Cardiac-gated MRI is widely used for the task of measuring parameters related to heart motion. More specifically, gated tagged MRI is the preferred modality to estimate local deformation (strain) and rotational motion (twist) of myocardial tissue. Many methods have been proposed to estimate cardiac motion from gated MRI sequences. However, when dealing with clinical data, evaluation of these methods is problematic due to the absence of gold-standards for cardiac motion. To overcome that, a linear regression scheme known as regression-without-truth (RWT) was proposed in the past. RWT uses priors to model the distribution of true values, thus enabling us to assess image-analysis algorithms without knowledge of the ground-truth. Furthermore, it allows one to rank methods by means of an objective figure-of-merit γ (i.e. precision). In this work we apply RWT to compare the performance of several gated MRI motion-tracking methods (e.g. non-rigid registration, feature based, harmonic phase) at the task of estimating myocardial strain and left-ventricle (LV) twist, from a population of 18 clinical human cardiac-gated tagged MRI studies.
Image reconstruction from Fourier-domain measurements is a specialized problem within the general area of image reconstruction using prior information. The structure of the equations in Fourier imaging is challenging, since the observation equation matrix is non-sparse in the spatial domain but diagonal in the Fourier domain. Recently, the Bayesian image reconstruction with prior edges (BIRPE) algorithm has been proposed for image reconstruction from Fourier-domain samples using edge information automatically extracted from a high-resolution prior image. In the BIRPE algorithm, the maximum a posteriori (MAP) estimate of the reconstructed image and edge variables involves high-dimensional, non-convex optimization, which can be computationally prohibitive. The BIRPE algorithm performs this optimization by iteratively updating the estimate of the image then updating the estimate of the edge variables. In this paper, we propose two techniques for updating the image based on fixed edge variables one based on iterated conditional modes (ICM) and the other based on Jacobi iteration. ICM is guaranteed to converge, but, depending on the structure of the Fourier-domain samples, can be computationally prohibitive. The Jacobi iteration technique is more computationally efficient but does not always converge. In this paper, we study the convergence properties of the Jacobi iteration technique and its parameter sensitivity.
We propose the Bayesian image reconstruction with prior edges (BIRPE) algorithm for reconstructing an image from Fourier-domain samples with prior edge information from a higher resolution image. A major difference between BIRPE and previous methods is that all edges are detected automatically, and no segmentation of the prior image is required. Also, an edge found in the prior image does not need to be confirmed by the observations; smoothing is reduced across the edge if either the prior image or the observations suggest an edge. Simulations and results on magnetic resonance spectroscopic data are presented that demonstrate the effectiveness of the BIRPE method.
Digital still cameras typically use a single optical sensor overlaid with RGB color filters to acquire a scene. Only one of the three primary colors is observed at each pixel and the full color image must be reconstructed (demosaicked) from available data. We consider the problem of demosaicking for images sampled in the commonly used Bayer pattern.
The full color image is obtained from the sampled data as a MAP estimate. To exploit the greater sampling rate in the green channel in defining the presence of edges in the blue and red channels, a Gaussian MRF model that considers the presence of edges in all three color channels is used to define a prior. Pixel values and edge estimates are computed iteratively using an algorithm based on Besag's iterated conditional modes (ICM) algorithm. The reconstruction algorithm iterates alternately to perform edge detection and spatial smoothing. The proposed algorithm is applied to a variety of test images and its performance is quantified by using the CIELAB delta E measure.
In this paper, we present a new method for optimizing knot positions for a multi-dimensional B-spline model. Using the results from from univariate polynomial approximation theory, spline approximation theory and multivariate tensor product theory, we develop the algorithm in three steps. First, we derive a local upper bound for the L∞ error in a multivariate B-spline tensor product approximation over a span. Second, we use this result to bound the approximation error for a multi-dimensional B-spline tensor product approximation. Third, we developed two knot position optimization methods based on the minimization of two global approximation errors: L∞ global error and L2 global error. We test our method with 2D surface fitting experiments using B-spline models defined in both 2D Cartesian and polar coordinates. Simulation results demonstrate that the optimized knots can fit a surface more accurately than fixed uniformly spaced knots.
KEYWORDS: Magnetic resonance imaging, Data modeling, Imaging spectroscopy, Spectroscopy, Reconstruction algorithms, Image restoration, Signal to noise ratio, Data acquisition, Fourier transforms, Image resolution
Spectroscopic imaging (SI) techniques combine the ability of NMR spectroscopy to identify and measure biochemical constituents with the ability of MR imaging to localize NMR signals. The basic imaging technique acquires a set of spatial-frequency-domain samples on a regular grid and takes an inverse Fourier transform of the acquired data to obtain the spatial-domain image. Unfortunately, the time
required to gather the data while maintaining an adequate signal-to-noise ratio (SNR) limits the number of spatial-frequency-domain samples that can be acquired. In this paper, we use a high-resolution MR scout image to obtain edge locations in the sample imaged with MRSI. MRI discontinuities represent boundaries between different tissue types, and these discontinuities are likely to appear in the spectroscopic image as well. We propose a new model that encourages edge formation in the MRSI image reconstruction wherever MR image edges occur. A major difference between our model and previous methods is that an edge found in the MR image need not be confirmed by the data; smoothing is reduced across the edge
if either the MR image or the MRSI data suggests an edge. Simulations and results on in vivo MRSI data are presented that demonstrate the effectiveness of the method.
Magnetic resonance tagging has been shown to be a useful technique for non-invasively measuring the deformation of an in vivo heart. Tagged images appear with a spatially encoded pattern of lines called tag lines that move with the tissue and can be analyzed to reconstruct a description of left ventricular (LV) displacement during a portion of the cardiac cycle. Existing analysis methods require user- defined epicardial and endocardial contours. In this paper we present a method based on edge-preserving regularization techniques for reconstructing dense 2D left ventricular displacement field from tag line position data without prior knowledge of the LV contours. Our methods are demonstrated on both simulated and in vivo data.
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