3:30, IMDSP-L7.1
A TOMOGRAPHIC FRAMEWORK FOR LIDAR IMAGING
P. SHARGO, N. CADALLI, A. SINGER, D. MUNSON, JR.
Detection and localization of underwater mines remains a challenging and important problem for safe operation of naval platforms. A number of new technologies exploit airborne LIDARs, which can penetrate the air-water interface and optically detect and localize underwater mines. Such systems process the received optical field generated by scattering within the water column, and have proven to be an effective technology for mine detection and localization. In this work, we consider the use of multiple looks at a single target to form a three-dimensional representation of the scatterers within the water column. To form such images, we account for the integration within the receive sensors, and formulate the problem in a tomographic framework. We will present preliminary image formation results generated from data collected at sea with a state-of-the-art Navy mine imaging system.

3:50, IMDSP-L7.2
NOVEL INVERSE METHODS IN LAND MINE IMAGING
T. WELDON, Y. GRYAZIN, M. KLIBANOV
The imaging of buried land mines continues to present significant signal-processing challenges in the development of inverse methods for the detection of plastic mines buried in soil. To address this difficult problem, recent mathematical advances in the development of the Elliptic Systems Method are used to generate images of the buried land mines. The proposed approach adapts earlier methods, successfully applied in laser tomography of breast tumors using the diffusion equation, to the present problem of land mine imaging using the Helmholtz equation. The images generated by the new method represent electromagnetic properties of underground regions, providing effective differentiation of plastic land mines from surrounding soil. Experimental results are presented to demonstrate the new method. See http://wws2.uncc.edu/tpw/ for additional information.

4:10, IMDSP-L7.3
UNWRAPPING PHASES BY RELAXED MEAN FIELD INFERENCE
K. ACHAN, B. FREY, R. KOETTER, D. MUNSON, JR.
Some types of medical and topographic imaging device produce images in which the pixel values are ``phase-wrapped'', i.e., measured modulus a known scalar. Phase unwrapping can be viewed as the problem of inferring the number of shifts between each and every pair of neighboring pixels, subject to an a priori preference for smooth surfaces, and subject to a zero curl constraint, which requires that the shifts must sum to 0 around every loop. We formulate phase unwrapping as a mean field inference problem in a probability model, where the prior favors the zero curl constraint. We compare our mean field technique with the least squares method on a synthetic 100 x 100 image, and give results on a larger 512 x 512 image.

4:30, IMDSP-L7.4
PHASE RETRIEVAL OF IMAGES FROM ZEROS OF EVEN UNWRAPPED SIGNALS
S. PETROUDI, A. YAGLE
The 2-D discrete phase retrieval problem is to reconstruct an image defined at integer coordinates and having known finite spatial extent from the magnitude of its discrete Fourier transform. Most methods for solving this problem are iterative but not POCS, and they tend to stagnate. Recently we developed a new approach that unwrapped the 2-D problem into a 1-D problem with bands of zeros in it, using the Good-Thomas FFT. However, this approach reconstructed the even part of the image much better than the odd part, and it was sensitive to the zero locations. This paper presents a modification of this approach. New features include: (1) an overdetermined problem less sensitive to the zero locations; (2) the solution of a Toeplitz-block-Toeplitz-plus-Hankel-block-Hankel linear system; and (3) details on characteristics of images for which the approach works best.

4:50, IMDSP-L7.5
SPECT IMAGE RECONSTRUCTION USING COMPOUND MODELS
A. LÓPEZ, R. MOLINA, A. KATSAGGELOS, J. MATEOS
SPECT (Single Photon Emission Computed Tomography) is used in nuclear medicine to determine the distribution of a radioactive isotope within a patient from tomographic views or projection data. These images are severely degraded due to the presence of noise and several physical factors like attenuation and scattering. In this paper we use, within the Bayesian framework, Compound Gauss Markov Random Fields (CGMRF) as prior model to reconstruct such images. In order to find the Maximum a Posteriori (MAP) estimate we propose a new iterative method, which is stochastic for the line process and deterministic for the reconstruction. The proposed method is tested and compared with other reconstruction methods on both synthetic and real SPECT images.

5:10, IMDSP-L7.6
SEQUENTIAL FORWARD SAMPLE SELECTION IN ARRAY-BASED IMAGE FORMATION
Y. GAO, S. REEVES
In some types of imaging, the signal is strictly limited in one domain while sampling takes places in another. If sampling is done in a rectangular array pattern at sub-Nyquist density, the array must be dithered to sample the image at the Nyquist density in each dimension. However, the Nyquist density oversamples the image due to the nonrectangular support in the transform domain. We present an efficient forward selection algorithm for optimizing the dithering pattern so that the image can be reconstructed as reliably as possible from a periodic nonuniform set of samples, which can be obtained from a dithered rectangular-grid array. Our examples show that this new algorithm makes selective sampling possible in a real-time image acquisition setting for MR spectroscopic imaging.