Area weighted convolutional interpolation for data reprojection in single photon emission computed tomography

A data reprojection algorithm has been developed for use in single photon emission computed tomography on an array processor equipped computer system. The algorithm makes use of an accurate representation of pixel activity (uniform square pixel model of intensity distribution), and is rapidly performed due to the efficient handling of an array-based algorithm and the fast Fourier transform on parallel processing hardware. The algorithm consists of using a pixel driven nearest-neighbor projection operation to an array of subdivided projection bins. The subdivided project bin array is then convolved with the angle-dependent projection of the area of a uniform square pixel and compressed to original bin size. The new algorithm has thus been named the area weighted convolution (AWC) method of interpolation. When compared to nearest-neighbor and linear interpolation algorithms, the new AWC algorithm was found to be more accurate, having an accuracy approaching that of the line length algorithm. It also yielded an easier and more efficient implementation on parallel hardware than line length or linear interpolation, with faster execution times than either.     

A field-programmable gate array based system for high frame rate laser Doppler blood flow imaging

This paper presents a general embedded processing system implemented in a field-programmable gate array providing high frame rate and high accuracy for a laser Doppler blood flow imaging system. The proposed system can achieve a basic frame rate of flow images at 1 frame/second for 256×256 images with 1024 fast Fourier transform (FFT) points used in the processing algorithm. Mixed fixed-floating point calculations are utilized to achieve high accuracy but with a reasonable resource usage. The implementation has a root mean square deviation of the relative difference in flow values below 0.1% when compared with a double-precision floating point implementation. The system can contain from one or more processing units to obtain the required frame rate and accuracy. The performance of the system is significantly higher than other methods reported to date. Furthermore, a dedicated field-programmable gate array (FPGA) board has been designed to test the proposed processing system. The board is linked with a laser line scanning system, which uses a 64×1 photodetector array. Test results with various operating parameters show that the performance of the new system is better, in terms of noise and imaging speed, than has been previously achieved.     

1024点高速FFT处理器的FPGA设计与实现

目的 设计满足高速实时信号处理需要的快速傅里叶变换(FFT)处理器。方法采取基-2按频率抽取( DIF)FFT算法,蝶形运算单元采用流水线方式,接收数据采用乒乓操作的方法设计基于现场可编程门阵列(FPGA)的1 024点、32位字长、定点复数FFT处理器。结果在时钟100 MHz下,计算1次1 024点定点FFT耗时约...     

A general method for three-dimensional filter computation

Application of the Fourier space deconvolution algorithm to three-dimensional (3D) reconstruction problems necessitates the computation of a frequency space filter; which requires taking the 3D Fourier transform of the system response function. In this paper, it is shown that for system response functions of the specific form d(theta, phi)/r2, with d(theta, phi) an angular function describing the imaging system, the filter computation can always be reduced to a single integration which, in many cases, may be performed analytically. Complete expressions are derived for the general 3D filter, and two examples are given to illustrate the use of such expressions.     

Comparison of methods for the dynamic calibration of electromagnetic flowmeters

The response characteristics of an electromagnetic blood flowmeter and associated recording system were determined both by an electronic method and by Fourier transform of the impulse response. Amplitude and phase responses were measured to 25Hz with the flow-meter filters set at nominal 5, 15 and 50 Hz. Agreement between the two methods was good unless the 50 Hz filter was used. The amplitude of the input was reduced by approximately 50% at 10 Hz using the 5 Hz filter and by 10% using the 50 Hz filter. The use of these filters in the clinical situation may cause significant loss of information. Alternatively, the use of signal-averaging techniques may extend the range of reliable recordings.     

一种新型自适应动态滤波器在超声成像中的应用

目的 为使动态滤波器的中心频率可实时匹配回波信号中心频率,本文设计了一种新型的自适应动态滤波器.方法 本文自适应机制是以快速傅里叶变换（fast Fourier transform,FFT）算法实时分析真实回波信号的频率特性,根据频率编号自适应匹配动态滤波器的系数.该滤波器的所有模块基于现场可编程门阵列（field programmable gate array,FPGA）硬件实现,最后将加入白噪声的正弦信号使用Modelsim时序仿真工具进行仿真.结果 仿真结果表明,这种滤波器能良好匹配回波信号中心频率,消除噪声.结论 本文提出的自适应动态滤波器满足高速实时系统的要求,为超声系统中滤波器的设计提供了可靠依据.     

用STFT分析瞬态诱发耳声发射的时频特征

瞬态诱发耳声发射是一种时变的声信号,用传统的傅立叶变换无法完全表示其信息.本文介绍了用短时傅立叶变换分析瞬态诱发耳声发射方法,并给出了其时频分布的实验结果,分析了其各个频率成份出现的不同时刻及持续时间.本文还对瞬态诱发耳声发射中的伪迹出现的时间和频率作了分析,指出伪迹在时频域是和有用信号分离的,理论上可以通过时频滤波器去除.     

超声成像中投影初始化壁滤波器的设计及实现

壁滤波是彩色超声血流成像系统中的一项关键技术.如果不对来自静止和慢动组织的壁信号进行充分的滤除,低速血流很难被检测到,高速血流的估计也会有很大偏差,在各种壁滤波器中,基于投影初始化的无限冲击响应(IlR)壁滤波器具有过渡带窄和阻带衰减大等特性,性能优于其他的壁滤波器.然而目前对此类滤波器的研究仅限于理论层面,并没有发表切实可行的设计和实现方法.我们从实现和应用的角度,给出了一种新的投影初始化滤波器的设计和实现方案,将滤波器的实现转换为矩阵乘法操作,并在可编程逻辑器件上对其进行了实现.实验结果表明,这是一种简单有效的壁滤波器设计实现方法,性能优于传统的壁滤波器.     

On the use of frequency-domain reconstruction algorithms for photoacoustic imaging

We investigate the use of a frequency-domain reconstruction algorithm based on the nonuniform fast Fourier transform (NUFFT) for photoacoustic imaging (PAI). Standard algorithms based on the fast Fourier transform (FFT) are computationally efficient, but compromise the image quality by artifacts. In our previous work we have developed an algorithm for PAI based on the NUFFT which is computationally efficient and can reconstruct images with the quality known from temporal backprojection algorithms. In this paper we review imaging qualities, such as resolution, signal-to-noise ratio, and the effects of artifacts in real-world situations. Reconstruction examples show that artifacts are reduced significantly. In particular, image details with a larger distance from the detectors can be resolved more accurately than with standard FFT algorithms.     

Time-domain digital filter to improve signal-to-noise ratio in respiratory impedance measurements

The mechanical impedance of the respiratory system Zrs is usually measured by forced excitation while the patient breathes spontaneously. Pressure and flow signals due to breathing contaminate the excitation signals, leading to a poor signal-to-noise ratio (SNR) and thus to errors in impedance estimation, especially at low frequencies (up to 8 Hz). To enhance SNR in the recorded signals we designed an infinite impulse response digital filter for the frequent case in which the excitation is pseudorandom. The algorithm is based on narrowband second-order bandpass elements centred at the excitation frequencies. The performance of the filter was assessed in a simulation study by superposing forced excitation signals (2-32 Hz) from a reference model and the signals of breathing recorded from 16 subjects. When compared with a conventional high-pass filtering, the devised filtering resulted in an increase in SNR which was almost constant over the whole frequency band: 6.30 +/- 0.98 dB (mean +/- SD). This improvement in SNR was reflected in an increase in the number of subjects for which the corresponding coherence y2 attained a value greater than the conventional threshold of acceptability (y2 = 0.95). At the lowest frequency (2 Hz) only two (12.5 per cent) simulated subjects had y2 greater than or equal to 0.95 with the conventional high-pass filtering. By contrast, when using the devised comb filter the number of subjects with y2 greater than or equal to 0.95 increased up to 13 (81 per cent). The results obtained suggest that this filter may be useful to improve SNR and thus Zrs estimation.     

A filtering approach to image reconstruction in 3D SPECT

We present a new approach to three-dimensional (3D) image reconstruction using analytical inversion of the exponential divergent beam transform, which can serve as a mathematical model for cone-beam 3D SPECT imaging. We apply a circular cone-beam scan and assume constant attenuation inside a convex area with a known boundary, which is satisfactory in brain imaging. The reconstruction problem is reduced to an image restoration problem characterized by a shift-variant point spread function which is given analytically. The method requires two computation steps: backprojection and filtering. The modulation transfer function (MTF) of the filter is derived by means of an original methodology using the 2D Laplace transform. The filter is implemented in the frequency domain and requires 2D Fourier transform of transverse slices. In order to obtain a shift-invariant cone-beam projection-backprojection operator we resort to an approximation, assuming that the collimator has a relatively large focal length. Nevertheless, numerical experiments demonstrate surprisingly good results for detectors with relatively short focal lengths. The use of a wavelet-based filtering algorithm greatly improves the stability to Poisson noise.     

Recursive running DCT algorithm and its application in adaptive filtering of surface electrical recording of small intestine

A rhythmic electrical signal is present in the human small intestine and can be recorded using surface electrodes. Surface electrical recordings of the small intestine contain severe interference that obscures the electrical signal of the small intestine. An adaptive system is proposed in the paper for the enhancement of the small-intestinal signal. To obtain better performance, adaptive signal enhancement is performed in the transform domain using a discrete cosine transform (DCT). A fast recursive algorithm is developed for the calculation of running DCT. The computational complexity of the proposed recursive algorithm is only 2/N (N=length of the adaptive filter) of the direct calculation of the running DCT. A series of simulations are conducted to investigate the performance of the proposed transform-domain adaptive filtering using DCT in comparison with time-domain adaptive filtering and with transform-domain adaptive filtering using a discrete Fourier transform (DFT). The parameters of the proposed adaptive system are optimised, and their effects on system performance are investigated. The application of the proposed method for the enhancement of the small-intestinal signal is presented and discussed.     

Analytic reconstruction of magnetic resonance imaging signal obtained from a periodic encoding field

We have proposed a two-dimensional PERiodic-Linear (PERL) magnetic encoding field geometry B(x,y) = g(y)y cos(q(x)x) and a magnetic resonance imaging pulse sequence which incorporates two fields to image a two-dimensional spin density: a standard linear gradient in the x dimension, and the PERL field. Because of its periodicity, the PERL field produces a signal where the phase of the two dimensions is functionally different. The x dimension is encoded linearly, but the y dimension appears as the argument of a sinusoidal phase term. Thus, the time-domain signal and image spin density are not related by a two-dimensional Fourier transform. They are related by a one-dimensional Fourier transform in the x dimension and a new Bessel function integral transform (the PERL transform) in the y dimension. The inverse of the PERL transform provides a reconstruction algorithm for the y dimension of the spin density from the signal space. To date, the inverse transform has been computed numerically by a Bessel function expansion over its basis functions. This numerical solution used a finite sum to approximate an infinite summation and thus introduced a truncation error. This work analytically determines the basis functions for the PERL transform and incorporates them into the reconstruction algorithm. The improved algorithm is demonstrated by (1) direct comparison between the numerically and analytically computed basis functions, and (2) reconstruction of a known spin density. The new solution for the basis functions also lends proof of the system function for the PERL transform under specific conditions.     

Comparison of analog and digital Fourier transforms in medical image analysis

The effectiveness and limitations of medical image processing using analog and digital methods are studied. Several types of errors introduced during the image processing are analyzed. For the analog optical Fourier transform, errors are introduced by the vignetting effect and lens aberration. For the digital Fourier transform, errors are introduced by the aliasing effect and the band limit. To compare the results obtained by the two techniques, a set of x-ray images was processed both optically and digitally. The former was achieved by an optical system containing a large Fourier telephoto lens and the latter by a personal computer using a Fourier transform algorithm. The veracity of both the optical and digital Fourier spectra is analyzed. Our results indicate that the optical method has high speed due to parallel processing. High veracity can be achieved in high frequency regions by using an optimal optical system. In comparison, the digital method has the advantages of high processing precision and programmability, but has low processing speed. The comparison of the two different techniques presented in this article can provide a basis for selection of the processing method in different clinical settings. Even with today's fast computers, the optical method is still suitable for many clinical applications. The best choice lies in an analog-digital combination.     

Terahertz pulsed imaging in vivo: measurements and processing methods

This paper presents a number of data processing algorithms developed to improve the accuracy of results derived from datasets acquired by a recently designed terahertz handheld probe. These techniques include a baseline subtraction algorithm and a number of algorithms to extract the sample impulse response: double Gaussian inverse filtering, frequency-wavelet domain deconvolution, and sparse deconvolution. In vivo measurements of human skin are used as examples, and a comparison is made of the terahertz impulse response from a number of different skin positions. The algorithms presented enables both the spectroscopic and time domain properties of samples measured in reflection geometry to be better determined compared to previous calculation methods.     

A comparison of the speeds of three convolution algorithms

The speeds of three computer algorithms suitable for use in three-dimensional radiotherapy planning codes were compared. Two of the algorithms are based on ray-tracing methods, the first algorithm uses a fast ray-tracing procedure directly and the second employs a table lookup procedure; the table was originally calculated by ray tracing. The third algorithm was a convolution procedure using the fast Fourier transform. Benchmark programs were written to compare the fundamental running speeds of the three algorithms operating on three-dimensional arrays of various sizes. The convolution procedure employing the three-dimensional fast Fourier transform had the shortest running times on a VAX/750 (Digital Equipment Corp.) computer. We concluded that this algorithm holds significant potential for practical three-dimensional dose calculations.     

Automatic seizure detection with different time delays using SDFT and time-domain feature extraction

Automatic seizure detection is important for fast detection of the seizure because the way that the expert denotes and searches for seizure in the long signal takes time. The most common way to detect seizures automatically is to use an electroencephalogram(EEG). Many studies have used feature extraction that needs time for calculation. In this study, sliding discrete Fourier transform(SDFT) was applied for conversion to a frequency domain without using a window, which was compared with using wi...     

基于对数域连续小波变换电路的心电图QRS波检测

为满足植入式心脏起搏器之类的医疗设备低功耗、实时处理等应用要求的需要,提出了基于低电压、低功耗对数域连续小波变换电路的心电图QRS波检测方法。为便于用模拟VLSI实现小波变换,用混合粒子群算法构造了类高斯一阶导数小波。以平衡式对数域积分器为积木块,设计了用于QRS波检测的连续小波变换电路,该电路由冲激响应为类高斯一阶导数小波函数的反褶及其伸缩的滤波器组构成。由该电路实现心电信号的小波变换,进行QRS波检测。仿真结果表明了该方法的可行性。     

Improved characterisation of aortic tortuosity

Tortuosity can be described as the variation in blood vessel curvature. Abnormal tortuosity is an important clinical indicator of various conditions. Despite considerable research, there has been very little agreement on an accurate, unique measure of this phenomenon for clinical applications. It has been demonstrated that a single value is insufficient to describe vessel tortuosity. In this work, the fast Fourier transform of the vessel's curvature as a measure of tortuosity is introduced. Spectral analysis of a suite of computed-simulated vessels, a phantom and clinical data is carried out. Observation of the acquired spectra permits detection of the local curvature variations. Spectral analysis of curvature provides a compact and graphic representation of tortuosity. This paper also describes two new highly automated MATLAB algorithms for obtaining the vessel centrelines: a heuristic image processing algorithm, and an algorithm based on the probabilistic Hough transform. We demonstrate the accuracy of both algorithms comparing with a manual method to extract the vessel centreline. Both algorithms reduce potential errors and user time and only require the manual selection of one centroid.     

An x-ray CT polymer gel dosimetry prototype: I. Remnant artefact removal

In this study a new x-ray CT polymer gel dosimetry (PGD) filtering technique is presented for the removal of (i) remnant ring and streak artefacts, and (ii) 'structured' noise in the form of minute, intrinsic gel density fluctuations. It is shown that the noise present within x-ray CT PGD images is not purely stochastic (pixel by pixel) in nature, but rather is 'structured', and hence purely stochastic-based noise-removal filters fail in removing this significant, unwanted noise component. The remnant artefact removal (RAR) technique is based on a class of signal stripping (i.e. baseline-estimation) algorithms typically used in the estimation of unwanted non-uniform baselines underlying spectral data. Here the traditional signal removal algorithm is recast, whereby the 'signal' that is removed is the structured noise and remnant artefacts, leaving the desired polymer gel dose distribution. The algorithm is extended to 2D and input parameters are optimized for PGD images. RAR filter results are tested on (i) synthetic images with measured gel background images added, in order to accurately represent actual noise present in PGD images, and (ii) PGD images of a three-field gel irradiation. RAR results are compared to a top-performing noise filter (adaptive mean, AM), used in previous x-ray CT PGD studies. It is shown that, in all cases, the RAR filter outperforms the AM filter, particularly in cases where either (i) a low-dose gel image has been acquired or (ii) the signal-to-noise ratio of the PG image is low, as in the case when a low number of image averages are acquired within a given experiment. Guidelines for the implementation of the RAR filter are given.