Iterative method for the design of a nonperiodic grating-assisted directional coupler.

We propose and investigate the optimal design of a nonperiodic grating-assisted directional coupler by iterative methods using the beam propagation method. Computer simulations were carried out at wavelengths of 0.8, 1.3, and 1.5 mum, which are often used in optical communications and networking. We found that the complete power coupling lengths can be reduced considerably in comparison with those in the case of the periodic grating-assisted waveguides with the same set of parameters.

Neural network schemes for detecting rare events in human genomic DNA.

MOTIVATION: Many problems in molecular biology as well as other areas involve detection of rare events in unbalanced data. We develop two sample stratification schemes in conjunction with neural networks for rare event detection in such databases. Sample stratification is a technique for making each class in a sample have equal influence on decision making. The first scheme proposed stratifies a sample by adding up the weighted sum of the derivatives during the backward pass of training. The second scheme proposed uses a technique of modified bootstrap aggregating. After training neural networks with multiple sets of bootstrapped examples of the rare event classes and subsampled examples of common event classes, multiple voting for classification is performed. RESULTS: These two schemes make rare event classes have a better chance of being included in the sample used for training neural networks and thus improve the classification accuracy for rare event detection. The experimental performance of the two schemes using two sets of human DNA sequences as well as another set of Gaussian data indicates that proposed schemes have the potential of significantly improving accuracy of neural networks to recognize rare events.

Parallel consensual neural networks.

A new type of a neural-network architecture, the parallel consensual neural network (PCNN), is introduced and applied in classification/data fusion of multisource remote sensing and geographic data. The PCNN architecture is based on statistical consensus theory and involves using stage neural networks with transformed input data. The input data are transformed several times and the different transformed data are used as if they were independent inputs. The independent inputs are first classified using the stage neural networks. The output responses from the stage networks are then weighted and combined to make a consensual decision. In this paper, optimization methods are used in order to weight the outputs from the stage networks. Two approaches are proposed to compute the data transforms for the PCNN, one for binary data and another for analog data. The analog approach uses wavelet packets. The experimental results obtained with the proposed approach show that the PCNN outperforms both a conjugate-gradient backpropagation neural network and conventional statistical methods in terms of overall classification accuracy of test data.

Detection of ECG waveforms by neural networks.

In this study, ECG waveform detection was performed by using artificial neural networks (ANNs). Initially, the R peak of the QRS complex is detected, and then feature vectors are formed by using the amplitudes of the significant frequency components of the DFT spectrum. Grow and Learn (GAL) and Kohonen networks are comparatively investigated to detect four different ECG waveforms. The comparative performance results of GAL and Kohonen networks are reported.

Parallel, self-organizing, hierarchical neural networks with continuous inputs and outputs.

Parallel, self-organizing, hierarchical neural networks (PSHNN's) are multistage networks in which stages operate in parallel rather than in series during testing. Each stage can be any particular type of network. Previous PSHNN's assume quantized, say, binary outputs. A new type of PSHNN is discussed such that the outputs are allowed to be continuous-valued. The performance of the resulting networks is tested in the problem of predicting speech signal samples from past samples. Three types of networks in which the stages are learned by the delta rule, sequential least-squares, and the backpropagation (BP) algorithm, respectively, are described. In all cases studied, the new networks achieve better performance than linear prediction. A revised BP algorithm is discussed for learning input nonlinearities. When the BP algorithm is to be used, better performance is achieved when a single BP network is replaced by a PSHNN of equal complexity in which each stage is a BP network of smaller complexity than the single BP network.

Multistage parallel algorithm for diffraction tomography.

A multistage parallel algorithm with iterative processing is discussed for the processing of information in diffraction tomography. The algorithm is based on matrix partitioning, which results in mostly parallel stages of processing. Each successive stage is designed to minimize the remaining error. The process is iterated until convergence. The major advantages of the multistage algorithm are the reduced computational time from faster convergence as compared with a single-stage iterative algorithm, further reduction of computation time if the stages are implemented mostly in parallel, and better performance in terms of reduced reconstruction error.

Diffractive-phase-element design that implements several optical functions.

A scheme for the design of diffractive phase elements (DPE's) that integrates several optical functions is presented in a consistent sense based on the general theory of amplitude-phase retrieval and the Yang-Gu algorithm [Appl. Opt. 33, 209 (1994)]. We extend the original Yang-Gu algorithm to treat a system illuminated by a beam of incident light whose components are at different wavelengths, and a set of equations for determining the phase distribution of the DPE is derived. The profile of a surface-relief DPE can be designed with an iterative algorithm. Numerical simulations are carried out for the design of one-dimensional DPE's capable of both demultiplexing different wavelength components and focusing each partial wave at predetermined positions. The influence of the extension of sampling points in the DPE's from ideal geometric points to physical spots on design results is also investigated. The numerical simulation results show that the new algorithm can be used successfully to design the desired DPE's. It is therefore expected to be useful in the design of DPE's for micro-optical systems.

Iterative optimization of diffractive phase elements simultaneously implementing several optical functions.

The design of diffractive optical elements that incorporate several optical functions in a single element is discussed. The technique used involves iterative optimization. Aprevious paper is continued, in which initial results with few sampling points were reported. Here new results that involve a large number of sampling points are reported. Because the algorithm is computationally intensive with a large number of data points, the parallel implementation of the algorithm on a MASPAR machine is described. MASPAR is a single-instruction multiple-data machine with 16,384 processors. The computer simulations discussed involve simultaneous wavelength demultiplexing, focusing, and the filtering out of a particular wavelength component. It is shown that satisfactory designs of diffractive optical elements can be achieved by the assignment of only a small number of sampling points on the output plane that adequately specify what is required at each wavelength.

Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison.

A detailed comparison of the original Gerchberg-Saxton and the Yang-Gu algorithms for the reconstruction of model images from two intensity measurements in a nonunitary transform system is presented. The Yang-Gu algorithm is a generalization of the Gerchberg-Saxton algorithm and is effective in solving the general amplitude-phase-retrieval problem in any linear unitary or nonunitary transform system. For a unitary transform system the Yang-Gu algorithm is identical to the Gerchberg-Saxton algorithm. The reconstruction of images from data corrupted with random noise is also investigated. The simulation results show that the Yang-Gu algorithm is relatively insensitive to the presence of noise in data. In all cases studied the Yang-Gu algorithm always resulted in a highly accurate recovered phase.

Iterative interlacing error diffusion for synthesis of computer-generated holograms.

The iterative interlacing error-diffusion technique is a combination of the error-diffusion and the modified iterative interlacing techniques for synthesizing computer-generated holograms. The iterative interlacing error-diffusion technique leads to a dramatic improvement in the quality of reconstructed images, provided that the two constant parameters involved in iterations are chosen properly.

Iterative interlacing approach for synthesis of computer-generated holograms.

An approach for optimizing computer-generated holograms is discussed. The approach can be summarized most generally as hierarchically designing a number of holograms to add up coherently to a single desired reconstruction. In the case of binary holograms, this approach results in the interlacing technique (IT) and the iterative interlacing technique (IIT). In the IT, a number of subholograms are designed and interlaced together to generate the total binary hologram. The first subhologram is designed to reconstruct the desired image. The succeeding subholograms are designed to correct the remaining error image. In the IIT, the remaining error image after the last subhologram is circulated back to the first subhologram, and the process is continued a number of sweeps until convergence. Both techniques can be used together with most computer-generated-hologram synthesis algorithms and result in a substantial reduction in reconstruction error as well as an increased speed of convergence in the case of iterative algorithms.

Parallel, self-organizing, hierarchical neural networks.

A new neural-network architecture called the parallel, self-organizing, hierarchical neural network (PSHNN) is presented. The new architecture involves a number of stages in which each stage can be a particular neural network (SNN). At the end of each stage, error detection is carried out, and a number of input vectors are rejected. Between two stages there is a nonlinear transformation of input vectors rejected by the previous stage. The new architecture has many desirable properties, such as optimized system complexity (in the sense of minimized self-organizing number of stages), high classification accuracy, minimized learning and recall times, and truly parallel architectures in which all stages operate simultaneously without waiting for data from other stages during testing. The experiments performed indicated the superiority of the new architecture over multilayered networks with back-propagation training.

Electrooptical processing of signal transforms.

New architectures are discussed for the implementation of signal transforms using new techniques in optical computing and signal processing. These architectures are based on the factorization of any discrete trigonometric transform matrix into a simple preprocessing matrix followed by a matrix consisting of the direct sum of circular convolutions.