Sampling below the Nyquist density using spectral subtiles.

An image is assumed to have a spectrum zero outside of a defined support. To avoid aliasing, the replicated support due to sampling cannot overlap. The minimum sampling density corresponding to nonoverlapping supports is the Nyquist density. Replication often necessitate gaps. Support shapes that fill the frequency plane without gaps are tiles. We offer a strategy for achieving minimum sampling density when the spectrum is confined to a subtile. Cookie cutter versions of the subtile shape, when rotated, translated, and/or flipped, result in a tile. The composite signal can have symmetric redundancies that allow reduction of the sampling density to the area of the subtile. We analyze the cases for tiles with twofold point symmetry and mirror symmetry. Two subtiles are required to construct a tile. Threefold, fourfold, and sixfold symmetry is also considered. In the cases considered, the overall sampling density in terms of the samples' required storage is reduced to the area of the support of the subtile.

Real-time neural network inversion on the SRC-6e reconfigurable computer.

Implementation of real-time neural network inversion on the SRC-6e, a computer that uses multiple field-programmable gate arrays (FPGAs) as reconfigurable computing elements, is examined using a sonar application as a specific case study. A feedforward multilayer perceptron neural network is used to estimate the performance of the sonar system (Jung et al., 2001). A particle swarm algorithm uses the trained network to perform a search for the control parameters required to optimize the output performance of the sonar system in the presence of imposed environmental constraints (Fox et al., 2002). The particle swarm optimization (PSO) requires repetitive queries of the neural network. Alternatives for implementing neural networks and particle swarm algorithms in reconfigurable hardware are contrasted. The final implementation provides nearly two orders of magnitude of speed increase over a state-of-the-art personal computer (PC), providing a real-time solution.

Emergent behaviors of protector, refugee, and aggressor swarms.

Simple rules, when executed by individual agents in a large group, or swarm, can lead to complex behaviors that are often difficult or impossible to predict knowing only the rules. However, aggregate behavior is not always unpredictable-even for swarm models said to be beyond analysis. For the class of swarming algorithms examined herein, we analytically identify several possible emergent behaviors and their underlying causes: clustering, drifting, and explosion. They also analyze the likelihood of these behaviors emerging from randomly selected swarm configurations and present a few examples. The analytic results are illustrated via simulation.

Recovery of image blocks using the method of alternating projections.

A technique for block-loss restoration in block-based image and video coding, dubbed recovery of image blocks using the method of alternating projections (RIBMAP), is developed. The algorithm is based on orthogonal projections onto constraint sets in a Hilbert space. For the recovery of a linear dimension N size block, a total of 8N vectors are extracted from the surrounding area of an N x N missing block. These vectors form a library from which the best matching spatial information for the missing block is extracted. Recovery vectors, including both undamaged and restored damaged pixels, are introduced. The vectors are used to find highly correlated information relating to the lost pixels. To assure continuity with the surrounding undamaged area, three additional convex constraints are formulated. Adherance to these sets is imposed using alternating projections. Simulation results using orthogonal projections demonstrate that RIBMAP recovers spatial structure faithfully. Simulation comparisons with other procedures are presented: Ancis and Giusto's hybrid edge-based average-median interpolation technique, Sun and Kwok's projections onto convex sets-based method, Hemami and Meng's interblock correlation interpolation approach, Shirani et al.'s modified interblock correlation interpolation scheme, and Alkachouh and Bellanger's fast discrete cosine transformation-based spatial domain interpolation algorithm. Characteristic of the results are those of the "Lena" JPEG image when one fourth of periodically spaced blocks in the image have errors. The peak signal-to-noise ratio of the restored image is 28.68, 29.99, 31.86, 31.69, 31.57, and 34.65 dB using that of Ancis and Giusto, Sun and Kwok, Hemami and Meng, Shirani et al., Alkachouh and Bellanger, and RIPMAP, respectively.

Detection and correction of patient movement in prostate brachytherapy seed reconstruction.

Intraoperative dosimetry of prostate brachytherapy can help optimize the dose distribution and potentially improve clinical outcome. Evaluation of dose distribution during the seed implant procedure requires the knowledge of 3D seed coordinates. Fluoroscopy-based seed localization is a viable option. From three x-ray projections obtained at different gantry angles, 3D seed positions can be determined. However, when local anaesthesia is used for prostate brachytherapy, the patient movement during fluoroscopy image capture becomes a practical problem. If uncorrected, the errors introduced by patient motion between image captures would cause seed mismatches. Subsequently, the seed reconstruction algorithm would either fail to reconstruct or yield erroneous results. We have developed an algorithm that permits detection and correction of patient movement that may occur between fluoroscopy image captures. The patient movement is decomposed into translational shifts along the tabletop and rotation about an axis perpendicular to the tabletop. The property of spatial invariance of the co-planar imaging geometry is used for lateral movement correction. Cranio-caudal movement is corrected by analysing the perspective invariance along the x-ray axis. Rotation is estimated by an iterative method. The method can detect and correct for the range of patient movement commonly seen in the clinical environment. The algorithm has been implemented for routine clinical use as the preprocessing step for seed reconstruction.

Three-dimensional seed reconstruction from an incomplete data set for prostate brachytherapy.

Intra-operative dosimetry in prostate brachytherapy requires 3D coordinates of the implanted, radioactive seeds. Since CT is not readily available during the implant operation, projection x-rays are commonly used for intra-operative seed localization. Three x-ray projections are usually used. The requirement of the current seed reconstruction algorithms is that the seeds must be identified on all three projections. However, in practice this is often difficult to accomplish due to the problem of heavily clustered and overlapping seeds. We have developed an algorithm that permits seed reconstruction from an incomplete data set. Instead of all three projections, the new algorithm requires only one of the three projections to be complete. Furthermore, even if all three projections are incomplete, it can reconstruct 100% of the implanted seeds depending on how the undetected seeds are distributed among the projections. The method utilizes the principles of epipolar imaging geometry and pseudo-matching of the undetected seeds. The algorithm was successfully applied to a large number of clinical cases where seeds imperceptibly overlap in some projections.

Content-based adaptive spatio-temporal methods for MPEG repair.

Block loss and propagation error due to cell loss or missing packet information during the transmission over lossy networks can cause severe degradation of block and predictive-based video coding. Herein, new fast spatial and temporal methods are presented for block loss recovery. In the spatial algorithm, missing block recovery and edge extention are performed by pixel replacement based on range constraints imposed by surrounding neighborhood edge information and structure. In the temporal algorithm, an adaptive temporal correlation method is proposed for motion vector (MV) recovery. Parameters for the temporal correlation measurement are adaptively changed in accordance to surrounding edge information of a missing macroblock (MB). The temporal technique utilizes pixels in the reference frame as well as surrounding pixels of the lost block. Spatial motion compensation is applied after MV recovery when the reference frame does not have sufficient information for lost MB restoration. Simulations demonstrate that the proposed algorithms recover image information reliably using both spatial and temporal restoration. We compare the proposed algorithm with other procedures with consistently favorable results.

Three-dimensional seed reconstruction for prostate brachytherapy using Hough trajectories.

In order to perform intra-operative or post-implant dosimetry in prostate brachytherapy, the 3D coordinates of the implanted radioactive seeds must be determined. Film or fluoroscopy based seed reconstruction techniques use back projection of x-ray data obtained at two or three x-ray positions. These methods, however, do not perform well when some of the seed images are undetected. To overcome this problem we have developed an alternate technique for 3D seed localization using the principle of Hough transform. The Hough method utilizes the fact that, for each seed coordinate in three dimensions, there exists a unique trajectory in Hough feature space. In this paper we present the Hough transform parametric equations to describe the path of the seed projections from one view to the next and a method to reconstruct the 3D seed coordinates. The results of simulation and phantom studies indicate that the Hough trajectory method can accurately determine the 3D seed positions even from an incomplete dataset.

Fast cross-projection algorithm for reconstruction of seeds in prostate brachytherapy.

A fast method of seed matching and reconstruction in prostate brachytherapy is proposed. Previous approaches have required all seeds to be matched with all other seeds in other projections. The fast cross-projection algorithm for the reconstruction of seeds (Fast-CARS) allows for matching of a given seed with a subset of seeds in other projections. This subset lies in a proximal region centered about the projection of a line, connecting the seed to its source, onto other projection planes. The proposed technique permits a significant reduction in computational overhead, as measured by the required number of matching tests. The number of multiplications and additions is also vastly reduced at no trade-off in accuracy. Because of its speed, Fast-CARS can be used in applications requiring real-time performance such as intraoperative dosimetry of prostate brachytherapy. Furthermore, the proposed method makes practical the use of a larger number of views as opposed to previous techniques limited to a maximum use of three views.