The standard approach for magnetic resonance imaging is to discretely sample a central portion of the spatial frequency domain uniformly and inversely Fourier transform the acquired data to form an image. While the uniform sampling approach is generally accepted, nonstandard sampling approaches may be more efficient for some applications. The present authors describe several alternative approaches in data acquisition and reconstruction developed for specific applications. The paper describes the details of the methods and presents the experimental results obtained using these techniques.>

The problem of extracting the local shape information of a 3-D texture surface from a single 2-D image by tracking the perceived systematic deformations the texture undergoes by virtue of being present on a 3-D surface and by virtue of being imaged is examined. The surfaces of interest are planar and developable surfaces. The textured objects are viewed as originating by laying a rubber planar sheet with a homogeneous parent texture on it onto the objects. The homogeneous planar parent texture is modeled by a stationary Gaussian Markov random field (GMRF). A probability distribution function for the texture data obtained by projecting the planar parent texture under a linear camera model is derived, which is an explicit function of the parent GMRF parameters, the surface shape parameters. and the camera geometry. The surface shape parameter estimation is posed as a maximum likelihood estimation problem. A stereo-windows concept is introduced to obtain a unique and consistent parent texture from the image data that, under appropriate transformations, yields the observed texture in the image. The theory is substantiated by experiments on synthesized as well as real images of textured surfaces.>

A new iterative technique to reduce the ringing artifacts in chemical shift images due to the truncation of the high spatial frequency is presented. In this approach the authors extrapolate the high spatial frequency data guided by the edge information obtained from a high resolution anatomic image of the region of interest. The fact that the edge information obtained from the anatomic image can be off by a few pixels (due to factors such as chemical shift artifact, error in edge detection or misregistration) is taken into account by assuming a confidence interval of several pixels around the anatomic edges. The algorithm is validated on simulated and in vivo data, and excellent results were obtained.

The problem of extracting the local shape information of a 3D textured surface from a single 2D image is addressed. The textured objects of interest are planar and developable surfaces that are viewed as originating by laying down a rubber planar sheet with a homogeneous parent texture on it onto the objects. The homogeneous planar parent texture is modeled by a stationary Gaussian Markov random field (GMRF). The probability density function of the projected planar parent texture is an explicit function of the parent GMRF parameters, the surface shape parameters, and the camera geometry. The surface shape parameter estimation is posed as a maximum-likelihood estimation problem. A stereo-windows concept is introduced to obtain a unique and consistent parent texture from the image data.>

Consideration is given to the problem of classifying a test textured image that is obtained from one of C possible parent texture classes, after possibly applying unknown rotation and scale changes to the parent texture. The training texture images (parent classes) are modeled by Gaussian Markov random fields (GMRFs). To classify a rotated and scaled test texture, the rotation and scale changes are incorporated in the texture model through an appropriate transformation of the power spectral density of the GMRF. For the rotated and scaled image, a bona fide likelihood function that shows the explicit dependence of the likelihood function on the GMRF parameters, as well as on the rotation and scale parameters, is derived. Although, in general, the scaled and/or rotated texture does not correspond to a finite-order GMRF, it is possible nonetheless to write down a likelihood function for the image data. The likelihood function of the discrete Fourier transform of the image data corresponds to that of a white nonstationary Gaussian random field, with the variance at each pixel (i,j) being a known function of the rotation, the scale, the GMRF model parameters, and (i,j). The variance is an explicit function of the appropriately sampled power spectral density of the GMRF. The estimation of the rotation and scale parameters is performed in the frequency domain by maximizing the likelihood function associated with the discrete Fourier transform of the image data. Cramer-Rao error bounds on the scale and rotation estimates are easily computed. A modified Bayes decision rule is used to classify a given test image into one of C possible texture classes. The classification power of the method is demonstrated through experimental results on natural textures from the Brodatz album.>