Spatially-varying Point Spread Function Research Articles

Resolution recovery on list mode MLEM reconstruction for dynamic cardiac SPECT system

The Dynamic Cardiac SPECT (DC-SPECT) system is being developed at the Massachusetts General Hospital, featuring a static cardio focus asymmetrical geometry enabling simultaneous high-resolution and high-sensitivity imaging. Among 14 design iterations of the DC-SPECT with varying number of detector heads, system sensitivity and resolution, the current version under development features 10 mm FWHM geometrical resolution (without resolution recovery) and 0.07% sensitivity at the center of the FOV, this is 1.5× resolution gain and 7× sensitivity gain compared to a conventional dual head gamma camera (0.01% sensitivity and 15-mm resolution). This work presents improvement in imaging resolution by implementing a spatially variant point spread function (SV-PSF) with list mode MLEM reconstruction. A resolution recovery method by PSF deconvolution is validated on list mode MLEM reconstruction for the DC-SPECT. A spatial invariant PSF is included as an additional test to show the influence of the PSF modelling accuracy on reconstructed image quality. We compare the MLEM reconstruction with and without PSF deconvolution; an analytic model is used for the calculation of system response, and the results are compared to the reconstruction with system modelling using Monte Carlo (MC) based methods. Results show that with PSF modelling applied, the quality of the reconstructed image is improved, and the DC-SPECT system can achieve a 4.5 mm central spatial resolution with average 795 counts/Mbq. Both the SV-PSF and the spatial-invariant PSF improve the image quality, and the reconstruction with SV-PSF generates line profiles closer to the ground truth. The results show substantial improvement over the GE Discovery 570c performance (7 mm spatial resolution with an average 460 counts/MBq, 5.8 mm resolution at the FOV center). The impact of PSF deconvolution is significant, improvement of the reconstructed image quality is evident in comparison to MC simulated system matrix with the same sampling size in the simulation.

Learning Time-multiplexed phase-coded apertures for snapshot spectral-depth imaging.

Depth and spectral imaging are essential technologies for a myriad of applications but have been conventionally studied as individual problems. Recent efforts have been made to optically encode spectral-depth (SD) information jointly in a single image sensor measurement, subsequently decoded by a computational algorithm. The performance of single snapshot SD imaging systems mainly depends on the optical modulation function, referred to as codification, and the computational methods used to recover the SD information from the coded measurement. The optical modulation has been conventionally realized using coded apertures (CAs), phase masks, prisms or gratings, active illumination, and many others. In this work, we propose an optical modulation (codification) strategy that employs a color-coded aperture (CCA) in conjunction with a time-varying phase-coded aperture and a spatially-varying pixel shutter, thus yielding an effective time-multiplexed coded aperture (TMCA). We show that the proposed TMCA entails a spatially-variant point spread function (PSF) for a constant depth in a scene, which, in turn, facilitates the distinguishability, and therefore, better recovery of the depth information. Further, the selective filtering of specific spectral bands by the CCA encodes relevant spectral information that is disentangled using a reconstruction algorithm. We leverage the advances of deep learning techniques to jointly learn the optical modulation and the computational decoding algorithm in an end-to-end (E2E) framework. We demonstrate via simulations and with a real testbed prototype that the proposed TMCA strategy outperforms state-of-the-art snapshot SD imaging alternatives in both spectral and depth reconstruction quality.

Reconstruction of multi-animal PET acquisitions with anisotropically variant PSF

Among other factors such as random, attenuation and scatter corrections, uniform spatial resolution is key to performing accurate quantitative studies in Positron emission tomography (PET). Particularly in preclinical PET studies involving simultaneous acquisition of multiple animals, the degradation of image resolution due to the depth of interaction (DOI) effect far from the center of the Field of View (FOV) becomes a significant concern. In this work, we incorporated a spatially-variant resolution model into a real time iterative reconstruction code to obtain accurate images of multi-animal acquisition. We estimated the spatially variant point spread function (SV-PSF) across the FOV using measurements and Monte Carlo (MC) simulations. The SV-PSF obtained was implemented in a GPU-based Ordered subset expectation maximization (OSEM) reconstruction code, which includes scatter, attenuation and random corrections. The method was evaluated with acquisitions from two preclinical PET/CT scanners of the SEDECAL Argus family: a Derenzo phantom placed 2 cm off center in the 4R-SuperArgus, and a multi-animal study with 4 mice in the 6R-SuperArgus. The SV-PSF reconstructions showed uniform spatial resolution without significant increase in reconstruction time, with superior image quality compared to the uniform PSF model.

Computational optical system design: a global optimization method in a simplified imaging system.

An optical imaging system often has problems of high complexity and low energy transmittance to compensate for aberrations. Here we propose a method to correct aberrations by coupling an optical subsystem with a digital subsystem. Specifically, in the global optimization process, the two subsystems correct their respective, easily handled aberrations so that the final imaging aberration is minimized. We design simple lenses with this method and assess imaging quality. In addition, we conduct a tolerance analysis for the proposed method and verify the effectiveness of deconvolution using a spatially varying point spread function (SVPSF) in the actual imaging process. Simulation results show the superiority of the proposed method compared with the conventional design and the feasibility of simplifying the optical system. Experimental results prove the effectiveness of deconvolution using SVPSF.

Validation of a spatially variant resolution model for small animal brain PET studies

In small animal positron emission tomography (PET) studies, given the spatial resolution of preclinical PET scanners, quantification in small regions can be challenging. Moreover, in scans where animals are placed away from the center of the field of view (CFOV), e.g. in simultaneous scans of multiple animals, quantification accuracy can be compromised due to the loss of spatial resolution towards the edge of the FOV. Here, we implemented a spatially variant resolution model to improve quantification in small regions and to allow simultaneous scanning of multiple animals without compromising quantification accuracy. The scanner’s point spread function (PSF) was characterized across the FOV and modelled using a spatially variant and asymmetric Gaussian function. The spatially variant PSF (SVPSF) was then used for resolution modelling in the iterative reconstruction. To assess the image quality, a line source phantom in a cold and warm background, as well as mouse brain [18F]FDG scans, were performed. The SVPSF and the vendor’s maximum a posteriori (MAP3D) reconstructions produced uniform spatial resolution across the scanner FOV, but MAP3D resulted in lower spatial resolution. The line sources recovery coefficient using SVPSF was similar at the CFOV and at the edge of the FOV. In contrast, the other tested reconstructions produced lower recovery coefficient at the edge of the FOV. In mouse brain reconstructions, less spill-over from hot regions to cold regions, as well as more symmetric regional brain uptake was observed using SVPSF. The contrast in brain images was the highest using SVPSF, in mice scanned at the CFOV and off-center. Incorporation of a spatially variant resolution model for small animal brain PET improves quantification accuracy in small regions and produces consistent image spatial resolution across the FOV. Therefore, simultaneous scanning of multiple animals can benefit by using spatially variant resolution modelling.

On-chip fluorescence microscopy with a random microlens diffuser.

We present an on-chip, widefield fluorescence microscope, which consists of a diffuser placed a few millimeters away from a traditional image sensor. The diffuser replaces the optics of a microscope, resulting in a compact and easy-to-assemble system with a practical working distance of over 1.5 mm. Furthermore, the diffuser encodes volumetric information, enabling refocusability in post-processing and three-dimensional (3D) imaging of sparse samples from a single acquisition. Reconstruction of images from the raw data requires a precise model of the system, so we introduce a practical calibration scheme and a physics-based forward model to efficiently account for the spatially-varying point spread function (PSF). To improve performance in low-light, we propose a random microlens diffuser, which consists of many small lenslets randomly placed on the mask surface and yields PSFs that are robust to noise. We build an experimental prototype and demonstrate our system on both planar and 3D samples.

Spatially-Variant CNN-based Point Spread Function Estimation for Blind Deconvolution and Depth Estimation in Optical Microscopy.

Optical microscopy is an essential tool in biology and medicine. Imaging thin, yet non-flat objects in a single shot (without relying on more sophisticated sectioning setups) remains challenging as the shallow depth of field that comes with highresolution microscopes leads to unsharp image regions and makes depth localization and quantitative image interpretation difficult. Here, we present a method that improves the resolution of light microscopy images of such objects by locally estimating image distortion while jointly estimating object distance to the focal plane. Specifically, we estimate the parameters of a spatiallyvariant Point Spread Function (PSF) model using a Convolutional Neural Network (CNN), which does not require instrument- or object-specific calibration. Our method recovers PSF parameters from the image itself with up to a squared Pearson correlation coefficient of 0.99 in ideal conditions, while remaining robust to object rotation, illumination variations, or photon noise. When the recovered PSFs are used with a spatially-variant and regularized Richardson-Lucy (RL) deconvolution algorithm, we observed up to 2.1 dB better Signal-to-Noise Ratio (SNR) compared to other Blind Deconvolution (BD) techniques. Following microscope-specific calibration, we further demonstrate that the recovered PSF model parameters permit estimating surface depth with a precision of 2 micrometers and over an extended range when using engineered PSFs. Our method opens up multiple possibilities for enhancing images of non-flat objects with minimal need for a priori knowledge about the optical setup.

Depth-Aware Motion Deblurring Using Loopy Belief Propagation

Most motion-blurred images captured in the real world have spatially-varying point-spread functions, and some are caused by different positions and depth values, which cannot be handled by most state-of-the-art deblurring methods based on deconvolution. To overcome this problem, we propose a depth-aware motion blur model that treats a blurred image as an integration of a sequence of clear images. To restore the clear latent image, we extend the Richardson-Lucy method to incorporate our blur model with a given depth image. The empty holes in the depth image, caused by occlusion or device limitations, are fixed by PatchMatch-based depth filling. We regard the depth image as a Markov random field and select candidate labels by using belief propagation to set and smooth depth values for empty areas. Deblurring and depth filling are performed iteratively to refine the results. Our method can also be applied to real-world images with the assistance of motion estimation. The deblurring process is shown to be convergent; moreover, the number of iterations and the level of noise amplification are acceptable. The experimental results show that our method can not only handle depth-variant motion blur but also refine depth images.

GREAT3 results – I. Systematic errors in shear estimation and the impact of real galaxy morphology

We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically-varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially-varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by $\sim 1$ per cent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the S\'{e}rsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods' results support the simple model in which additive shear biases depend linearly on PSF ellipticity.

Reservoir Computing for Prediction of the Spatially-Variant Point Spread Function

A new method is presented which provides prediction of the spatially variant point spread function for the restoration of astronomical images, distorted by atmospheric turbulence when viewed using ground-based telescopes. Our approach uses reservoir computing to firstly learn the spatio-temporal evolution of aberrations caused by turbulence, and secondly, predicts the space-varying point spread function (PSF) for application of widely-used deconvolution algorithms, resulting in the restoration of astronomical images. In this article, a reservoir-based, recurrent neural network is used to predict modal aberrations that comprise the spatially variant PSF over a wide field-of-view using a time-series ensemble from multiple reference beacons.

Massively parallel spatially variant maximum-likelihood restoration of Hubble Space Telescope imagery

We present results of concurrent maximum-likelihood restoration implementations with a spatially variant point-spread function (SV-PSF) on both synthetic and real data sets from the Hubble Space Telescope. We demonstrate that SV-PSF restoration exhibits superior performance compared with restoration with a spatially invariant point-spread function. We realize concurrency on a network of Unix workstations and on a SV-PSF model from sparse point-spread function reference information by means of bilinear interpolation. We then use the interpolative point-spread function model to implement several different SV-PSF restoration methods. These restoration methods are tested on a standard synthetic Hubble Space Telescope test case, and the results are compared on a computational effort–restoration performance basis. These methods are further applied to actual Hubble Space Telescope data, including an application that corrects for motion blur, and the results are presented.