4D-PET reconstruction using a spline-residue model with spatial and temporal roughness penalties

4D reconstruction of dynamic positron emission tomography (dPET) data can improve the signal-to-noise ratio in reconstructed image sequences by fitting smooth temporal functions to the voxel time-activity-curves (TACs) during the reconstruction, though the optimal choice of function remains an open question. We propose a spline-residue model, which describes TACs as weighted sums of convolutions of the arterial input function with cubic B-spline basis functions. Convolution with the input function constrains the spline-residue model at early time-points, potentially enhancing noise suppression in early time-frames, while still allowing a wide range of TAC descriptions over the entire imaged time-course, thus limiting bias. 
 Spline-residue based 4D-reconstruction is compared to that of a conventional (non-4D) maximum a posteriori (MAP) algorithm, and to 4D-reconstructions based on adaptive-knot cubic B-splines, the spectral model and an irreversible two-tissue compartment ('2C3K') model. 4D reconstructions were carried out using a nested-MAP algorithm including spatial and temporal roughness penalties. The algorithms were tested using Monte-Carlo simulated scanner data, generated for a digital thoracic phantom with uptake kinetics based on a dynamic [18F]-Fluromisonidazole scan of a non-small cell lung cancer patient. For every algorithm, parametric maps were calculated by fitting each voxel TAC within a sub-region of the reconstructed images with the 2C3K model. 
 Compared to conventional MAP reconstruction, spline-residue-based 4D reconstruction achieved >50% improvements for 5 of the 8 combinations of the 4 kinetics parameters for which parametric maps were created with the bias and noise measures used to analyse them, and produced better results for 5/8 combinations than any of the other reconstruction algorithms studied, while spectral model-based 4D reconstruction produced the best results for 2/8. 2C3K model-based 4D reconstruction generated the most biased parametric maps. Inclusion of a temporal roughness penalty function improved the performance of 4D reconstruction based on the cubic B-spline, spectral and spline-residue models.&#13

preliminary clinical evaluation of the ASTRA4D algorithm

Objectives. To propose and evaluate a four-dimensional (4D) algorithm for joint motion elimination and spatiotemporal noise reduction in low-dose dynamic myocardial computed tomography perfusion (CTP). Methods. Thirty patients with suspected or confirmed coronary artery disease were prospectively included und underwent dynamic contrast-enhanced 320-row CTP. The presented deformable image registration method ASTRA4D identifies a low-dimensional linear model of contrast propagation (by principal component analysis, PCA) of the ex-ante temporally smoothed time-intensity curves (by local polynomial regression). Quantitative (standard deviation, signal-to-noise ratio (SNR), temporal variation, volumetric deformation) and qualitative (motion, contrast, contour sharpness; 1, poor; 5, excellent) measures of CTP quality were assessed for the original and motion-compensated volumes (without and with temporal filtering, PCA/ASTRA4D). Following visual myocardial perfusion deficit detection by two readers, diagnostic accuracy was evaluated using 1.5T magnetic resonance (MR) myocardial perfusion imaging as the reference standard in 15 patients. Results. Registration using ASTRA4D was successful in all 30 patients and resulted in comparison with the benchmark PCA in significantly (p<0.001) reduced noise over time (-83%, 178.5 vs 29.9) and spatially (-34%, 21.4 vs 14.1) as well as improved SNR (+47%, 3.6 vs 5.3) and subjective image quality (motion, contrast, contour sharpness: +1.0, +1.0, +0.5). ASTRA4D resulted in significantly improved per-segment sensitivity of 91% (58/64) and similar specificity of 96% (429/446) compared with PCA (52%, 33/64; 98%, 435/446; p=0.011) and the original sequence (45%, 29/64; 98%, 438/446; p=0.003) in the visual detection of perfusion deficits. Conclusions. The proposed functional approach to temporal denoising and morphologic alignment was shown to improve quality metrics and sensitivity of 4D CTP in the detection of myocardial ischemia.Zielsetzung. Die Entwicklung und Bewertung einer Methode zur simultanen Rauschreduktion und Bewegungskorrektur für niedrig dosierte dynamische CT Myokardperfusion. Methoden. Dreißig prospektiv eingeschlossene Patienten mit vermuteter oder bestätigter koronarer Herzkrankheit wurden einer dynamischen CT Myokardperfusionsuntersuchung unterzogen. Die präsentierte Registrierungsmethode ASTRA4D ermittelt ein niedrigdimensionales Modell des Kontrastmittelflusses (mittels einer Hauptkomponentenanalyse, PCA) der vorab zeitlich geglätteten Intensitätskurven (mittels lokaler polynomialer Regression). Quantitative (Standardabweichung, Signal-Rausch-Verhältnis (SNR), zeitliche Schwankung, räumliche Verformung) und qualitative (Bewegung, Kontrast, Kantenschärfe; 1, schlecht; 5, ausgezeichnet) Kennzahlen der unbearbeiteten und bewegungskorrigierten Perfusionsdatensätze (ohne und mit zeitlicher Glättung PCA/ASTRA4D) wurden ermittelt. Nach visueller Beurteilung von myokardialen Perfusionsdefiziten durch zwei Radiologen wurde die diagnostische Genauigkeit im Verhältnis zu 1.5T Magnetresonanztomographie in 15 Patienten ermittelt. Resultate. Bewegungskorrektur mit ASTRA4D war in allen 30 Patienten erfolgreich und resultierte im Vergleich mit der PCA Methode in signifikant (p<0.001) verringerter zeitlicher Schwankung (-83%, 178.5 gegenüber 29.9) und räumlichem Rauschen (-34%, 21.4 gegenüber 14.1) sowie verbesserter SNR (+47%, 3.6 gegenüber 5.3) und subjektiven Qualitätskriterien (Bewegung, Kontrast, Kantenschärfe: +1.0, +1.0, +0.5). ASTRA4D resultierte in signifikant verbesserter segmentweiser Sensitivität 91% (58/64) und ähnlicher Spezifizität 96% (429/446) verglichen mit der PCA Methode (52%, 33/64; 98%, 435/446; p=0.011) und dem unbearbeiteten Perfusionsdatensatz (45%, 29/64; 98%, 438/446; p=0.003) in der visuellen Beurteilung von myokardialen Perfusionsdefiziten. Schlussfolgerungen. Der vorgeschlagene funktionale Ansatz zur simultanen Rauschreduktion und Bewegungskorrektur verbesserte Qualitätskriterien und Sensitivität von dynamischer CT Perfusion in der visuellen Erkennung von Myokardischämie

Smoothing dynamic positron emission tomography time courses using functional principal components

A functional smoothing approach to the analysis of PET time course data is presented. By borrowing information across space and accounting for this pooling through the use of a nonparametric covariate adjustment, it is possible to smooth the PET time course data thus reducing the noise. A new model for functional data analysis, the Multiplicative Nonparametric Random Effects Model, is introduced to more accurately account for the variation in the data. A locally adaptive bandwidth choice helps to determine the correct amount of smoothing at each time point. This preprocessing step to smooth the data then allows Subsequent analysis by methods Such as Spectral Analysis to be substantially improved in terms of their mean squared error

Non-parametric PSF estimation from celestial transit solar images using blind deconvolution

Context: Characterization of instrumental effects in astronomical imaging is important in order to extract accurate physical information from the observations. The measured image in a real optical instrument is usually represented by the convolution of an ideal image with a Point Spread Function (PSF). Additionally, the image acquisition process is also contaminated by other sources of noise (read-out, photon-counting). The problem of estimating both the PSF and a denoised image is called blind deconvolution and is ill-posed. Aims: We propose a blind deconvolution scheme that relies on image regularization. Contrarily to most methods presented in the literature, our method does not assume a parametric model of the PSF and can thus be applied to any telescope. Methods: Our scheme uses a wavelet analysis prior model on the image and weak assumptions on the PSF. We use observations from a celestial transit, where the occulting body can be assumed to be a black disk. These constraints allow us to retain meaningful solutions for the filter and the image, eliminating trivial, translated and interchanged solutions. Under an additive Gaussian noise assumption, they also enforce noise canceling and avoid reconstruction artifacts by promoting the whiteness of the residual between the blurred observations and the cleaned data. Results: Our method is applied to synthetic and experimental data. The PSF is estimated for the SECCHI/EUVI instrument using the 2007 Lunar transit, and for SDO/AIA using the 2012 Venus transit. Results show that the proposed non-parametric blind deconvolution method is able to estimate the core of the PSF with a similar quality to parametric methods proposed in the literature. We also show that, if these parametric estimations are incorporated in the acquisition model, the resulting PSF outperforms both the parametric and non-parametric methods.Comment: 31 pages, 47 figure