconvolution for ultra- sound images within a Bayesian framework. The prior of the un- known ultrasound image to be estimated is assumed to be a product of generalized Gaussian distributions. The point spread function of the system is also assumed to be unknown and is assigned a Gaus- sian prior distribution. These priors are combined with the likeli- hood function to build the joint posterior distribution of the image and PSF. However, it is difficult to derive closed-form expressions of the Bayesian estimators associated with this posterior. Thus, this paper proposes to build estimators of the unknown model parameters from samples generated according to the model posterior using a hy- brid Gibbs sampler. Simulation results performed on synthetic data allow the performance of the proposed algorithm to be appreciated.
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Joint Bayesian Deconvolution And Point Spread  Function Estimation For Ultrasound Imaging

Joint Bayesian Deconvolution And Point Spread Function Estimation For Ultrasound Imaging

Index Terms— Ultrasound imaging, image deconvolution, Bayesian inference, Gibbs sampler. 1. INTRODUCTION Ultrasound (US) imaging is widely used due to its advantages such as being portable, cost effective and noninvasive. However, the US images are contaminated by an intrinsic noise called speckle and have low contrast and relatively low spatial resolution at a given fre- quency. A 2D convolution model between the tissue reflectivity im- age and the system point spread function (PSF) is commonly used to model US images. As a consequence, deconvolution methods are widely used to improve the quality of US images.
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Blind Deconvolution of Medical Ultrasound Images Using a Parametric Model for the Point Spread Function

Blind Deconvolution of Medical Ultrasound Images Using a Parametric Model for the Point Spread Function

noise (AWGN) and H ∈ R N ×N is the system impulse re- sponse/point spread function (PSF) assumed to be a circulant matrix [3, 4]. In US imaging systems, the PSF is usually un- known. Existing methods to address this problem include ei- ther the estimation of the PSF in a pre-processing step [3,5] or the estimation of the PSF and the TRF simultaneously [6, 7]. In this paper, we follow the second strategy to estimate the US TRF and PSF jointly. In particular, a parametric model for the PSF of the form of a modulated 2D Gaussian function is proposed. This parametric model allows us to reduce the estimation of the PSF during the blind deconvolution process to the estimation of a few parameters of the PSF model. In addition, a generalized Gaussian distribution is proposed for
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A deconvolution-based algorithm for crowded field photometry with unknown point spread function

A deconvolution-based algorithm for crowded field photometry with unknown point spread function

Received 8 December 2004 / Accepted 5 September 2006 ABSTRACT A new method is presented for determining the point spread function (PSF) of images that lack bright and isolated stars. It is based on the same principles as the MCS image deconvolution algorithm. It uses the information contained in all stellar images to achieve the double task of reconstructing the PSFs for single or multiple exposures of the same field and to extract the photometry of all point sources in the field of view. The use of the full information available allows us to construct an accurate PSF. The possibility to simultaneously consider several exposures makes it well suited to the measurement of the light curves of blended point sources from data that would be very di fficult or even impossible to analyse with traditional PSF fitting techniques. The potential of the method for the analysis of ground-based and space-based data is tested on artificial images and illustrated by several examples, including HST /NICMOS images of a lensed quasar and VLT/ISAAC images of a faint blended Mira star in the halo of the giant elliptical galaxy NGC 5128 (Cen A).
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Nonconvex optimization for 3D point source localization using a rotating point spread function

Nonconvex optimization for 3D point source localization using a rotating point spread function

spread function ∗ Chao Wang † , Raymond Chan † , Mila Nikolova ‡ , Robert Plemmons § , and Sudhakar Prasad ¶ Abstract. We consider the high-resolution imaging problem of 3D point source image recovery from 2D data using a method based on point spread function (PSF) engineering. The method involves a new technique, recently proposed by S. Prasad, based on the use of a rotating PSF with a single lobe to obtain depth from defocus. The amount of rotation of the PSF encodes the depth position of the point source. Applications include high-resolution single molecule localization microscopy as well as the problem addressed in this paper on localization of space debris using a space-based telescope. The localization problem is discretized on a cubical lattice where the coordinates of nonzero entries represent the 3D locations and the values of these entries the fluxes of the point sources. Finding the locations and fluxes of the point sources is a large-scale sparse 3D inverse problem. A new nonconvex regularization method with a data-fitting term based on Kullback-Leibler (KL) divergence is proposed for 3D localization for the Poisson noise model. In addition, we propose a new scheme of estimation of the source fluxes from the KL data-fitting term. Numerical experiments illustrate the efficiency and stability of the algorithms that are trained on a random subset of image data before being applied to other images. Our 3D localization algorithms can be readily applied to other kinds of depth-encoding PSFs as well.
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Optimal transport-based dictionary learning and its application to Euclid-like Point Spread Function representation

Optimal transport-based dictionary learning and its application to Euclid-like Point Spread Function representation

We apply our method to a dataset of Euclid-like simulated PSFs (Point Spread Function). ESA’s Euclid mission will cover a large area of the sky in order to accurately measure the shape of billions of galaxies. PSF estimation and correction is one of the main sources of systematic errors on those galaxy shape measurements. PSF variations across the field of view and with the incoming light’s wavelength can be highly non-linear, while still retaining strong geometrical information, making the use of Optimal Transport distances an attractive prospect. We show that our representation does indeed succeed at capturing the PSF’s variations.
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Blind Deconvolution of Medical Ultrasound Images Using a Parametric Model for the Point Spread Function

Blind Deconvolution of Medical Ultrasound Images Using a Parametric Model for the Point Spread Function

noise (AWGN) and H ∈ R N ×N is the system impulse re- sponse/point spread function (PSF) assumed to be a circulant matrix [3, 4]. In US imaging systems, the PSF is usually un- known. Existing methods to address this problem include ei- ther the estimation of the PSF in a pre-processing step [3,5] or the estimation of the PSF and the TRF simultaneously [6, 7]. In this paper, we follow the second strategy to estimate the US TRF and PSF jointly. In particular, a parametric model for the PSF of the form of a modulated 2D Gaussian function is proposed. This parametric model allows us to reduce the estimation of the PSF during the blind deconvolution process to the estimation of a few parameters of the PSF model. In addition, a generalized Gaussian distribution is proposed for
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Spectrally resolved point-spread-function engineering using a complex medium

Spectrally resolved point-spread-function engineering using a complex medium

acts as a dispersive optical element for ultrashort pulses of light. In this regime, the optical transformation of the field induced by the medium is very complex but still remains linear and deterministic, hence controllable. Owing to the availability of spatial light modulators (SLMs), several techniques based on wavefront shaping were developed to experimentally characterize this process. A recurrent application is to find the incident wavefront that counterbalances the effects of scattering and thus re-compress the pulse to its initial duration and focus it to a diffraction limited spot. For instance it can be achieved by iteratively optimizing the incident wavefront [ 19 , 20 ] but also by using digital phase conjugation [ 21 ], spectral pulse shaping [ 22 ], or time-gating techniques [ 23 ]. Another and more global approach to describe and manipulate the outgoing broadband light consists of measuring the multi-spectral transmission matrix (MSTM) [ 24 ]. The MSTM is a set of N λ ≈ ∆λ laser /δλ m monochromatic transmission matrices (TMs); each TM linearly relates the input field to the output field of the medium [ 25 ] for a given spectral component of the pulse. The full set of matrices provides both spatial and spectral/temporal information for controlling the transmitted pulse; in particular enhancing a single spectral component of the output pulse or focusing it at a given time can be performed [ 26 – 28 ]. The key point here is that these techniques manipulate both spatial and spectral degrees of freedom of the pulse by only using a single SLM. This is possible thanks to the spatio-spectral coupling resulting from the propagation through the medium. This is what we exploit here, now implemented as 3D spatio-spectral control, relying on a single SLM. Although pulse control in complex media has already been studied in the last years, to our knowledge, the spatio-temporal degrees of freedom of a scattering medium have never been used to spectrally engineer the point-spread function (PSF) of an ultrashort pulse.
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Tensor-Factorization-Based 3D Single Image Super-Resolution with Semi-Blind Point Spread Function Estimation

Tensor-Factorization-Based 3D Single Image Super-Resolution with Semi-Blind Point Spread Function Estimation

50/a Pr´ater utca, H-1083 Budapest 118 r. de Narbonne, F-31062 Toulouse ABSTRACT A volumetric non-blind single image super-resolution tech- nique using tensor factorization has been recently introduced by our group. That method allowed a 2-order-of-magnitude faster high-resolution image reconstruction with equivalent image quality compared to state-of-the-art algorithms. In this work a joint alternating recovery of the high-resolution im- age and of the unknown point spread function parameters is proposed. The method is evaluated on dental computed to- mography images. The algorithm was compared to an ex- isting 3D super-resolution method using low-rank and total variation regularization, combined with the same alternating PSF-optimization. The two algorithms have shown similar improvement in PSNR, but our method converged roughly 40 times faster, under 6 minutes both in simulation and on exper- imental dental computed tomography data.
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POINT-SPREAD FUNCTION MODEL FOR FLUORESCENCE MACROSCOPY IMAGING

POINT-SPREAD FUNCTION MODEL FOR FLUORESCENCE MACROSCOPY IMAGING

In this paper, we model the point-spread function (PSF) of a fluo- rescence MACROscope with a field aberration. The MACROscope is an imaging arrangement that is designed to directly study small and large specimen preparations without physically sectioning them. However, due to the different optical components of the MACRO- scope, it cannot achieve the condition of lateral spatial invariance for all magnifications. For example, under low zoom settings, this field aberration becomes prominent, the PSF varies in the lateral field, and is proportional to the distance from the center of the field. On the other hand, for larger zooms, these aberrations become gradually ab- sent. A computational approach to correct this aberration often relies on an accurate knowledge of the PSF. The PSF can be defined either theoretically using a scalar diffraction model or empirically by ac- quiring a three-dimensional image of a fluorescent bead that approx- imates a point source. The experimental PSF is difficult to obtain and can change with slight deviations from the physical conditions. In this paper, we model the PSF using the scalar diffraction approach, and the pupil function is modeled by chopping it. By comparing our modeled PSF with an experimentally obtained PSF, we validate our hypothesis that the spatial variance is caused by two limiting optical apertures brought together on different conjugate planes.
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Point-spread function retrieval for fluorescence microscopy

Point-spread function retrieval for fluorescence microscopy

In this paper we propose a method for retrieving the Point Spread Function (PSF) of an imaging system given the ob- served image sections of a fluorescent microsphere. Theoret- ically calculated PSFs often lack the experimental or micro- scope specific signatures while empirically obtained data are either over sized or (and) too noisy. The effect of noise and the influence of the microsphere size can be mitigated from the experimental data by using a Maximum Likelihood Ex-

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The non-parametric sub-pixel local point spread function estimation is a well posed problem

The non-parametric sub-pixel local point spread function estimation is a well posed problem

method [23], which is an extension of the step-edge tech- nique to achieve sub pixel resolution on the estimation. By aligning the step-edge slightly off the orthogonal scan direction the effective sampling rate is increased. Also, scan-line averaging successfully suppresses noise and increases signal-to-noise ratio making the estima- tion more stable. In [29] the authors propose a slanted- edge non-parametric sub-pixel psf estimation method that admits geometrical distortions. A parametric and non-parametric edge spread function estimation proce- dure is proposed in [9]. Non-uniform illumination is also taken into account. However, the differentiation step that gives back the psf requires regularization and therefore loses accuracy. Since the previous methods are based on estimating several one-dimensional responses, several images or symmetry assumptions are needed to reconstruct a full bi-dimensional psf.
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Space non-invariant point-spread function and its estimation in fluorescence microscopy

Space non-invariant point-spread function and its estimation in fluorescence microscopy

shifted in depth but not in the radial plane. If the sphere is assumed to be pla ed at a relative position (x o , y o , z o ) in a given volume, then the observed image will have the entroid in the volume as (x i , y i , z i ) , with x i ≈ x o and y i ≈ y o . Another point to be noted is that due to photon loss, although uniformly distributed, the true intensity of the observed sphere s is unknown. In Subse tion 1.1.3 , we saw how a bandlimited obje t ould be simulated for the

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Asymmetries in adaptive optics point spread functions

Asymmetries in adaptive optics point spread functions

For this generation of instruments and the next, understand- ing the point spread function (PSF) of AO instruments on giant telescopes will be important for the development of algorithms optimized in the search for planets. 5 , 6 The analysis in this paper expands on our previous work, 7 which demonstrated the origin of azimuthal asymmetry in the PSF as a consequence of the time lag error, to explore asymmetry along the preferential axis intro- duced by scintillation. This effect has been demonstrated previ- ously by Cantalloube et al. 8 We will expand on their discussion using a more general method of analyzing the structure of the AO-corrected PSF analytically, as well as validating our conclu- sions with observations and atmospheric datasets. More specifi- cally, our formalism demonstrates that the asymmetry grows linearly only for small spatial frequencies, and at higher spatial frequencies becomes nonlinear. We include solutions for the zeros of the log of the asymmetry metric, which are image loca- tions with an observable return to symmetry.
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Conformal blocks for the four-point function in conformal quantum mechanics

Conformal blocks for the four-point function in conformal quantum mechanics

The usual route to conformal blocks is through the short- distance expansion for ’ 1 ðt 1 Þ’ 2 ðt 2 Þ. In our construction ’ 1 ðt 1 Þ is replaced by O y ðt 1 Þ, which does not have an evident short distance expansion with ’ 2 ðt 2 Þ. Nevertheless, within our approach we are able to derive a block representation for the four-point function. This puts into evidence once again that our method, with its cancellation of defects, preserves conformal covariance.

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Urban point sources of nutrients were the leading cause for the historical spread of hypoxia across European lakes.

Urban point sources of nutrients were the leading cause for the historical spread of hypoxia across European lakes.

Submitted to Proceedings of the National Academy of Sciences of the United States of America Enhanced phosphorus export from land into streams and lakes is a primary factor driving the expansion of deep-water hypoxia in lakes during the Anthropocene. However, the interplay of regional scale environmental stressors and the lack of long-term instrumen- tal data often impede analyses attempting to associate changes in land cover with downstream aquatic responses. Herein we performed a synthesis of data that link paleolimnological recon- structions of lake bottom-water oxygenation to changes in land cover/use and climate over the last 300 years in order to evaluate whether the spread of hypoxia in European lakes was primarily associated with enhanced phosphorus exports from either grow- ing urbanization, intensified agriculture or climatic change. We showed that hypoxia started spreading in European lakes around CE 1850 and was greatly accelerated after CE 1900. Socio-economic changes in Europe beginning in CE 1850 resulted in widespread urbanization as well as a larger and more intensively cultivated surface area. However, our analysis of temporal trends demon- strated that the onset and intensification of lacustrine hypoxia were more strongly related to the growth of urban areas than to changes in agricultural areas and the application of fertilizers. These results suggest that anthropogenically-triggered hypoxia in European lakes were primarily caused by enhanced phosphorus discharges from urban point sources. To date, there have been no signs of sustained recovery of bottom water oxygenation in lakes following the enactment of European water legislation in the 1970s to 1980s, and the subsequent decrease in domestic phosphorus consumption.
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Epidemic spread on weighted networks

Epidemic spread on weighted networks

As many earlier methods, ours analyses model disease spread on networks from a node centric summary statistics, by considering the number of contacts and transmission events per time. Therefore, it inherently neglects correlation between nodes. In other words there is no consideration of assortativity between individuals based on their number of contacts or transmission events per time. At the same time, individuals share their activity randomly among all their contacts (weights are homogeneously, or multinomially, distributed among edges that leave a node), which can enforce correlations among nodes in certain networks. Also clustering is observed in many contact networks [38] and this issue should be addressed in an extended version of our model.
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A two-point function approach to  connectedness of  drops in convex potentials

A two-point function approach to connectedness of drops in convex potentials

Finally we would like to underline the fact that the combination of the two-point function technique with the assumption of positive second variation is quite natural. In fact, on a general stationary point the Jacobi operator does not satisfy the maximum principle. It is precisely the stability condition which guarantees its validity. We hope that this simple observation can be useful also in other contexts.

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