Chair: Yoram Bresler, University of Illinois (USA)
Carlos Mosquera, Universidad de Vigo (SPAIN)
Pablo Irarrazabal, Stanford University (USA)
Dwight G. Nishimura, Stanford University (USA)
This paper addresses the properties of the noise in Gridding reconstruction, an algorithm for reconstruction from nonuniform samples . Sequences with time-varying gradients, such as Spiral or Projection Reconstruction (PR) techniques, are being increasingly used in Magnetic Resonance Imaging (MRI). Since these techniques sample k-space nonuniformly, some kind of algorithm is needed to map the data onto a Cartesian frame to allow an inverse Fourier transform through an FFT. We present here an analytical characterization of the image noise after Gridding and inverse Fourier transform for the most popular sampling techniques used in MRI.
Jennifer L.H. Webb, University of Illinois at Urbana-Champaign (USA)
David C. Munson Jr., University of Illinois at Urbana-Champaign (USA)
We consider the problem of spotlight-mode synthetic aperture radar (SAR) imaging for an arbitrary radar path. A general imaging scenario involves a 3-D scattering surface with data collected along an arbitrary 3-D radar path. This approach is useful, for example, in military applications where the radar platform may undergo some maneuvers, and in radar astronomy where the relative motion is, at least in part, determined by the natural paths of celestial bodies. We show that nonideal platform motion can create phase variations in the data which lead to spatially-varying shifts and blurring. A correction procedure is proposed and demonstrated.
Victor Solo, Macquarie University (AUSTRALIA)
We present a new variational approach to the problem of computed tomography reconstruction from sparse data. We use a Tikhonov regularisation ( quite different from that of Louis(1985)) which deals without approximation with discrete or nonuniform grids.
Jeffrey A. Fessler, University of Michigan (USA)
Many estimators in signal processing problems are defined implicitly as the maximum of an objective function, such as maximum likelihood (ML) and maximum a posteriori (MAP) methods. Exact analytical expressions for the mean and variance of such estimators are usually unavailable, so investigators usually resort to numerical simulations. This paper describes approximate analytical expressions for the mean and variance of implicitly defined estimators. The expressions are defined solely in terms of the partial derivatives of whatever objective function one uses for estimation. We demonstrate the utility and accuracy of the approximations in a PET transmission computed tomography application with Poisson statistics. The approximations should be useful in a wide range of estimation problems.
Alexander H. Delaney, University of Illinois at Urbana-Champaign (USA)
Yoram Bresler, University of Illinois at Urbana-Champaign (USA)
We use a series-expansion approach and an operator framework to derive a new, fast and accurate, iterative tomographic reconstruction algorithm applicable for parallel-ray projections that have been collected at a finite number of arbitrary view angles and have been radially sampled at a rate high enough so that aliasing errors are small. We use the conjugate gradient algorithm to minimize a regularized least squares criterion, and we prove that the main step in each iteration is equivalent to a 2-D discrete convolution, which can be cheaply and exactly implemented via the FFT. The proposed algorithm requires on the order of $N^{2}$ log(N) multiplies per iteration to reconstruct an N x N image from P view angles, and requires the storage of half of a 2N x 2N PSF.
Berkman Sahiner, University of Michigan (USA)
Andrew E. Yagle, University of Michigan (USA)
We combine several ideas, including nonuniform sampling and circular harmonic expansions, into a new procedure for reconstructing a small region of interest (ROI) of an image from a set of its projections that are densely sampled in the ROI and coarsely sampled outside the ROI. The radial sampling density of both the projections and the reconstructed image decreases exponentially with increasing distance from the ROI. This is reminiscent of the recently formulated local tomography problem; however, our algorithm reconstructs the ROI of the image itself, not the filtered version of it obtained using local tomography. The new algorithm has the added advantages of speed (it can be implemented entirely using the FFT) and parallelizability (each image harmonic is independent).
Mary H. Johnson, University of Washington (USA)
Eve A. Riskin, University of Washington (USA)
We form a multiresolution VQ (MVQ) codebook for progressive transmission using principal components partitioning of a full search VQ codebook. Downsized intermediate codewords provide fast reconstruction of coarse images appropriate for browsing satellite image databases in X-Window environments. Browse images can be expanded in size and improved in quality progressively. Any single band of a Landsat image has very low contrast, but contrast enhancement by global histogram equalization produces a visually informative image. When VQ codebook design incorporates contrast enhancement to produce the decoder, the VQ requires no additional operations to produce contrast enhanced final images. We adapt this technique for better performance in our multiresolution scheme by first designing the decoder codebook from a contrast enhanced training set. Using our inverse technique, reverse mapping, we then derive the encoder from the decoder. Thus the decoder is optimized for contrast enhanced images, a necessity for expansion into our multiresolution decoder.
Yong Zhang, University of Michigan (USA)
Jeffrey A. Fessler, University of Michigan (USA)
Neal H. Clinthorne, University of Michigan (USA)
W. Leslie Rogers, University of Michigan (USA)
The University of Michigan Ann Arbor, MI 48109-0552 (USA) Single Photon Emission Computed Tomographic Images (SPECT) have relatively poor resolution. In an attempt to improve SPECT image quality, many methods have been developed for including anatomi information, extracted from higher resolution, structurally correlated Magnetic Resonance images (MRI), into SPECT reconstruction process. These methods provide improved SPECT reconstruction accuracy if the anatomic information is perfectly correlated with the SPECT functional information. However there exist mismatches between MRI anatomical structures and SPECT functional structures due to different imaging mechanisms. It has been reported that if the MR structures are applied into SPECT, the mismatched part will cause artifacts. This paper describes a joint estimation approach which unifies MR information extraction and SPECT reconstruction processes to avoid these artifacts. Both qualitative and quantitative evaluations show that the method improves the SPECT reconstructioin where the MR information matches and is robust to mismatched MR information.
Herve Carfantan, CNRS- ESE-UPS (FRANCE)
Ali Mohmammad-Djafari, CNRS- ESE-UPS (FRANCE)
We propose a new method to solve the nonlinear inverse problem of tomographic imaging using microwave or ultrasound probing, beyond the classical first order Born or Rytov approximations. The relation between the data and the measurement is given by two coupled nonlinear equations. We set this problem as one of estimation and propose a solution within the Bayesian probability framework. The Maximum A Posteriori estimate determination leads to a multi-modal criterion minimisation. Global minimisation using Simulated Annealing is not practicable due to the high calculation cost. We propose a feasible deterministic relaxation algorithm inspired by the Graduated Non Convexity principle to perform this minimisation.
Mahmoud E. Allam, Mayo Foundation (USA)
James F. Greenleaf, Mayo Foundation (USA)
Phase aberration due to tissues with inhomogeneous acoustic speeds is a major source for image degradation in medical ultrasound. In most phased array pulse-echo ultrasound systems, the delay used to steer and focus the beams are calculated assuming constant speed. In practice, however, the acoustic speed varies for different types of tissue. In this paper, we present a method to estimate the phase errors between the elements of a linear array, based on signal representation in the spatial-temporal Fourier domain. Compared to the standard cross-correlation methods used for time delay estimation, the proposed technique shows better performance.