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Steve Titus, University of Michigan - Ann Arbor (U.S.A.)
Alfred Olivier Hero, University of Michigan - Ann Arbor (U.S.A.)
Jeffrey Fessler, University of Michigan - Ann Arbor (U.S.A.)
In this paper, a method is introduced for incorporating perfectly registered MRI boundary information into a penalized likelihood emission reconstruction scheme. The boundary curve is modeled as a periodic spline whose coefficients are estimated from the MRI image. The resulting boundary estimate is mapped to a spatially variant set of Gibbs weights. When incorporated into a quadratic roughness penalty, these weights improve emission reconstruction bias/variance performance by preventing smoothing across the estimated boundary.
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Axel Busboom, RWTH Aachen (Germany)
Harald Elders-Boll, RWTH Aachen (Germany)
Hans Dieter Schotten, RWTH Aachen (Germany)
In coded aperture imaging the attainable quality of the reconstructed images strongly depends on the choice of the aperture pattern. Optimum mask patterns can be designed from binary arrays with constant sidelobes of their periodic autocorrelation function, the so-called URAs. However, URAs exist for a restricted number of aperture sizes and open fractions only. Using a mismatched filter decoding scheme, artifact-free reconstructions can be obtained even if the aperture array violates the URA condition. A general expression and an upper bound for the signal-to-noise ratio as a function of the aperture array and the relative detector noise level are derived. Combinatorial optimization algorithms, such as the Great Deluge algorithm, are employed for the design of near-optimum aperture arrays. The signal-to-noise ratio of the reconstructions is predicted to be only slightly inferior to the URA case while no restrictions with respect to the aperture size or open fraction are imposed.
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Myriam Grandchamp, CTSN (France)
Jean François Cavassilas, University of Toulon (France)
The multilook technique used in synthetic aperture radar image formation consists in adding incoherently M looks. As these looks can be obtained in their complex form and are correlated, the phase and correlation informations should be taken into account in the speckle reduction process. In this paper, we propose an improved multilook technique based on the use of these two informations. We apply it on SAR images displaying ship wakes. Our technique consists in enhancing a specific texture in the image, using a set of filters matched to it, while simultaneously reducing speckle. The filters are applied on each look, and the resulting images are projected onto a particular basis. The final image is constituted by the quadratic sum of the processed looks, after their projection on the same geographic plane. Illustrative results as images comparison and analysis will show the effectiveness of the proposed algorithm.
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Lun Daniel Pak-Kong, The Hong Kong Polytechnic University (Hong Kong)
Hsung Tai-Chiu, The Hong Kong Polytechnic University (Hong Kong)
The wavelet localization technique was recently applied to the application of Region-of-Interest tomography. It achieves a significant saving in the required projections if only a small region of a tomographic image is of interest. In this paper, we firstly show that, with the same sampling requirement, a simple interpolation scheme applied on the samples can give a result at least as good as that achieved by using the wavelet localization approach. It means that we can use a much simple approach to achieve the same performance. Second, we propose a new sampling scheme such that the required projections of each angle are further reduced in a multiresolution form. With this sampling scheme, more than 84% of projections are saved to reconstruct a 32x32 pixels region of a 256x256 pixels image. The signal-to-error ratio of the reconstructed region-of-interest is over 50dB as compare with the case of full projection. Moreover, we also investigate the effect of applying the interlaced sampling scheme on the proposed method. It is seen that a further reduction in the sampling requirement can be achieved although a slight decrease in signal-to-error ratio may result.
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Ning Li, University of Maryland (U.S.A.)
Tülay Adal, University of Maryland (U.S.A.)
Moriel NessAiver, University of Maryland Medical System (U.S.A.)
In this paper, we consider the problem of magnetic resonance (MR) image reconstruction from non-uniformly sampled data acquired by echo-planar imaging (EPI) and spiral scan imaging (SSI) techniques. In EPI, mismatches in the timings of the odd and even echoes collected with readout gradients of alternating polarity will result in ``N/2'' ghosting in the reconstructed images. We propose a new method using a calibration data set to correct this mismatch and hence to calculate accurate k-space trajectories. In order to reconstruct images at real-time speeds, we utilize a high speed optoelectronic device to perform two-dimensional discrete Fourier transform (DFT). Images reconstructed from EPI data are presented to demonstrate that our method can successfully suppress the ``N/2'' ghosting and provide good contrast at real-time speeds. Image reconstructed from SSI data are also presented to show that our method can provide better sharp features and more details in the reconstructed images.
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Fatma Ayhan Sakarya, TUBITAK (Turkey)
Dong Wei, The University of Texas at Austin (U.S.A.)
Serkan Emek, Yildiz Technical University (Turkey)
Transform coding based on the Karhunen-Loève Transform (KLT), the Discrete Cosine Transform (DCT), and the Discrete Wavelet Transform (DWT) is well-understood for optical images. Transform coding applied to synthetic aperture radar (SAR) data, however, has not been well-studied. This paper compares the results of compressing SAR images using KLT, DCT, and DWT coders. We compare the compression results based on six performance criteria--- mean-squared error, mean absolute error, peak signal-to-noise ratio, energy compaction, transform gain, and compression ratio.
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Hervé Carfantan, LSS-CNRS (France)
Ali Mohammad Djafari, LSS-CNRS (France)
Jérôme Idier, LSS-CNRS (France)
We focus on the nonlinear inverse problem of diffraction tomography. We set the problem as one of estimation within the Bayesian framework and define the solution as the maximum a posteriori (MAP) estimate which corresponds to the global minimum of a multimodal criterion. The objective of this paper is to present a new deterministic single site update algorithm specially designed to compute this solution. The term of fidelity to the data, function of one pixel value, can be written as a second order rational fraction. Thus, the 1-D MAP criterion can be evaluated -- and minimized -- at a very low computational cost. Moreover, for certain MRF models the global minimum can even be computed explicitly as roots of a polynomial. The proposed algorithm turns these properties to advantage and moreover performs the updates of intermediate quantities at a particularly low cost compared to the criterion evaluation. Even if not guaranteed to converge towards the global minimum, the algorithm has shown itself to give satisfactory practical results.
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Otmar Loffeld, Center for Sensorsystems (ZESS) (Germany)
Christoph Arndt, Center for Sensorsystems (ZESS) (Germany)
The paper considers the problem of phase unwrapping which means generating absolute phase values from noisy, modulo-2p mapped phase observations. Phase unwrapping is the central key element in any kind of interferometric application. Nearly all known phase unwrapping techniques try to unwrap the mapped phases by a sequence of differentiating, taking the principal value of the discrete derivative and integrating again. This procedure, conceptually appealing as it may appear, however, yields strongly biased phase derivatives and thus strongly biased phase estimates. It can be shown mathematically, that computing the discrete derivative of noisy modulo-2p mapped phase yields estimates of the un-ambiguous discrete derivative, which are always biased towards lower ab-solute values. The bias clearly depends on the phase slope itself as well as on the coherence or on the signal to noise ratio (SNR), respectively. Considering the practical application of Synthetic Aperture Radar Interferometry, the paper presents the theoretical analysis, and gives some numerical results.
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Samit Basu, University of Illinois Coordinated Science Laboratory (U.S.A.)
Yoram Bresler, University of Illinois Coordinated Science Laboratory (U.S.A.)
We address the problem of parallel beam tomographic reconstruction when the angles at which the projections are taken are unkown. The problem arises in medical imaging owing to patient motion, and in imaging of viruses from a single projection of many identical units at random orientations. We determine conditions for unique identifiability of the angles from the projection data alone, and derive bounds on the variance of estimators of those angles in the presence of noise. Finally, we present a maximum likelihood estimator, along with a heuristic initialization procedure. Numerical simulations on a test phantom show excellent agreement with the bounds, and nearly perfect reconstructions at moderate noise levels.
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Alfred Olivier Hero, University of Michigan - Ann Arbor (U.S.A.)
Yong Zhang, University of Michigan - Ann Arbor (U.S.A.)
W. Leslie Rogers, University of Michigan - Ann Arbor (U.S.A.)
We give a novel method for performing statistically significant detection of specified object features which operates directly on X-ray (Gaussian) or radio-isotope (Poisson) tomographic projection data. The method is based on constructing an exact confidence region on the object derived by backprojecting a projection-domain confidence region into object space. The projection-domain confidence region is a minimal volume hyper-rectangle specified by the projection data and the appropriate quantiles of the standard Gaussian or Poisson distribution. By testing whether this object-domain confidence region contains objects with hypothesized features we obtain a feature detection algorithm which has constant false alarm rate adaptive in the sense that no image reconstruction is required and no unknown nuisance parameters need be estimated.
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Etienne G. Huot, INRIA Rocquencourt (France)
Isaac Cohen, INRIA Rocquencourt (France)
Isabelle L. Herlin, INRIA Rocquencourt (France)
To analyze SAR interferometric data, an unwrapping process must be first performed. Most so far proposed solutions use either local or global methods. In this paper we propose a mixed method to solve this problem, based on a 3-step iterative process: a local unwrapping is first performed and then improved through a markovian segmentation, false unwrapped residues are finally detected and corrected. A deterministic algorithm is used for the relaxation process; wrong unwrapped areas are corrected by a backtracking mechanism. Some results obtained by this approach, which presents a lower computational cost compared to complex stochastic unwrapping methods, are also presented.
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Ariel Rischal, SUNY at Buffalo (U.S.A.)
Susan S. Young, Eastman Kodak Company (U.S.A.)
Mehrdad Soumekh, SUNY at Buffalo (U.S.A.)
This paper presents a method for volumetric reconstruction from Helical Computerized Tomography (H-CT) data which are collected with a fan beam source. An interpretation of the H-CT data in terms of the Axial Computerized Tomography (A-CT) data is provided. This analysis indicates that the H-CT data for positive and negative detector angles can be combined to form periodically nonuniform hexagonal samples of the A-CT data. A Fourier-based method to reconstruct the A-CT data from this form of data coverage is presented. The target function is then reconstructed using the conventional fan beam computed tomography algorithms for A-CT.
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