Focused local learning with wavelet neural networks.

A novel objective function is presented that incorporates both local and global errors as well as model parsimony in the construction of wavelet neural networks. Two methods are presented to assist in the minimization of this objective function, especially the local error term. First, during network initialization, a locally adaptive grid is utilized to include candidate wavelet basis functions whose local support addresses the local error of the local feature set. This set can be either user-defined or determined using information derived from the wavelet transform modulus maxima representation. Next, during the network construction, a new selection procedure based on a subspace projection operator is presented to help focus the selection of wavelet basis functions to reduce the local error. Simulation results demonstrate the effectiveness of these methodologies in minimizing local and global error while maintaining model parsimony and incurring a minimal increase on computational complexity.

Left-ventricle boundary detection from nuclear medicine images.

We present here a new algorithm for segmentation of nuclear medicine images to detect the left-ventricle (LV) boundary. In this article, other image segmentation techniques, such as edge detection and region growing, are also compared and evaluated. In the edge detection approach, we explored the relationship between the LV boundary characteristics in nuclear medicine images and their radial orientations: we observed that no single brightness function (eg, maximum of first or second derivative) is sufficient to identify the boundary in every direction. In the region growing approach, several criteria, including intensity change, gradient magnitude change, gradient direction change, and running mean differences, were tested. We found that none of these criteria alone was sufficient to successfully detect the LV boundary. Then we proposed a simple but successful region growing method--Contour-Modified Region Growing (CMRG). CMRG is an easy-to-use, robust, and rapid image segmentation procedure. Based on our experiments, this method seems to perform quite well in comparison to other automated methods that we have tested because of its ability to handle the problems of both low signal-to-noise ratios (SNR) as well as low image contrast without any assumptions about the shape of the left ventricle.

Noise removal from multiple MRI images.

We introduce a novel technique for magnetic resonance image (MRI) restoration, using a physical model (spin equation). We determine a set of three basis images (proton density and nuclear relaxation times) from the MRI data using a nonlinear optimization method, and use those images to obtain restorations of the original image. MRIs depend nonlinearly on proton density, two nuclear relaxation times, T1 and T2, and two control parameters, echo time (TE) and relaxation time (TR). We model images as Markov random fields and introduce a maximum a posteriori restoration method, based on nonlinear optimization, which reduces noise while preserving resolution.

Mean field annealing: a formalism for constructing GNC-like algorithms.

Optimization problems are approached using mean field annealing (MFA), which is a deterministic approximation, using mean field theory and based on Peierls's inequality, to simulated annealing. The MFA mathematics are applied to three different objective function examples. In each case, MFA produces a minimization algorithm that is a type of graduated nonconvexity. When applied to the ;weak-membrane' objective, MFA results in an algorithm qualitatively identical to the published GNC algorithm. One of the examples, MFA applied to a piecewise-constant objective function, is then compared experimentally with the corresponding GNC weak-membrane algorithm. The mathematics of MFA are shown to provide a powerful and general tool for deriving optimization algorithms.