Standard Point Spread Function Research Articles

Synthesized Image Reconstruction for Post-Reconstruction Resolution Recovery.

Resolution recovery (RR) techniques in positron emission tomography (PET) imaging aim to mitigate spatial resolution losses and related inaccuracies in quantification by using a model of the system's point spread function (PSF) during reconstruction or post-processing. However, including PSF modeling in fully 3-D image reconstruction is far from trivial as access to the scanner-specific forward and back-projectors is required, along with access to the 3-D sinogram data. Hence, post-reconstruction RR methods, such as the Richardson-Lucy (RL) algorithm, can be more practical. However, the RL method leads to relatively rapid noise amplification in early image iterations, giving inferior image quality compared to iterates obtained by placing the PSF model in the reconstruction algorithm. We propose a post-reconstruction RR method by synthesizing PET data by a forward projection of an initial real data reconstruction (such reconstructions are usually available via a scanner's standard reconstruction software). The synthetic PET data are then used to reconstruct an image, but crucially now including a modeled PSF within the system model used during reconstruction. Results from simulations and real data demonstrate the proposed method improves image quality compared to the RL algorithm, whilst avoiding the need for scanner-specific projectors and raw sinogram data (as required by standard PSF modeling within reconstruction).

Joint Estimation of Trajectory and Motion Model Parameters in Three-Dimensional Single Particle Tracking using the Double-Helix Point Spread Function

Single particle tracking (SPT) is a powerful tool for studying and analyzing dynamic mechanisms of biomolecules. Our approach to analyzing SPT data uses a generic Expectation Maximization (EM)-based framework for simultaneous localization refinement and parameter estimation. This approach has benefits in terms of estimation accuracy across a wide range of signal to noise levels. When observing a particle of interest moving in three-dimensions, the acquired data is typically a sequence of images of a 2-D slice of the point spread function (PSF) determined by the relative position of the focal plane and the particle. Unlike the standard PSF, which has only one bright spot in the image plane, the Double-Helix point spread function (DH-PSF) forms two bright spots. As the particle moves along the optical axis, these spots rotate, thereby encoding the axial position of the particle. In this work, we extend our EM-based scheme to handle the DH-PSF. Our method begins with the segmented images, using the camera data directly to jointly estimate particle locations and motion model parameters. We consider two representative methods in our framework: one uses a direct sequential importance resampling (SIR) based particle filter (PF) and particle smoother (PS), the other uses the alternative Gaussian particle filter (aGPF) and the backward-simulation particle smoother (BSPS). The aGPF/BSPS is less general but has significantly less computational load when compared to the PF/PS. Using extensive simulation studies, we demonstrate that both methods produce reliable estimates of both particle position and model parameters. In future work, we plan to consider the additional influence of readout noise determined by specific camera sensors.

MADX – a simple technique for source detection and measurement using multiband imaging from the Herschel–ATLAS survey

ABSTRACT We describe the method used to detect sources for the Herschel–ATLAS (Herschel Astrophysical Terahertz Large Area Survey) survey. The method is to filter the individual bands using a matched filter, based on the point spread function (PSF) and confusion noise, and then form the inverse variance-weighted sum of the individual bands, including weights determined by a chosen spectral energy distribution. Peaks in this combined image are used to estimate the source positions. The fluxes for each source are estimated from the filtered single-band images, interpolated to the exact subpixel position. We test the method by creating simulated maps in three bands with PSFs, pixel sizes, and Gaussian instrumental noise that match the 250, 350, and 500 μm bands of Herschel–ATLAS. We use our method to detect sources and compare the measured positions and fluxes to the input sources. The multiband approach allows reliable source detection a factor 1.2–3 lower in flux compared to single-band source detection, depending on the source colours. The false detection rate is reduced by a factor between 4 and 10, and the variance of the source position errors is reduced by about a factor 1.5. We also consider the effect of confusion noise and find that the appropriate matched filter gives a further improvement in completeness and noise over the standard PSF filter approach. Overall the two modifications give a factor of 1.5–3 improvement in the depth of the recovered catalogues compared to a single-band PSF filter approach.

Synthetic Aperture Radar Correlation Imaging

In synthetic aperture radar (SAR) imaging, a scene of interest is illuminated by electromagnetic waves. The goal is to reconstruct an image of the scene from the measurement of the scattered waves using airborne antenna(s). A new imaging algorithm, known as correlation imaging, is suggested in which an image is formed of the reflectivity function squared. The algorithm uses what is often called the correlation function in place of the standard slow- and fast-time data. The correlation function is found via a simple preprocessing step applied to the collected data. A backprojection algorithm is formulated using microlocal analysis. It is found that range and cross-range resolution are improved compared to standard SAR imaging. In addition, the point-spread function (PSF) of the correlation image-fidelity operator exhibits reduced side lobes in comparison with the standard SAR PSF. We also show that the contribution to the image from clutter displaying volume scattering behavior is reduced when certain pairs of correlated data sets are avoided. Note that by clutter we refer to scatterers on the ground that are not of interest; we do not address the case of propagating through a random (i.e., cluttered) medium.

Practical considerations for image-based PSF and blobs reconstruction in PET

Iterative reconstructions in positron emission tomography (PET) need a model relating the recorded data to the object/patient being imaged, called the system matrix (SM). The more realistic this model, the better the spatial resolution in the reconstructed images. However, a serious concern when using a SM that accurately models the resolution properties of the PET system is the undesirable edge artefact, visible through oscillations near sharp discontinuities in the reconstructed images. This artefact is a natural consequence of solving an ill-conditioned inverse problem, where the recorded data are band-limited. In this paper, we focus on practical aspects when considering image-based point-spread function (PSF) reconstructions. To remove the edge artefact, we propose to use a particular case of the method of sieves (Grenander 1981 Inference New York: Wiley), which simply consists in performing a standard PSF reconstruction, followed by a post-smoothing using the PSF as the convolution kernel. Using analytical simulations, we investigate the impact of different reconstruction and PSF modelling parameters on the edge artefact and its suppression, in the case of noise-free data and an exactly known PSF. Using Monte-Carlo simulations, we assess the proposed method of sieves with respect to the choice of the geometric projector and the PSF model used in the reconstruction. When the PSF model is accurately known, we show that the proposed method of sieves succeeds in completely suppressing the edge artefact, though after a number of iterations higher than typically used in practice. When applying the method to realistic data (i.e. unknown true SM and noisy data), we show that the choice of the geometric projector and the PSF model does not impact the results in terms of noise and contrast recovery, as long as the PSF has a width close to the true PSF one. Equivalent results were obtained using either blobs or voxels in the same conditions (i.e. the blob’s density function being the same as the voxel-based PSF). From a practical point-of-view, the method can be used to perform fast reconstructions based on very simple models (compared to sinogram-based PSF modelling), producing artefact-free images with a better compromise between noise and spatial resolution than images reconstructed without or with under-estimated PSF. Besides, the method inherently limits the spatial resolution in the reconstructed images to the intrinsic one of the PET system.

Motion frozen 18F-FDG cardiac PET

BackgroundPET reconstruction incorporating spatially variant 3D Point Spread Function (PSF) improves contrast and image resolution. “Cardiac Motion Frozen” (CMF) processing eliminates the influence of cardiac motion in static summed images. We have evaluated the combined use of CMF- and PSF-based reconstruction for high-resolution cardiac PET. MethodsStatic and 16-bin ECG-gated images of 20 patients referred for 18F-FDG myocardial viability scans were obtained on a Siemens Biograph-64. CMF was applied to the gated images reconstructed with PSF. Myocardium to blood contrast, maximum left ventricle (LV) counts to defect contrast, contrast-to-noise (CNR) and wall thickness with standard reconstruction (2D-AWOSEM), PSF, ED-gated PSF, and CMF-PSF were compared. ResultsThe measured wall thickness was 18.9 ± 5.2 mm for 2D-AWOSEM, 16.6 ± 4.5 mm for PSF, and 13.8 ± 3.9 mm for CMF-PSF reconstructed images (all P < .05). The CMF-PSF myocardium to blood and maximum LV counts to defect contrasts (5.7 ± 2.7, 10.0 ± 5.7) were higher than for 2D-AWOSEM (3.5 ± 1.4, 6.5 ± 3.1) and for PSF (3.9 ± 1.7, 7.7 ± 3.7) (CMF vs all other, P < .05). The CNR for CMF-PSF (26.3 ± 17.5) was comparable to PSF (29.1 ± 18.3), but higher than for ED-gated dataset (13.7 ± 8.8, P < .05). ConclusionCombined CMF-PSF reconstruction increased myocardium to blood contrast, maximum LV counts to defect contrast and maintained equivalent noise when compared to static summed 2D-AWOSEM and PSF reconstruction.

In vivo Three-Dimensional Superresolution Fluorescence Tracking using a Double-Helix Point Spread Function.

The point spread function (PSF) of a widefield fluorescence microscope is not suitable for three-dimensional super-resolution imaging. We characterize the localization precision of a unique method for 3D superresolution imaging featuring a double-helix point spread function (DH-PSF). The DH-PSF is designed to have two lobes that rotate about their midpoint in any transverse plane as a function of the axial position of the emitter. In effect, the PSF appears as a double helix in three dimensions. By comparing the Cramer-Rao bound of the DH-PSF with the standard PSF as a function of the axial position, we show that the DH-PSF has a higher and more uniform localization precision than the standard PSF throughout a 2 μm depth of field. Comparisons between the DH-PSF and other methods for 3D super-resolution are briefly discussed. We also illustrate the applicability of the DH-PSF for imaging weak emitters in biological systems by tracking the movement of quantum dots in glycerol and in live cells.

Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system

We demonstrate three-dimensional tracking of fluorescent microparticles, with a computational optical system whose point spread function (PSF) has been engineered to have two twisting lobes along the optical axis, generating a three-dimensional (3D) double-helix (DH) PSF. An information theoretical comparison in photon limited systems shows that the DH-PSF delivers higher Fisher information for 3D localization than the standard PSF. Hence, DH-PSF systems provide better position estimation accuracy. Experiments demonstrate average position estimation accuracies under 14nm and 37nm in the transverse and axial dimensions respectively. The system determines the 3D position of multiple particles with a single image and tracks them over time while providing their velocities.