Estimating the Center of Rotation of Tomographic Imaging Systems with a Limited Number of Projections.

For a tomographic imaging system, image reconstruction quality is dependent on the accurate determination of coordinates for the true center of rotation (COR). A significant COR offset error may introduce ringing, streaking, or other artifacts, while smaller error in determining COR may blur the reconstructed image. Well known COR correction techniques including image registration, center of mass calculation, or reconstruction evaluation work well under certain conditions. However, many of these methods do not consider various real-world cases such as a tilted sensor or non-parallel projections. Furthermore, a limited number of projections introduces stripe artifacts into the image reconstruction that interfere with many of these classic COR correction techniques. In this paper, we propose a revised variance-based algorithm to find the correct COR position automatically prior to tomographic reconstruction. The algorithm was tested on both simulated phantoms and acquired datasets, and our results show improved reconstruction accuracy.

Trust Region Methods for the Estimation of a Complex Exponential Decay Model in MRI With a Single-Shot or Multi-Shot Trajectory.

Joint estimation of spin density R2* decay and OFF-resonance frequency maps is very useful in many magnetic resonance imaging applications. The standard multi-echo approach can achieve high accuracy but requires a long acquisition time for sampling multiple k-space frames. There are many approaches to accelerate the acquisition. Among them, single-shot or multi-shot trajectory-based sampling has recently drawn attention due to its fast data acquisition. However, this sampling strategy destroys the Fourier relationship between k-space and images, leading to a great challenge for the reconstruction. In this paper, we present two trust region methods based on two different linearization strategies for the nonlinear signal model. A trust region is defined as a local area in the variable space where a local linear approximation is trustable. In each iteration, the method minimizes a local approximation within a trust region so that the step size can be kept in a suitable scale. A continuation scheme is applied to reduce the regularization gradually over the parameter maps and facilitates convergence from poor initializations. The two trust region methods are compared with the two other previously proposed methods--the nonlinear conjugate gradients and the gradual refinement algorithm. Experiments based on various synthetic data and real phantom data show that the two trust region methods have a clear advantage in both speed and stability.

Selection of optimal spectral sensitivity functions for color filter arrays.

A color image meant for human consumption can be appropriately displayed only if at least three distinct color channels are present. Typical digital cameras acquire three-color images with only one sensor. A color filter array (CFA) is placed on the sensor such that only one color is sampled at a particular spatial location. This sparsely sampled signal is then reconstructed to form a color image with information about all three colors at each location. In this paper, we show that the wavelength sensitivity functions of the CFA color filters affect both the color reproduction ability and the spatial reconstruction quality of recovered images. We present a method to select perceptually optimal color filter sensitivity functions based upon a unified spatial-chromatic sampling framework. A cost function independent of particular scenes is defined that expresses the error between a scene viewed by the human visual system and the reconstructed image that represents the scene. A constrained minimization of the cost function is used to obtain optimal values of color-filter sensitivity functions for several periodic CFAs. The sensitivity functions are shown to perform better than typical RGB and CMY color filters in terms of both the s-CIELAB ∆E error metric and a qualitative assessment.

Basic properties of SS-PARSE parameter estimates.

Single shot parameter assessment by retrieval from signal encoding (SS-PARSE) is a recently introduced method to obtain quantitative parameter maps from a single-shot (typically 65 ms) magnetic resonance imaging (MRI) signal. Because it explicitly models local magnetization decay and phase evolution occurring during the signal 1) it can provide quantitative estimates of local transverse magnetization magnitude and phase, frequency, and relaxation rate and 2) it is free of geometric distortion or blurring due to field nonuniformities within the tissues. These properties promise to be advantageous in functional brain MRI (fMRI) and other dynamic imaging applications. In this paper, the basic phenomena underlying the performance of SS-PARSE in practice are discussed. Basic sources of bias errors in the parameter estimates are discussed, and performance of the method is characterized in terms of parameter estimates from simulation, experimental phantoms, and in vivo studies. Characteristics of the sum-of-square-error cost function and the iterative search algorithm are discussed, and their relative roles in determining estimation accuracy are described. Practical guidelines for use of the method are presented and discussed. In vivo parameter maps are also presented.

Efficient Huber-Markov edge-preserving image restoration.

The regularization of the least-squares criterion is an effective approach in image restoration to reduce noise amplification. To avoid the smoothing of edges, edge-preserving regularization using a Gaussian Markov random field (GMRF) model is often used to allow realistic edge modeling and provide stable maximum a posteriori (MAP) solutions. However, this approach is computationally demanding because the introduction of a non-Gaussian image prior makes the restoration problem shift-variant. In this case, a direct solution using fast Fourier transforms (FFTs) is not possible, even when the blurring is shift-invariant. We consider a class of edge-preserving GMRF functions that are convex and have nonquadratic regions that impose less smoothing on edges. We propose a decomposition-enabled edge-preserving image restoration algorithm for maximizing the likelihood function. By decomposing the problem into two subproblems, with one shift-invariant and the other shift-variant, our algorithm exploits the sparsity of edges to define an FFT-based iteration that requires few iterations and is guaranteed to converge to the MAP estimate.

Fast spectroscopic imaging using online optimal sparse k-space acquisition and projections onto convex sets reconstruction.

Long acquisition times, low resolution, and voxel contamination are major difficulties in the application of magnetic resonance spectroscopic imaging (MRSI). To overcome these difficulties, an online-optimized acquisition of k-space, termed sequential forward array selection (SFAS), was developed to reduce acquisition time without sacrificing spatial resolution. A 2D proton MRSI region of interest (ROI) was defined from a scout image and used to create a region of support (ROS) image. The ROS was then used to optimize and obtain a subset of k-space (i.e., a subset of nonuniform phase encodings) and hence reduce the acquisition time for MRSI. Reconstruction and processing software was developed in-house to process and reconstruct MRSI using the projections onto convex sets method. Phantom and in vivo studies showed that good-quality MRS images are obtainable with an approximately 80% reduction of data acquisition time. The reduction of the acquisition time depends on the area ratio of ROS to FOV (i.e., the smaller the ratio, the greater the time reduction). It is also possible to obtain higher-resolution MRS images within a reasonable time using this approach. MRSI with a resolution of 64 x 64 is possible with the acquisition time of the same as 24 x 24 using the traditional full k-space method.

Fast image restoration without boundary artifacts.

Fast Fourier transform (FFT)-based restorations are fast, but at the expense of assuming that the blurring and deblurring are based on circular convolution. Unfortunately, when the opposite sides of the image do not match up well in intensity, this assumption can create significant artifacts across the image. If the pixels outside the measured image window are modeled as unknown values in the restored image, boundary artifacts are avoided. However, this approach destroys the structure that makes the use of the FFT directly applicable, since the unknown image is no longer the same size as the measured image. Thus, the restoration methods available for this problem no longer have the computational efficiency of the FFT. We propose a new restoration method for the unknown boundary approach that can be implemented in a fast and flexible manner. We decompose the restoration into a sum of two independent restorations. One restoration yields an image that comes directly from a modified FFT-based approach. The other restoration involves a set of unknowns whose number equals that of the unknown boundary values. By summing the two, the artifacts are canceled. Because the second restoration has a significantly reduced set of unknowns, it can be calculated very efficiently even though no circular convolution structure exists.

On the optimality of magnetic resonance tag patterns for heart wall motion estimation.

Tracking of cardiac motion using magnetic resonance tagging has attracted increasing attention in recent years. Several methods for tagging the cardiac tissue and tracking the motion of the tags have been developed. However, the choice of tag pattern that minimizes tracking error has received less attention. In this paper, we are concerned with the optimal tagging and acquisition of MR tagged images for cardiac motion analysis. We formulate the measurement of tissue deformation as a multidimensional parametric estimation problem which can be solved using the nonlinear least squares estimator. Along with this, we derive the Cramer-Rao lower bound (CRLB) on the average estimation error variance. We then show that under certain conditions a complex sinusoidal tag shape minimizes the CRLB. We validate our results with computer simulations. Finally, based on the previous findings, we make recommendations concerning the most desirable imaging strategy for images tagged with a complex sinusoidal tag pattern.