Long Exposure Point Spread Function Modeling with Gaussian Processes

Lesion-detection performance in oncologic PET depends in part upon count statistics, with shorter scans having higher noise and reduced lesion detectability. However, advanced techniques such as time-of-flight (TOF) and point spread function (PSF) modeling can improve lesion detectability. This work investigates the relationship between reducing count levels (as a surrogate for scan time) and reconstructing with PSF model and TOF. A series of 24 whole-body phantom scans was acquired on a Biograph mCT TOF PET/CT scanner using the experimental methodology prescribed for the Utah PET Lesion Detection Database. Six scans were acquired each day over 4 days, with up to 23 68Ge shell-less lesions (diam. 6, 8, 10, 12, 16mm) distributed throughout the phantom thorax and pelvis. Each scan acquired 6 bed positions at 240s/bed in listmode format. The listmode files were then statistically pruned, preserving Poisson statistics, to equivalent count levels for scan times of 180s, 120s, 90s, 60s, 45s, 30s, and 15s per bed field-of-view. Each dataset was reconstructed using ordinary Poisson line-of-response (LOR) OSEM, with PSF model, with TOF, and with PSF+TOF. Localization receiver operating characteristics (LROC) analysis was then performed using the channelized non-prewhitened (CNPW) observer. The results were analyzed to delineate the relationship between scan time, reconstruction method, and strength of post-reconstruction filter. Lesion-detection performance degraded as scan time was reduced, and progressively stronger filters were required to maximize performance for the shorter scans. PSF modeling and TOF were found to improve detection performance, offsetting in part the reduced detectability for shorter scans. Notably, PSF+TOF at 120s per bed position preserved essentially the same detection performance as the baseline reconstruction at 240s/bed — effectively cutting whole-body scan time in half without degrading lesion-detection performance in these data.

The Siemens Biograph TruePoint TrueV (B-TPTV) positron emission tomography (PET) scanner performs 3D PET reconstruction using a system matrix with point spread function (PSF) modeling (called the True X reconstruction). PET resolution was dramatically improved with the True X method. In this study, we assessed the spatial resolution and image quality on a B-TPTV PET scanner. In addition, we assessed the feasibility of animal imaging with a B-TPTV PET and compared it with a microPET R4 scanner. Spatial resolution was measured at center and at 8 cm offset from the center in transverse plane with warm background activity. True X, ordered subset expectation maximization (OSEM) without PSF modeling, and filtered back-projection (FBP) reconstruction methods were used. Percent contrast (% contrast) and percent background variability (% BV) were assessed according to NEMA NU2-2007. The recovery coefficient (RC), non-uniformity, spill-over ratio (SOR), and PET imaging of the Micro Deluxe Phantom were assessed to compare image quality of B-TPTV PET with that of the microPET R4. When True X reconstruction was used, spatial resolution was <3.65 mm with warm background activity. % contrast and % BV with True X reconstruction were higher than those with the OSEM reconstruction algorithm without PSF modeling. In addition, the RC with True X reconstruction was higher than that with the FBP method and the OSEM without PSF modeling method on the microPET R4. The non-uniformity with True X reconstruction was higher than that with FBP and OSEM without PSF modeling on microPET R4. SOR with True X reconstruction was better than that with FBP or OSEM without PSF modeling on the microPET R4. This study assessed the performance of the True X reconstruction. Spatial resolution with True X reconstruction was improved by 45 % and its % contrast was significantly improved compared to those with the conventional OSEM without PSF modeling reconstruction algorithm. The noise level was higher than that with the other reconstruction algorithm. Therefore, True X reconstruction should be used with caution when quantifying PET data.

Lesion-detection performance in oncologic PET depends in part upon count statistics, with shorter scans having higher noise and reduced lesion detectability. However, advanced techniques such as time-of-flight (TOF) and point spread function (PSF) modeling can improve lesion detection. This work investigates the relationship between reducing count levels (as a surrogate for scan time) and reconstructing with PSF model and TOF. A series of twenty-four whole-body phantom scans was acquired on a Biograph mCT TOF PET/CT scanner using the experimental methodology prescribed for the Utah PET Lesion Detection Database. Six scans were acquired each day over four days, with up to 23 (68)Ge shell-less lesions (diam. 6, 8, 10, 12, 16 mm) distributed throughout the phantom thorax and pelvis. Each scan acquired 6 bed positions at 240 s/bed in listmode format. The listmode files were then statistically pruned, preserving Poisson statistics, to equivalent count levels for scan times of 180 s, 120 s, 90 s, 60 s, 45 s, 30 s, and 15 s per bed field-of-view, corresponding to whole-body scan times of 1.5-24 min. Each dataset was reconstructed using ordinary Poisson line-of-response (LOR) OSEM, with PSF model, with TOF, and with PSF+TOF. Localization receiver operating characteristics (LROC) analysis was then performed using the channelized non-prewhitened (CNPW) observer. The results were analyzed to delineate the relationship between scan time, reconstruction method, and strength of post-reconstruction filter. Lesion-detection performance degraded as scan time was reduced, and progressively stronger filters were required to maximize performance for the shorter scans. PSF modeling and TOF were found to improve detection performance, but the degree of improvement for TOF was much larger than for PSF for the large phantom used in this study. Notably, the images using TOF provided equivalent lesion-detection performance to the images without TOF for scan durations 40% shorter, suggesting that TOF may offset, at least in part, the need for longer scan times in larger patients.

Oblique plane microscopy-based single molecule localization microscopy (obSTORM) has shown great potential for super-resolution imaging of thick biological specimens. Despite its compatibility with tissues and small animals, prior uses of the Gaussian point spread function (PSF) model have resulted in limited imaging resolution and a narrow axial localization range. This is due to the poor fit of the Gaussian PSF model with the actual PSF shapes in obSTORM. To overcome these limitations, we have employed cubic splines for a more accurate modeling of the experimental PSF shapes. This refined PSF model enhances three-dimensional localization precision, leading to significant improvements in obSTORM imaging of mouse retina tissues, such as an approximately 1.2 times increase in imaging resolution, seamless stitching of single molecules between adjacent optical sections, and a doubling of the sectional interval in volumetric obSTORM imaging due to the extended axial range of usable section thickness. The cubic spline PSF model thus offers a path towards more accurate and faster volumetric obSTORM imaging of biological specimens.

Context. Weak gravitational lensing requires precise measurements of galaxy shapes and therefore accurate knowledge of the point spread function (PSF) model. The latter can be a source of systematics that affect the shear two-point correlation function. A key aspect of weak-lensing analysis is the forecasting of the systematics due to the PSF. Aims. Correlation functions of galaxies and the PSF, the so-called ρ and τ statistics, are used to evaluate the level of systematics coming from the PSF model and PSF corrections and contributing to the two-point correlation function used to perform cosmological inference. Our goal is to introduce a fast and simple method to estimate this level of systematics and to assess its agreement with state-of-the-art approaches. Methods. We introduce a new way to estimate the covariance matrix of τ statistics using analytical expressions. The covariance allows us to estimate parameters directly related to the level of systematics associated with the PSF and provides us with a tool to validate the PSF model used in a weak-lensing analysis. We applied these methods to data from the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS). Results. We show that semi-analytical covariance yields results comparable to those obtained by using covariances obtained from simulations or jackknife resampling. The approach requires less computation time and is therefore well suited to rapid comparison of the systematic level obtained from different catalogues. We also show how one can break degeneracies between parameters with a redefinition of the τ statistics. Conclusions. The methods developed in this work will be useful tools in the analysis of current weak-lensing data but also of Stage IV surveys such as Euclid, LSST, and Roman. They provide fast and accurate diagnostics on PSF systematics that are crucial in the context of cosmic shear studies.

Partial volume effect (PVE) plays an important role in both qualitative and quantitative PET image accuracy, especially for small structures. A previously proposed voxelwise PVE correction method applied on PET reconstructed images involves the use of Lucy-Richardson deconvolution incorporating wavelet-based denoising to limit the associated propagation of noise. The aim of this study is to incorporate the deconvolution, coupled with the denoising step, directly inside the iterative reconstruction process to further improve PVE correction. The list-mode ordered subset expectation maximization (OSEM) algorithm has been modified accordingly with the application of the Lucy-Richardson deconvolution algorithm to the current estimation of the image, at each reconstruction iteration. Acquisitions of the NEMA NU2-2001 IQ phantom were performed on a GE DRX PET/CT system to study the impact of incorporating the deconvolution inside the reconstruction [with and without the point spread function (PSF) model] in comparison to its application postreconstruction and to standard iterative reconstruction incorporating the PSF model. The impact of the denoising step was also evaluated. Images were semiquantitatively assessed by studying the trade-off between the intensity recovery and the noise level in the background estimated as relative standard deviation. Qualitative assessments of the developed methods were additionally performed on clinical cases. Incorporating the deconvolution without denoising within the reconstruction achieved superior intensity recovery in comparison to both standard OSEM reconstruction integrating a PSF model and application of the deconvolution algorithm in a postreconstruction process. The addition of the denoising step permitted to limit the SNR degradation while preserving the intensity recovery. This study demonstrates the feasibility of incorporating the Lucy-Richardson deconvolution associated with a wavelet-based denoising in the reconstruction process to better correct for PVE. Future work includes further evaluations of the proposed method on clinical datasets and the use of improved PSF models.

Adaptive optics (AO) enhances astronomical images by correcting perturbations in the optical system, resulting in complex point spread function (PSF) shapes, which provide critical information for optical design, calibration, and diagnostics. This paper presents a parametric model for an AO-corrected long-exposure PSF that adapts to complex shapes and various seeing conditions. A complementary estimation method is also introduced, addressing the inverse problem of estimating the atmospheric PSF or power spectral density (PSD) from observed PSF data. The model, based on Gaussian sum approximation (GSA), was tested using simulated PSF data from the OOMAO toolbox for Fried parameter (r0) values ranging from 0.10 to 0.20 m and on-sky data from the Very Large Telescope’s MUSE instrument. Two approaches were analyzed: (i) direct PSF estimation using GSA, and (ii) PSF estimation derived from atmospheric PSD estimation. Both methods were evaluated using root mean square error (RMSE). While approach (i) provided the best performance, approach (ii) produced more accurate atmospheric PSF estimates compared to the Moffat approximation and the Fetick method. Additionally, approach (ii) enabled the estimation of key physical parameters, such as the Fried parameter (r0) and residual AO variance ($\sigma _{AO}^2$). The proposed methods effectively estimate atmospheric PSF and PSD, even for complex PSF shapes influenced by spiders, central obstructions, or static aberrations.

The singlet plenoptic camera, which consists of a single lens, microlens array (MLA) and image sensor, possesses the superiority that the imaging system is compact and lightweight, which is beneficial to miniaturization. However, such plenoptic cameras suffer from severe optical aberrations and their imaging quality is inferior for post-capture processing. Therefore, this paper proposes an optical-aberrations-corrected light field re-projection method to obtain high-quality singlet plenoptic imaging. First, optical aberrations are modeled by Seidel polynomials and included into point spread function (PSF) modeling. The modeled PSF is subsequently used to reconstruct imaging object information. Finally, the reconstructed imaging object information is re-projected back to the plenoptic imaging plane to obtain high-quality plenoptic images without optical aberrations. PSF modeling is validated by a self-built singlet plenoptic camera and the utility of the proposed optical-aberrations-corrected light field re-projection method is verified by numerical simulations and real imaging experiments.

BackgroundThe maximum standardized uptake value (SUVmax) is a common clinical parameter for quantification in F18-fluorodeoxyglucose positron emission tomography/computed tomography (FDG-PET/CT), but it is influenced by image reconstruction. The aim of this study was to analyze the association of SUVmax deviations related to point spread function (PSF) and time-of-flight (TOF) reconstruction with tumor-to-background ratios (TBR) in colorectal liver metastases (CRLM).MethodsFifteen patients (f, 6; m, 9; median age, 59 years; range, 32 to 72 years) with 28 liver metastases were included retrospectively. FDG-PET/CT imaging (median activity, 237 MBq; range, 231 to 252 MBq; median uptake, 61 min; range, 55 to 67 min) was performed on a Siemens Biograph mCT 64 followed by image reconstruction using 3D-ordered subset expectation maximization (3D-OSEM) or 3D-OSEM with PSF modeling - both with and without TOF information. Differences in SUVmax were analyzed using the Friedman test and Wilcoxon test for paired non-parametric data. The correlation of inter-method differences with the lesions’ TBR was studied using Spearman’s rank correlation coefficient (rho). Differences between lesions with low (<4.8) and high (>4.8) TBR were analyzed using the Mann-Whitney U test (TBR measured with 3D-OSEM; binarized by its median).ResultsThere was a significant correlation of the lesions’ TBR with relative SUVmax differences related to PSF (PSF + TOF vs. 3D-OSEM + TOF, rho = 0.61; PSF vs. 3D-OSEM, rho = 0.52) or TOF (PSF + TOF vs. PSF, rho = −0.58; 3D-OSEM + TOF vs. 3D-OSEM, rho = −0.61). Accordingly, PSF algorithms only showed higher SUVmax than non-PSF algorithms in lesions with a high TBR (median differences at low/high TBR, +2.6%/+9.1% [PSF + TOF vs. 3D-OSEM + TOF]; +0.7%/+6.4% [PSF vs. 3D-OSEM]). TOF integration also led to higher SUVmax but mainly at low TBR (low/high TBR, +10.4%/+1.8% [PSF + TOF vs. PSF]; +8.6%/−0.1% [3D-OSEM + TOF vs. 3D-OSEM]).ConclusionsBoth PSF and TOF reconstruction resulted in a substantial alteration of SUVmax in CRLM. TOF provided the highest SUVmax increase in low-contrast lesions while - vice versa - PSF showed the most relevant increase in high-contrast lesions. Thus, one should be aware that quantitative analyses of lesions with varying TBR, e.g., in radiotherapy or follow-up studies, may be mainly affected by either PSF or TOF reconstruction, respectively.

Context. Fitting photometry algorithms can be very effective provided that an accurate model of the instrumental point spread function (PSF) is available. When high-precision time-resolved photometry is required, however, the use of point-source star images as empirical PSF models can be unsatisfactory, due to the limits in their spatial resolution. Theoretically-derived models, on the other hand, are limited by the unavoidable assumption of simplifying hypothesis, while the use of analytical approximations is restricted to regularly-shaped PSFs. Aims. This work investigates an innovative technique for space-based fitting photometry, based on the reconstruction of an empirical but properly-resolved PSF. The aim is the exploitation of arbitrary star images, including those produced under intentional defocus. The cases of both MOST and COROT, the first space telescopes dedicated to time-resolved stellar photometry, are considered in the evaluation of the effectiveness and performances of the proposed methodology. Methods. PSF reconstruction is based on a set of star images, periodically acquired and presenting relative subpixel displacements due to motion of the acquisition system, in this case the jitter of the satellite attitude. Higher resolution is achieved through the solution of the inverse problem. The approach can be regarded as a special application of super-resolution techniques, though a specialised procedure is proposed to better meet the PSF determination problem specificities. The application of such a model to fitting photometry is illustrated by numerical simulations for COROT and on a complete set of observations from MOST. Results. We verify that, in both scenarios, significantly better resolved PSFs can be estimated, leading to corresponding improvements in photometric results. For COROT, indeed, subpixel reconstruction enabled the successful use of fitting algorithms despite its rather complex PSF profile, which could hardly be modeled otherwise. For MOST, whose direct-imaging PSF is closer to the ordinary, comparison to other models or photometry techniques were carried out and confirmed the potential of PSF reconstruction in real observational conditions.

In this paper, we propose a novel means of single passive sensor based on depth map generation using PSF (Point Spread Function) model. PSF model was created based on disk-type in pre-processing step, and in the post-processing stage, reference images are generated through convolution operation. In considering the amount of operation and performance, we compared various equations of correlation. It also applied a histogram stretching for robust to different color of lighting. Also, it is designed in the hardware structure, and was verified processing in real-time (30 fps or more).

Respiratory motion and partial-volume effects are the two main sources of image degradation in whole-body PET imaging. Simultaneous PET-MR allows measurement of respiratory motion using MRI while collecting PET events. Improved PET images may be obtained by modeling respiratory motion and point spread function (PSF) within the PET iterative reconstruction process. In this study, the authors assessed the relative impact of PSF modeling and MR-based respiratory motion correction in phantoms and patient studies using a whole-body PET-MR scanner. An asymmetric exponential PSF model accounting for radially varying and axial detector blurring effects was obtained from point source acquisitions performed in the PET-MR scanner. A dedicated MRI acquisition protocol using single-slice steady state free-precession MR acquisitions interleaved with pencil-beam navigator echoes was developed to track respiratory motion during PET-MR studies. An iterative ordinary Poisson fully 3D OSEM PET reconstruction algorithm modeling all the physical effects of the acquisition (attenuation, scatters, random events, detectors efficiencies, PSF), as well as MR-based nonrigid respiratory deformations of tissues (in both emission and attenuation maps) was developed. Phantom and(18)F-FDG PET-MR patient studies were performed to evaluate the proposed quantitative PET-MR methods. The phantom experiment results showed that PSF modeling significantly improved contrast recovery while limiting noise propagation in the reconstruction process. In patients with soft-tissue static lesions, PSF modeling improved lesion contrast by 19.7%-109%, enhancing the detectability and assessment of small tumor foci. In a patient study with small moving hepatic lesions, the proposed reconstruction technique improved lesion contrast by 54.4%-98.1% and reduced apparent lesion size by 21.8%-34.2%. Improvements were particularly important for the smallest lesion undergoing large motion at the lung-liver interface. Heterogeneous tumor structures delineation was substantially improved. Enhancements offered by PSF modeling were more important when correcting for motion at the same time. The results suggest that the proposed quantitative PET-MR methods can significantly enhance the performance of tumor diagnosis and staging as compared to conventional methods. This approach may enable utilization of the full potential of the scanner in oncologic studies of both the lower abdomen, with moving lesions, as well as other parts of the body unaffected by motion.

Contribution of time of flight and point spread function modeling to the performance characteristics of the PET/CT Biograph mCT scanner

Context. One of the possible approaches to detecting optical counterparts of GRBs requires monitoring large parts of the sky. This idea has gained some instrumental support in recent years, such as with the “Pi of the Sky” project. The broad sky coverage of the “Pi of the Sky” apparatus results from using cameras with wide-angle lenses (20 20 field of view). Optics of this kind introduce significant deformations of the point spread function (PSF), increasing with the distance from the frame centre. A deformed PSFresults in additional uncertainties in data analysis. Aims. Our aim was to create a model describing highly deformed PSF in optical astronomy, allowing uncertainties caused by image deformations to be reduced. Methods. Detailed laboratory measurements of PSF, pixel sensitivity, and pixel response functions were performed. These data were used to create an eective high quality polynomial model of the PSF. Finally, tuning the model and tests in applications to the real sky data were performed. Results.We have developed a PSF model that accurately describes even very deformed stars in our wide-field experiment. The model is suitable for use in any other experiment with similar image deformation, with a simple tuning of its parameters. Applying this model to astrometric procedures results in a significant improvement over standard methods, while basic photometry precision performed with the model is comparable to the results of an optimised aperture algorithm. Additionally, the model was used to search for a weak signal – namely a possible gamma ray burst optical precursor – showing very promising results. Conclusions. Precise modelling of the PSF function significantly improves the astrometric precision and enhances the discovery potential of a wide-field system with lens optics.

Accurate 3D Fluorophore Localization using Phase Retrieved Pupil Functions