Reconstruction of SPECT images using generalized matrix inverses

Generalized matrix inverses are used to estimate source activity distributions from single photon emission computed tomography (SPECT) projection measurements. Image reconstructions for a numerical simulation and a clinical brain study are examined. The photon flux from the source region and photon detection by the gamma camera are modeled by matrices which are computed by Monte Carlo methods. The singular value decompositions (SVDs) of these matrices give considerable insight into the SPECT image reconstruction problem and the SVDs are used to form approximate generalized matrix inverses. Tradeoffs between resolution and error in estimating source voxel intensities are discussed, and estimates of these errors provide a robust means of stabilizing the solution to the ill-posed inverse problem. In addition to its quantitative clinical applications, the generalized matrix inverse method may be a useful research tool for tasks such as evaluating collimator design and optimizing gamma camera motion.     

Focused ion beam fabrication of curved structures using the concept of beam shaping and variable dwell time

This paper introduces a technique for the direct fabrication of curved structures using focused ion beams called beam shaping method (BSM). It is based on the concept of variable dwell time and simulations of sputtering and redeposition to shape overall ion dose profile which is composed of individual focused single pixel beam profile. The pixel dwell times are kept small enough to avoid sputtering yield enhancement due to a locally inclined surface. This provides better control over the fabrication process and allows the combination of the individual overlapped beams (separated by the pixel spacing) into a dose profile for use in the simulation. Varying the dwell time at each pixel we optimize the dose profile for the fabrication of the desired structure using repeated simulation. We demonstrate this technique on a silicon substrate by realizing fundamental structures such as circular and triangular optical gratings. The resultant fabricated structures agree well with the desired geometry within tolerance. Detailed explanation of the technique with experimental verifications is given, and the optimized ion dose profiles are discussed.     

基于仅相位加权的阵列天线波束赋形优化方法

给出了一种仅改变相位分布的阵列天线波束赋形优化算法.在不改变阵列天线各单元的馈电幅度分布的前提下,为了使天线的辐射波束形成给定的方向图形状,采用联合应用DFP和BFGS公式的变度量优化算法对阵列天线各单元的馈电相位分布进行优化,使得优化后的阵列天线主波束形状能够与预给的波束形状吻合,从而达到设计要求.该方法为N维函数无约束极小值方法,具有快速收敛、计算量小的优点,是一种阵列天线波束赋形的通用方法.     

Parametrically controlled noise shaping in variable state-step-back pseudo-Trellis SDM

Progress is reported in parametrically controlled noise shaping sigma delta modulator (SDM) design. As this SDM structure can provide a higher SNR than normal SDM structures, Philips Research Laboratories questioned whether further improvement could be obtained using techniques inspired by the Trellis SDM. Simulations are used here to illustrate the performance of a parametrically controlled pseudo-Trellis SDM. The technique uses uniquely a variable state step-back approach to mediate loop behaviour that is shown to achieve robust stability in the presence of aggressive noise shaping and high level signals. Comparisons are made with traditional SDM structures and LPCM systems for high-resolution audio applications.     

Pulse shaping and shortening by spatial filtering of aninduced-phase-modulated probe wave

All-optical deflection and spatial filtering have been used to theoretically model pulse shortening and shaping. Good agreement is obtained with the experimental results of other authors. Pulses with a shortening coefficient of the order of 10, and special forms such as super-Gaussian, triangular-like, and pairs of pulses with an adjustable peak-to-peak ratio are obtained     

Adaptive filtering in subbands using a weighted criterion

Transform-domain adaptive algorithms have been proposed to reduce the eigenvalue spread of the matrix governing their convergence, thus improving the convergence rate. However, a classical problem arises from the conflicting requirements between algorithm improvement requiring rather long transforms and the need to keep the input/output delay as small as possible, thus imposing short transforms. This dilemma has been alleviated by the so-called “short-block transform domain algorithms” but is still apparent. This paper proposes an adaptive algorithm compatible with the use of rectangular orthogonal transforms (e.g., critically subsampled, lossless, perfect reconstruction filter banks), thus allowing better tradeoffs between algorithm improvement, arithmetic complexity, and input/output delay. The method proposed makes a direct connection between the minimization of a specific weighted least squares criterion and the convergence rate of the corresponding stochastic gradient algorithm. This method leads to improvements in the convergence rate compared with both LMS and classical frequency domain algorithms     

On filtering by means of generalized integral images: a review and applications

In this paper the method of multidimensional (n-D) filtering based on prior signal integration is analyzed. This method has the advantage that the computational complexity for filtering is independent of the filter kernel size. An overview of recent 2-D image processing systems is presented where these types of filters are applied. Based on this overview a framework that covers this class of filters is derived using repeated integration. These filters include for example rect and triangle-filters which can be used to approximate Gaussian derivative filters. Furthermore the normalization of the filters, computational complexity, and storage cost are discussed. Finally, two image processing systems which benefit from the application of the filters are presented. They belong to the topic of advanced driver assistance systems.     

Multivariable control system synthesis utilizing the generalized inverse of a matrix

By utilizing the concept of the generalized inverse of a matrix, it is possible to obtain more complete multivariable control system design equations than have previously been published. Also, condition equations can define the limitations which must be imposed upon the desired system H' in order to realize a mathematical solution.     

Determination of glucose concentrations in an aqueous matrix fromNIR spectra using optimal time-domain filtering and partialleast-squares regression

The authors have investigated the use of a time-domain optimal filtering method to simultaneously minimize both the baseline variation and high-frequency noise in near-infrared (NIR) spectrophotometric absorption data of glucose dissolved in a simple aqueous (deionized water) matrix. By coupling a third-order (6-pole) digital Butterworth bandpass filter with partial least-squares (PLS) regression modeling, glucose concentrations were determined for a set of test data with a standard error of prediction (SEP) of 10.53 mg/dl (mean percent error: 4.24%) using 7 PLS factors. Compared to the unfiltered test data for 6 PLS factors and a SEP=17.00 (mean percent error: 7.38%) this results shows more than a 38% decrease in the error. The glucose concentrations ranged from 51 mg/dl to 493 mg/dl, and the NIR spectral region between 2088 nm and 2354 nm (4789 cm^-1 and 4248 cm^-1) was used to develop the optimal PLS model. The optimal PLS model was determined from a sequence of 3-dimensional performance response maps for different numbers of PLS factors (2-10). A total of 99 NIR spectra were generated for glucose dissolved in deionized water using a NIRsystems 5000 dispersive spectrophotometer. Nine of these spectra were generated for only water, which were averaged and subtracted from the remaining 90 spectra to generate the training and test data sets, thereby, removing the intrinsic high background absorption due to the water. The training set consisted of 57 spectra and associated glucose concentration target values, and the test set was comprised of the remaining 33 spectra and target values. Performance results were compared for 3 different digital Butterworth bandpass filters (4-poles, 6-poles, and 8-poles), and a digital Gaussian filter design approach (i.e., Fourier filtering)     

Seismic data filtering using a Gabor representation

Gabor representations are signal expansions using sets of functions that are localized and concentrated in time and frequency. This characteristic makes them suitable candidates for filtering data where the desired signal or noise is nonstationary or time-dependent. It is shown that Gabor representations formulated with frame theory can be used for time-dependent noise removal. Furthermore, their ability to filter noise in the presence of a nonstationary signal enables them to outperform singular value decomposition eigenimage filtering techniques in the removal of incoherent noise in common midpoint data with a moderate fold     

Deblocking filtering method using a perceptual map

A new method of deblocking is proposed. It aims to reduce the blocking artifacts in the compressed image by analyzing their visibility. A perceptual map is obtained using some Human Visual System (HVS) characteristics. This perceptual map is used as input to a recursive filter to reduce the blocking effect. The obtained results have been compared with a very recent efficient method.     

On the error matrix in optimal linear filtering of stationary processes

The error covariance matrix corresponding to optimal linear causal filtering of second-order stationary processes in additive noise is considered. Formulas expressing this error matrix in terms of the optimal transfer function are established, and in the nonsingular case the optimal transfer function is expressed in terms of the spectral densities. These are straightforward generalizations of previously published scalar results, and the derivation is similarly based on Hardy space theory. Explicit bounds on the minimal error (i.e., the trace of the optimal error covariance matrix) are obtained for filtering in white noise. Furthermore, an explicit expression for the error covariance matrix is derived for the case of transmitting the same signal over several white-noise channels.     

强激光的时间整形和空间整形——利用双折射透镜组实现激光束的空间整形

本文使用琼斯矩阵方法对双折射透镜组空间整形系统的光强透射率分布和工作特性进行了分析,并讨论了工程设计中参数的选择以及加工误差带来的影响等有关问题.     

一种新的变步长自适应滤波算法及分析

现有的变步长自适应滤波算法可分为步长一致和步长非一致两种情况,本文着重对步长一致的情况进行分析讨论,给出了统一的表达式,并定性地提出了步长变化的准则.同时在分析了几种现有变步长自适应滤波算法的基础上,提出了一种新的变步长自适应滤波算法.理论分析和不同情况下的仿真实验结果都表明,新算法能够符合文中提出的变步长准则,在保持算法简单的同时能够满足收敛速度,跟踪能力和收敛精度的要求.     

8/spl times/8 optical switch matrix using generalized Mach-Zehnder interferometers

We report an 8/spl times/8 strictly nonblocking optical cross connect (OXC) using multimode imaging (MMI)-based generalized Mach-Zehnder (MZ) interferometers realized in the silica-on-silicon planar waveguide system. Employing a router-selector architecture, this MMI-MZ OXC design results in a significantly smaller device than conventional directional-coupler based implementations. An average insertion loss of 6 dB and crosstalk of -34 dB, is demonstrated for the 8/spl times/8 OXC.     

On the definition of the generalized scattering matrix of a lossless radial line

In this paper, the generalized scattering matrix for a radial line (rGSM) is defined. The main problem lies in the fact that, for a radial line, a unique characteristic impedance cannot be defined since forward waves "see" an enlarging waveguide, while regressive waves "see" a reducing one. Hence, two different impedances are defined and the usual normalization based on /spl radic/(Z/sub 0/), valid for uniform lines, cannot be applied. An equivalent network, representing the transformation between voltages/currents and scattering amplitudes, is introduced. The transformers included in this circuit represent the normalization of electric quantities. The transformer ratios influence the properties of the rGSM, and this will be discussed at length. The rGSM is then applied to the analysis of a linear taper and the results are compared with those obtained with generalized telegraphists equations. Finally, a double linear taper has been realized and the experimental and theoretical results, obtained with rGSM, are compared, showing a very good agreement in a wide band.     

Alternate forms of the generalized composite scattering matrix

The author reconciles the differences in three forms of generalized composite scattering matrix derivations. Star matrix multiplication conversion of a generalized composite transmission matrix to its scattering equivalent and signal flow graph analysis are reviewed and analyzed     

Experimental demonstration of pulse shaping and shortening byspatial filtering of an induced-phase-modulated probe wave

An asymmetrically induced phase modulation resulting in an intensity-dependent spatial beam deflection and a subsequent spatial filtering have been used for all-optical pulse shaping and shortening. A compression factor of eight and controllable symmetrical super-Gaussian pulses and pulse trains have been observed in a good agreement with previous analyses in a pump-probe beam configuration     

Single fault location in a linear analogue system with variable sensitivity matrix

A method of locating a single fault in a linear analogue system by determining the consistency of the inaccessible nodal voltage vectors is proposed. It does not require the assumption of an invariable sensitivity matrix, and can thus be applied to catastrophe faults as well.