Multiresolution spatiotemporal mechanical model of the heart as a prior to constrain the solution for 4D models of the heart.

In several nuclear cardiac imaging applications (SPECT and PET), images are formed by reconstructing tomographic data using an iterative reconstruction algorithm with corrections for physical factors involved in the imaging detection process and with corrections for cardiac and respiratory motion. The physical factors are modeled as coefficients in the matrix of a system of linear equations and include attenuation, scatter, and spatially varying geometric response. The solution to the tomographic problem involves solving the inverse of this system matrix. This requires the design of an iterative reconstruction algorithm with a statistical model that best fits the data acquisition. The most appropriate model is based on a Poisson distribution. Using Bayes Theorem, an iterative reconstruction algorithm is designed to determine the maximum a posteriori estimate of the reconstructed image with constraints that maximizes the Bayesian likelihood function for the Poisson statistical model. The a priori distribution is formulated as the joint entropy (JE) to measure the similarity between the gated cardiac PET image and the cardiac MRI cine image modeled as a FE mechanical model. The developed algorithm shows the potential of using a FE mechanical model of the heart derived from a cardiac MRI cine scan to constrain solutions of gated cardiac PET images

Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

Multimodal Partial-Volume Correction: Application to 18F-Fluoride PET/CT Bone Metastases Studies

18F-fluoride PET/CT offers the opportunity for accurate skeletal metastasis staging, compared with conventional imaging methods. 18F-fluoride is a bone-specific tracer whose uptake depends on osteoblastic activity. Because of the resulting increase in bone mineralization and sclerosis, the osteoblastic process can also be detected morphologically in CT images. Although CT is characterized by high resolution, the potential of PET is limited by its lower spatial resolution and the resulting partial-volume effect. In this context, the synergy between PET and CT presents an opportunity to resolve this limitation using a novel multimodal approach called synergistic functional–structural resolution recovery (SFS-RR). Its performance is benchmarked against current resolution recovery technology using the point-spread function (PSF) of the scanner in the reconstruction procedure. Methods: The SFS-RR technique takes advantage of the multiresolution property of the wavelet transform applied to both functional and structural images to create a high-resolution PET image that exploits the structural information of CT. Although the method was originally conceived for PET/MR imaging of brain data, an ad hoc version for whole-body PET/CT is proposed here. Three phantom experiments and 2 datasets of metastatic bone 18F-fluoride PET/CT images from primary prostate and breast cancer were used to test the algorithm performances. The SFS-RR images were compared with the manufacturer’s PSF-based reconstruction using the standardized uptake value (SUV) and the metabolic volume as metrics for quantification. Results: When compared with standard PET images, the phantom experiments showed a bias reduction of 14% in activity and 1.3 cm3 in volume estimates for PSF images and up to 20% and 2.5 cm3 for the SFS-RR images. The SFS-RR images were characterized by a higher recovery coefficient (up to 60%) whereas noise levels remained comparable to those of standard PET. The clinical data showed an increase in the SUV estimates for SFS-RR images up to 34% for peak SUV and 50% for maximum SUV and mean SUV. Images were also characterized by sharper lesion contours and better lesion detectability. Conclusion: The proposed methodology generates PET images with improved quantitative and qualitative properties. Compared with standard methods, SFS-RR provides superior lesion segmentation and quantification, which may result in more accurate tumor characterization

Minimax Emission Computed Tomography using High-Resolution Anatomical Side Information and B-Spline Models

In this paper a minimax methodology is presented for combining information from two imaging modalities having different intrinsic spatial resolutions. The focus application is emission computed tomography (ECT), a low-resolution modality for reconstruction of radionuclide tracer density, when supplemented by high-resolution anatomical boundary information extracted from a magnetic resonance image (MRI) of the same imaging volume. The MRI boundary within the two-dimensional (2-D) slice of interest is parameterized by a closed planar curve. The Cramer-Rao (CR) lower bound is used to analyze estimation errors for different boundary shapes. Under a spatially inhomogeneous Gibbs field model for the tracer density a representation for the minimax MRI-enhanced tracer density estimator is obtained. It is shown that the estimator is asymptotically equivalent to a penalized maximum likelihood (PML) estimator with resolution-selective Gibbs penalty. Quantitative comparisons are presented using the iterative space alternating generalized expectation maximization (SAGE-FM) algorithm to implement the PML estimator with and without minimax weight averaging.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85822/1/Fessler86.pd

Tomographic reconstruction with non-linear diagonal estimators

In tomographic reconstruction, the inversion of the Radon transform in the presence of noise is numerically unstable. Reconstruction estimators are studied where the regularization is performed by a thresholding in a wavelet or wavelet packet decomposition. These estimators are efficient and their optimality can be established when the decomposition provides a near-diagonalization of the inverse Radon transform operator and a compact representation of the object to be recovered. Several new estimators are investigated in different decomposition. First numerical results already exhibit a strong metrical and perceptual improvement over current reconstruction methods. These estimators are implemented with fast non-iterative algorithms, and are expected to outperform Filtered Back-Projection and iterative procedures for PET, SPECT and X-ray CT devices

A Sparse Bayesian Estimation Framework for Conditioning Prior Geologic Models to Nonlinear Flow Measurements

We present a Bayesian framework for reconstruction of subsurface hydraulic properties from nonlinear dynamic flow data by imposing sparsity on the distribution of the solution coefficients in a compression transform domain