Optimal multichannel estimation of the location of a target with nonoverlapping noise

We propose a new algorithm for estimating the location of an object in multichannel images when the noise is spatially disjointed from (nonoverlapping with) the target. This algorithm is optimal for nonoverlapping noise and for multichannel images in the maximum-likelihood sense. We consider the case in which the statistical parameters of the input scene are unknown and are estimated by observation. We assess the results for simulated images with white and Gaussian background, for a large scale of variances of the background noise, and different values of the contrast in the scene. We compare the results of this algorithm with the results obtained with two other algorithms, the optimal algorithm for monochannel nonoverlapping noise and the optimal algorithm for multichannel additive noise, and we show that in both cases improvement can be obtained. We show the efficiency of the estimation for real input scenes when the background noise is correlated clutter noise. This algorithm has the same complexity as correlation, and the improvement is obtained with no more calculation cost than with classic methods.     

Fast three-step phase-shifting algorithm

We propose a new three-step phase-shifting algorithm, which is much faster than the traditional three-step algorithm. We achieve the speed advantage by using a simple intensity ratio function to replace the arctangent function in the traditional algorithm. The phase error caused by this new algorithm is compensated for by use of a lookup table. Our experimental results show that both the new algorithm and the traditional algorithm generate similar results, but the new algorithm is 3.4 times faster. By implementing this new algorithm in a high-resolution, real-time three-dimensional shape measurement system, we were able to achieve a measurement speed of 40 frames per second at a resolution of 532 x 500 pixels, all with an ordinary personal computer.     

基于边界表示的拔模算法及其应用

拔模操作是三维几何造型系统中给实体创建倾斜面特征的有效方法。笔者以商业造型软件 TiGems 为平台,提出了一个基于边界表示的拔模算法。针对现有拔模算法的不足,改进了拔模操作中边的计算方法,提高了算法的效率;增加了判断并消除形体自交的功能,提高了算法的鲁棒性。笔者将本文的算法应用到草图的倾斜拉伸操作中,取得了不错的效果。     

A batch,derivative-free algorithm for finding multiple local minima

We propose a derivative-free algorithm for finding high-quality local minima for functions that require significant computational resources to evaluate. Our algorithm efficiently utilizes the computational resources allocated to it and also has strong theoretical results, almost surely starting a finite number of local optimization runs and identifying all local minima. We propose metrics for measuring how efficiently an algorithm finds local minima, and we benchmark our algorithm on synthetic problems (with known local minima) and two real-world applications.     

Entanglement simulations of Shor's algorithm

We demonstrate that, in the case of Shor's algorithm for factoring, highly mixed states will allow efficient quantum computation, indeed factorization can be achieved efficiently with just one initial pure qubit and a supply of initially maximally mixed qubits (Parker, S. and Plenio, M. B., 2000, Phys. Rev. Lett., 85, 3049). This leads us to ask how this affects the entanglement in the algorithm. We thus investigate the behaviour of entanglement in Shor's algorithm for small numbers of qubits by classical computer simulation of the quantum computer at different stages of the algorithm. We find that entanglement is an intrinsic part of the algorithm and that the entanglement through the algorithm appears to be closely related to the amount of mixing. Furthermore, if the computer is in a highly mixed state any attempt to remove entanglement by further mixing of the algorithm results in a significant decrease in its efficiency.     

Computation of isotopic peak center-mass distribution by fourier transform

We derive a new efficient algorithm for the computation of the isotopic peak center-mass distribution of a molecule. With the use of Fourier transform techniques, the algorithm accurately computes the total abundance and average mass of all the isotopic species with the same number of nucleons. We evaluate the performance of the method with 10 benchmark proteins and other molecules; results are compared with BRAIN, a recently reported polynomial method. The new algorithm is comparable to BRAIN in accuracy and superior in terms of speed and memory, particularly for large molecules. An implementation of the algorithm is available for download.     

Robust inversion methods for aerosol spectroscopy

The Fast Aerosol Spectrometer (FASP) is a device for spectral aerosol measurements. Its purpose is to safely monitor the atmosphere inside a reactor containment. First we describe the FASP and explain its basic physical laws. Then we introduce our reconstruction methods for aerosol particle size distributions designed for the FASP. We extend known existence results for constrained Tikhonov regularization by uniqueness criteria and use those to generate reasonable models for the size distributions. We apply a Bayesian model-selection framework on these pre-generated models. We compare our algorithm with classical inversion methods using simulated measurements. We then extend our reconstruction algorithm for two-component aerosols, so that we can simultaneously retrieve their particle-size distributions and unknown volume fractions of their two components. Finally we present the results of a numerical study for the extended algorithm.     

Wavelet packet correlation methods in biometrics

We introduce wavelet packet correlation filter classifiers. Correlation filters are traditionally designed in the image domain by minimization of some criterion function of the image training set. Instead, we perform classification in wavelet spaces that have training set representations that provide better solutions to the optimization problem in the filter design. We propose a pruning algorithm to find these wavelet spaces by using a correlation energy cost function, and we describe a match score fusion algorithm for applying the filters trained across the packet tree. The proposed classification algorithm is suitable for any object-recognition task. We present results by implementing a biometric recognition system that uses the NIST 24 fingerprint database, and show that applying correlation filters in the wavelet domain results in considerable improvement of the standard correlation filter algorithm.     

A projection iterative algorithm boundary element method for the Signorini problem

We propose a projection iterative algorithm based on a fixed point equation for solving a certain class of Signorini problem. The satisfaction of the Signorini boundary conditions is verified in a projection iterative manner, and at each iterative step, an elliptic mixed boundary value problem is solved by a boundary element method which is suitable for any domain. We prove the convergence of the algorithm by the property of projection. The advantage of this algorithm is that it is easy to be implemented and converge quickly. Some numerical results show the accuracy and effectiveness of the algorithm.     

Calibration of stereo cameras from two perpendicular planes

We present a novel linear algorithm with which to calibrate stereo cameras from two perpendicular planes. Stereo cameras are two cameras aligned in a special configuration with coplanar image planes and parallel axes that are increasingly more widely used in computer vision tasks. Our objective is to present a more practical and simplified linear algorithm for these special configuration cameras, as traditional linear algorithms usually require too-strong constraints either on three-dimensional scenes or on the camera's motion. We developed the proposed algorithm from a new constraint by exploiting the orthogonality of two planes. The algorithm has much weaker constraints on three-dimensional scenes because two perpendicular planes are commonly found in daily life. We tested the algorithm with synthetic data and real image data. Experimental results show that it is both accurate and practical.     

Decentralized Searching of Multiple Unknown and Transient Radio Sources with Paired Robots

In this paper, we develop a decentralized algorithm to coord inate a group of mobile robots to search for unknown and transient radio sources. In addition to limited mobility and ranges of communication and sensing, the robot team has to deal with challenges from signal source anonymity, short transmission duration, and variable transmission power. We propose a two-step approach: First, we decentralize belief functions that robots use to track source locations using checkpoint-based synchronization, and second, we propose a decentralized planning strategy to coordinate robots to ensure the existence of checkpoints. We analyze memory usage, data amount in communication, and searching time for the proposed algorithm. We have implemented the proposed algorithm and compared it with two heuristics. The experimental results show that our algorithm successfully trades a modest amount of memory for the fastest searching time among the three methods.     

Working time constraints in operational fixed job scheduling

In this study we consider the operational fixed job scheduling problem under working time limitations. The problem has several practical implications in both production and service operations; however the relevant research is scarce. We analyse pre-emptive and non pre-emptive versions of the problem and its special cases. We provide polynomial-time algorithms for some special cases. We show that the non pre-emptive jobs problem is strongly NP-hard, and propose a branch-and-bound algorithm that employs efficient bounding procedures and dominance properties. We conduct a numerical experiment to observe the effects of parameters on the quality of the solution. The results of our computational tests for the branch-and-bound algorithm reveal that our algorithm can solve the instances with up to 100 jobs in reasonable times. To the best of our knowledge our branch-and-bound algorithm is the first optimisation attempt to solve the problem.     

Algorithm for the extraction of page-formatted binary digital data

We present an algorithm for fast and reliable extraction of page-formatted binary digital data. The advantages of the algorithm include a low raw bit-error rate, fast extraction speed, the use of a simple and density-efficient coding scheme, and large tolerance to a change of the signal-to-noise ratio. We used this algorithm to analyze shot-noise-limited binary data that had large interpage and intrapage intensity variations and obtained an improvement in the bit-error rate of 3-4 orders of magnitude compared with that in a single-threshold-detection scheme. Implications of our results for the development of high-speed, high-density holographic memories are discussed.     

Evaluation of microlens properties in the presence of high spherical aberration

Microlenses can be generated with various fabrication technologies. Some of these technologies cause large spherical aberrations in the resulting microlenses. We describe an algorithm based on Rayleigh's quarter-wave criterion, which allows the evaluation of lens parameters for those microlenses. Specifically, we investigate numerical aperture, focal length, and space-bandwidth product with respect to applications in optical microsystems. We apply our algorithm to different types of microlenses, three gradient-index lenses, and one surface-relief lens. The experimental results demonstrate that our algorithm provides a helpful characterization method for microlenses with large aberrations.     

Removal of Probe Liftoff Effects on Crack Detection and Sizing in Metals by the AC Field Measurement Technique

In the alternative current field measurement (ACFM) technique, the nonzero value of liftoff distance for the magnetic sensor acts as a low-pass filter on surface crack signals, causing errors in crack detection and sizing. We present a blind deconvolution algorithm for liftoff evaluation and surface crack signal restoration. The algorithm employs the available closed-form expressions for the distribution of electromagnetic fields at the metal surface in the vicinity of a crack. To examine the accuracy of the algorithm, we use the original and the restored signals for crack sizing by a wavelet network inversion method. We present simulated and experimental results to demonstrate the role of the proposed algorithm in improving the inversion process.      

Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: the convex case

We present a new algorithm for the numerical solution of problems of electromagnetic or acoustic scattering by large, convex obstacles. This algorithm combines the use of an ansatz for the unknown density in a boundary-integral formulation of the scattering problem with an extension of the ideas of the method of stationary phase. We include numerical results illustrating the high-order convergence of our algorithm as well as its asymptotically bounded computational cost as the frequency increases.     

Spatial fringe pattern analysis using the two-dimensional continuous wavelet transform employing a cost function

We present a novel ridge extraction algorithm for use with the two-dimensional continuous wavelet transform to extract the phase information from a fringe pattern. A cost function is employed for the detection of the ridge. The results of the proposed algorithm on simulated and real fringe patterns are illustrated. Moreover, the proposed algorithm outperforms the maximum ridge extraction algorithm and it is found to be robust and reliable.     

Practical issues in wave-front sensing by use of phase diversity

We present the results of the phase-diversity algorithm applied to simulated and laboratory data. We show that the exact amount of defocus distance does not need to be known exactly for the phase-diversity algorithm on extended scene imaging. We determine, through computer simulation, the optimum diversity distance for various scene types. Using laboratory data, we compare the aberrations recovered with the phase-diversity algorithm and those measured with a Fizeau interferometer that uses a He-Ne laser. The two aberration sets agree with a Strehl ratio of over 0.9. The contrast of the recovered object is found to be ten times that of the raw image.     

Improved algorithm for the isogeny problem for ordinary elliptic curves

A low storage algorithm for constructing isogenies between ordinary elliptic curves was proposed by Galbraith, Hess and Smart (GHS). We give an improvement of this algorithm by modifying the pseudorandom walk so that lower-degree isogenies are used more frequently. This is motivated by the fact that high degree isogenies are slower to compute than low degree ones. We analyse the running time of the parallel collision search algorithm when the partitioning is uneven. We also give experimental results. We conclude that our algorithm is around $14$ times faster than the GHS algorithm when constructing horizontal isogenies between random isogenous elliptic curves over a $160$ -bit prime field. The results apply to generic adding walks and the more general group action inverse problem; a speed-up is obtained whenever the cost of computing edges in the graph varies significantly.     

Phase-shifting holographic interferometry for breast cancer detection

Using a mild pressure stressing device and a pulsed ruby-laser system, we apply phase-shifted holographic interferometry to the detection of breast cancer. We compare a four-step algorithm and a Carré algorithm for their ability to evaluate the interferograms. The results show the feasibility of holographic interferometry in the detection of anomalies in the human female breast.