Jeffrey A. Fessier

Joint estimation of respiratory motion and activity in 4D PET using CT side information

In previous work, we proposed a Poisson statistical model for gated PET data in which the distribution was parametrized in terms of both image intensity and motion parameters. The motion parameters related the activity image in each gate to that of a base image in some fixed gate. By doing maximum loglikelihood (ML) estimation of all parameters simultaneously, one obtains an estimate of the base gate image that exploits the full set of measured sinogram data. Previously, this joint ML approach was compared, in a highly simplified single-slice setting, to more conventional methods. Performance was measured in terms of the recovery of tracer uptake in a synthetic lung nodule. This paper reports the extension to 3D with much more realistic simulated motion. Furthermore, in addition to pure ML estimation, we consider the use of side information from a breath-hold CT scan to facilitate regularization, while preserving hot lesions of the kind seen in FDG oncology studies

Tomographic Reconstruction of Tracer Gas Concentration Profiles in a Room with the Use of a Single OP-FTIR and Two Iterative Algorithms: ART and PWLS

ABSTRACT Computed tomographic (CT) reconstructions of air contaminant concentration fields were conducted in a room-sized chamber employing a single open-path Fourier transform infrared (OP-FTIR) instrument and a combination of 52 flat mirrors and 4 retroreflectors. A total of 56 beam path data were repeatedly collected for around 1 hr while maintaining a stable concentration gradient. The plane of the room was divided into 195 pixels (13 × 15) for reconstruction. The algebraic reconstruction technique (ART) failed to reconstruct the original concentration gradient patterns for most cases. These poor results were caused by the “highly underdetermined condition” in which the number of unknown values (156 pixels) exceeds that of known data (56 path integral concentrations) in the experimental setting. A new CT algorithm, called the penalized weighted least-squares (PWLS), was applied to remedy this condition. The peak locations were correctly positioned in the PWLS-CT reconstructions. A notable feature of the PWLS-CT reconstructions was a significant reduction of highly irregular noise peaks found in the ART-CT reconstructions. However, the peak heights were slightly reduced in the PWLS-CT reconstructions due to the nature of the PWLS algorithm. PWLS could converge on the original concentration gradient even when a fairly high error was embedded into some experimentally measured path integral concentrations. It was also found in the simulation tests that the PWLS algorithm was very robust with respect to random errors in the path integral concentrations. This beam geometry and the use of a single OP-FTIR scanning system, in combination with the PWLS algorithm, is a system applicable to both environmental and industrial settings.

Low dose CT image reconstruction with learned sparsifying transform

A major challenge in computed tomography (CT) is to reduce X-ray dose to a low or even ultra-low level while maintaining the high quality of reconstructed images. We propose a new method for CT reconstruction that combines penalized weighted-least squares reconstruction (PWLS) with regularization based on a sparsifying transform (PWLS-ST) learned from a dataset of numerous CT images. We adopt an alternating algorithm to optimize the PWLS-ST cost function that alternates between a CT image update step and a sparse coding step. We adopt a relaxed linearized augmented Lagrangian method with ordered-subsets (relaxed OS-LALM) to accelerate the CT image update step by reducing the number of forward and backward projections. Numerical experiments on the XCAT phantom show that for low dose levels, the proposed PWLS-ST method dramatically improves the quality of reconstructed images compared to PWLS reconstruction with a nonadaptive edge-preserving regularizer (PWLS-EP).

Quadratic regularization design for 3D cylindrical PET

Statistical methods for tomographic image reconstruction lead to improved spatial resolution and noise properties in PET. Penalized-likelihood (PL) image reconstruction methods involve maximizing an objective function that is based on the log-likelihood of the sinogram measurements and on a roughness penalty function to control noise. In emission tomography, PL methods (and MAP methods) based on conventional quadratic regularization functions lead to nonuniform and anisotropic spatial resolution, even for idealized shift-invariant imaging systems. We have previously addressed this problem for parallel-beam 2D emission tomography, and for fan-beam 2D transmission tomography by designing data-dependent, shift-variant regularizers that improve resolution uniformity and isotropy, even for idealized shift-invariant imaging systems. This paper extends those methods to 3D cylindrical PET, using an analytical design approach that is numerically efficient.

Gradient based image registration using importance sampling

Analytical gradient based non-rigid image registration methods, using intensity based similarity measures (e.g. mutual information), have proven to be capable of accurately handling many types of deformations. While their versatility is largely in part to their high degrees of freedom, the computation of the gradient of the similarity measure with respect to the many warp parameters becomes very time consuming. Recently, a simple stochastic approximation method using a small random subset of image pixels to approximate this gradient has been shown to be effective. We propose to use importance sampling to improve the accuracy and reduce the variance of this approximation by preferentially selecting pixels near image edges. Initial empirical results show that a combination of stochastic approximation methods and importance sampling greatly improves the rate of convergence of the registration process while preserving accuracy

Model-based estimation of T2 maps with dual-echo steady-state MR imaging

Fast and accurate quantification of spin-spin relaxation parameter T2 is of importance for clinical MRI applications. Classical spin echo (SE) sequences yield straightforward T2 estimates, but require undesirably long scans. By contrast, steady-state sequences such as the Dual-Echo Steady-State (DESS) sequence are considerably faster, but produce signals that depend on more complex functions of both desired and nuisance parameters. Conventional method-of-moments estimators exhibit systematic error because of the approximations used to bypass nuisance parameter estimation. To improve T2 mapping accuracy, we propose a novel, model-based approach to this nonlinear estimation problem. We use a fast scan to estimate nuisance parameters M0* and T1, and then use the exact DESS signal model for regularized T2 estimation from DESS data, with minimal approximations. MR brain simulation results show that the proposed approach substantially improves T2 estimation accuracy and precision, compared to conventional method-of-moments estimators.

Joint estimation of activity distribution and attenuation map for TOF-PET using alternating direction method of multiplier

Recent advances in TOF PET joint estimation of activity and attenuation showed that activity and attenuation can be determined up to a global constant scale without severe crosstalk. MLAA was first proposed to estimate activity and attenuation map simultaneously, and then MLACF was developed to estimate activity and attenuation compensation factor (ACF). MLAA incorporated prior knowledge on the zero attenuation value outside body area to determine global scalar, but was slow to converge. MLACF converged much faster than MLAA, but required knowing total activity level in advance. We propose a new optimization method based on variable splitting and alternating direction method of multiplier (MLADMM). Our proposed MLADMM achieved fast convergence rate comparable to MLACF without knowing total activity level. MLADMM also has a potential to use more sophisticated MR-based prior for attenuation in PET-MR.