Digital reference objects for evaluating algorithm performance in MR image formation.

PURPOSE: Digital Reference Objects (DROs) are mathematical phantoms that can serve as a basis for evaluating MR image quality (IQ) in an objective way. Their main purpose is to facilitate the establishment of fully automated and perfectly reproducible IQ metrics to objectively compare different algorithms in MR image formation in a standardized manner. They also allow to re-build parts of standard phantoms. METHODS: We sample DROs directly in k-space, using analytical formulas for the continuous Fourier transform of primitive shapes. We demonstrate this DRO approach by applying a state-of-the-art CNN-based denoising algorithm that is robust to varying noise levels to noisy images of the resolution section of the well-known ACR phantom for IQ assessment, reconstructed from both measured and simulated k-space data. RESULTS: Applying the CNN-based denoising algorithm to the measured and simulated version of the ACR phantom resolution section produced virtually identical results, as confirmed by visual and quantitative comparison. CONCLUSIONS: DROs can help guide technology selection during the development of new algorithms in MR image formation, e.g., via deep learning. This could be an important step towards reproducible MR image formation.

Quantizing Euclidean Motions via Double-Coset Decomposition.

Concepts from mathematical crystallography and group theory are used here to quantize the group of rigid-body motions, resulting in a "motion alphabet" with which robot motion primitives are expressed. From these primitives it is possible to develop a dictionary of physical actions. Equipped with an alphabet of the sort developed here, intelligent actions of robots in the world can be approximated with finite sequences of characters, thereby forming the foundation of a language in which robot motion is articulated. In particular, we use the discrete handedness-preserving symmetries of macromolecular crystals (known in mathematical crystallography as Sohncke space groups) to form a coarse discretization of the space SE(3) of rigid-body motions. This discretization is made finer by subdividing using the concept of double-coset decomposition. More specifically, a very efficient, equivolumetric quantization of spatial motion can be defined using the group-theoretic concept of a double-coset decomposition of the form Γ\SE(3)/Δ, where Γ is a Sohncke space group and Δ is a finite group of rotational symmetries such as those of the icosahedron. The resulting discrete alphabet is based on a very uniform sampling of SE(3) and is a tool for describing the continuous trajectories of robots and humans. An efficient coarse-to-fine search algorithm is presented to round off any motion sampled from the continuous group of motions to the nearest element of our alphabet. It is shown that our alphabet and this efficient rounding algorithm can be used as a geometric data structure to accelerate the performance of other sampling schemes designed for desirable dispersion or discrepancy properties. Moreover, the general "signals to symbols" problem in artificial intelligence is cast in this framework for robots moving continuously in the world.

Time-of-flight PET image reconstruction using origin ensembles.

The origin ensemble (OE) algorithm is a novel statistical method for minimum-mean-square-error (MMSE) reconstruction of emission tomography data. This method allows one to perform reconstruction entirely in the image domain, i.e. without the use of forward and backprojection operations. We have investigated the OE algorithm in the context of list-mode (LM) time-of-flight (TOF) PET reconstruction. In this paper, we provide a general introduction to MMSE reconstruction, and a statistically rigorous derivation of the OE algorithm. We show how to efficiently incorporate TOF information into the reconstruction process, and how to correct for random coincidences and scattered events. To examine the feasibility of LM-TOF MMSE reconstruction with the OE algorithm, we applied MMSE-OE and standard maximum-likelihood expectation-maximization (ML-EM) reconstruction to LM-TOF phantom data with a count number typically registered in clinical PET examinations. We analyzed the convergence behavior of the OE algorithm, and compared reconstruction time and image quality to that of the EM algorithm. In summary, during the reconstruction process, MMSE-OE contrast recovery (CRV) remained approximately the same, while background variability (BV) gradually decreased with an increasing number of OE iterations. The final MMSE-OE images exhibited lower BV and a slightly lower CRV than the corresponding ML-EM images. The reconstruction time of the OE algorithm was approximately 1.3 times longer. At the same time, the OE algorithm can inherently provide a comprehensive statistical characterization of the acquired data. This characterization can be utilized for further data processing, e.g. in kinetic analysis and image registration, making the OE algorithm a promising approach in a variety of applications.

Fat-constrained 18F-FDG PET reconstruction in hybrid PET/MR imaging.

UNLABELLED: Fusion of information from PET and MR imaging can increase the diagnostic value of both modalities. This work sought to improve (18)F FDG PET image quality by using MR Dixon fat-constrained images to constrain PET image reconstruction to low-fat regions, with the working hypothesis that fatty tissue metabolism is low in glucose consumption. METHODS: A novel constrained PET reconstruction algorithm was implemented via a modification of the system matrix in list-mode time-of-flight ordered-subsets expectation maximization reconstruction, similar to the way time-of-flight weighting is incorporated. To demonstrate its use in PET/MR imaging, we modeled a constraint based on fat/water-separating Dixon MR images that shift activity away from regions of fat tissue during PET image reconstruction. PET and MR imaging scans of a modified National Electrical Manufacturers Association/International Electrotechnical Commission body phantom simulating body fat/water composition and in vivo experiments on 2 oncology patients were performed on a commercial time-of-flight PET/MR imaging system. RESULTS: Fat-constrained PET reconstruction visibly and quantitatively increased resolution and contrast between high-uptake and fatty-tissue regions without significantly affecting the images in nonfat regions. CONCLUSION: The incorporation of MR tissue information, such as fat, in image reconstruction can improve the quality of PET images. The combination of a variety of potential other MR tissue characteristics with PET represents a further justification for merging MR data with PET data in hybrid systems.