Principles of parametric temporal imaging. I. System configurations

The recently developed process of temporal imaging expands or compresses time waveforms while preserving the shapes of their envelope profiles. A key element in a temporal imaging system is a time lens which imparts a quadratic phase modulation to the waveform being imaged. Several methods, such as electrooptic modulation, can be used to produce the phase modulation. In this paper, we concentrate on the parametric mixing of a signal waveform with a linearly chirped optical pump as the time lens mechanism. We analyze all single-lens system configurations including sum- and difference-frequency mixing schemes with positive and negative group velocity dispersions using temporal ray diagrams as an aid in understanding their operation     

Segmentation of the left ventricle of the heart in 3-D+t MRI data using an optimized nonrigid temporal model

Modern medical imaging modalities provide large amounts of information in both the spatial and temporal domains and the incorporation of this information in a coherent algorithmic framework is a significant challenge. In this paper, we present a novel and intuitive approach to combine 3-D spatial and temporal (3-D + time) magnetic resonance imaging (MRI) data in an integrated segmentation algorithm to extract the myocardium of the left ventricle. A novel level-set segmentation process is developed that simultaneously delineates and tracks the boundaries of the left ventricle muscle. By encoding prior knowledge about cardiac temporal evolution in a parametric framework, an expectation-maximization algorithm optimally tracks the myocardial deformation over the cardiac cycle. The expectation step deforms the level-set function while the maximization step updates the prior temporal model parameters to perform the segmentation in a nonrigid sense.     

Joint azimuth, elevation, and time of arrival estimation of diffuse sources

In this paper, we estimate the azimuth, the elevation, and the time of arrival of diffuse sources using the covariance matching estimator (COMET) algorithm. Previous works dealt with azimuth estimation of diffuse sources or azimuth and time of arrival estimation of point sources. However, in realistic situations, a tridimensional diffuse source localization is needed, which is the main objective of this paper. We show that the dimensionality of the COMET algorithm can be reduced by separating the estimation of the different source powers and the noise variance from that of the remaining parameters, namely the azimuth, the elevation, the time of arrival, and the corresponding angular and temporal spreads. As COMET still involves a multidimensional nonlinear optimization, we choose, in this purpose, the alternating projection algorithm to alleviate the corresponding complexity. The multiple signal classification (MUSIC) algorithm is processed to initialize the so-resulted algorithm. Simulations of the proposed algorithm are carried in different contexts and compared to the Cramér-Rao Bound, MUSIC algorithm, and dispersed signal parametric estimation simulation results.     

Bearing estimation for a distributed source: modeling, inherentaccuracy limitations and algorithms

The problem of using sensor array measurements to estimate the bearing of a radiating source surrounded by local scatterers is considered. The concept of “partial coherence” is introduced to account for temporal as well as spatial correlation effects often encountered in a Rayleigh fading-type propagation channel formed between a source and sensor array elements. A simple parametric model for temporal channel correlation is presented, yielding an overall spatio-temporal channel model that is more realistic than formerly proposed models (which assume either full or zero temporal channel correlation). Thus, previously proposed “distributed source” models for bearing estimation problems are generalized to a parametric spatio-temporal model for what is called “partially coherently distributed (PCD) sources”. A study of the associated Cramer-Rao Bound (CRB) is undertaken for a simple but illustrative problem formulation. The inherent limitations in bearing estimation accuracy for this spatio-temporal problem are seen to lie between the cases of zero and full temporal correlation, becoming more severe as temporal channel correlation increases. In addition, the associated maximum likelihood estimators for source bearing are proposed, and their performance is compared with that predicted by the CRB     

典型线面目标合成孔径雷达参数化成像

在复杂场景(特别是城区场景)合成孔径雷达(SAR)遥感成像中,存在大量线、面目标,如城区中的道路和建筑物边缘等目标,这些线面目标微波散射信号方向性强。传统SAR从单一视角获取场景的散射信息,且传统成像算法均基于点目标模型,使得传统SAR图像中线面目标主要特征表现为一系列的强散射点,而非线散射特征和面散射特征,最终造成SAR图像中目标不连续,SAR图像解译困难。因此,该文通过建立典型线段、三角面元目标的参数化回波模型,对线面目标SAR成像机理进行了深入细致的研究;并基于提出的参数化模型对线面目标进行参数化成像,即首先基于贝叶斯理论和所提的参数化模型对典型的线面目标进行分类判决,随后采用再成像的方式获得有效表征线、面目标散射特征的SAR图像,为线、面目标SAR图像解译提供有效支撑。最后,数值仿真实验成功验证了所提算法的有效性和正确性。      

Diagnosis of Dental Caries Using Terahertz Technology

Recently, the diagnoses of dental caries and other dental issues are in a queue as only X-ray-based techniques are available in most hospitals around the world. Terahertz (THz) parametric imaging (TPI) is the latest technology that can be applied for medical applications, especially dental caries. This technology is harmless and thus suitable for biological samples owing to the low energy of THz emission. In this paper, a developed TPI system is used to investigate the two-dimensional (2D) and three-dimensional (3D) images of different samples from human teeth. After analyzing the measured images of human teeth, the results suggest that the THz parametric technology is capable of investigating the inner side structure of the teeth. This technique can be useful in detecting the defects in all types of human and animal teeth. The measurement and analytical calculations have been performed by using the TPI system and MATLAB, respectively, and both are in good agreement. The characteristics of THz waves and their interactions with the tooth samples are summarized. And the available THz-based technologies, such as TPI, and their potential applications of diagnoses are also presented.     

Diagnosis of dental problem by using terahertz technology

Recently the diagnoses of dental caries and other dental issues are in a queue as only X-ray-based techniques are available in most hospitals around the world. Terahertz (THz) parametric imaging (TPI) is the latest technology that can be applied for medical applications, especially dental caries. This technology is harmless and thus suitable for biological samples owing to the low energy of THz emission. In this paper, a developed TPI system is used to investigate the two-dimensional (2D) and three-dimensional (3D) images of different samples from human teeth. After analyzing the measured images of the human tooth, the results suggest that the novel THz parametric technology is capable of investigating the inner side structure of the teeth. The technique can be useful in detecting the defects in all types of human and animal teeth. The measurement and analytical calculations have been performed by using the TPI system and MATLAB, respectively, and both are in good agreement. The characteristics of THz waves and their interactions with the tooth samples are summarized. And the available THz-based technologies, such as TPI, and their potential applications of diagnoses are also presented.     

Fast spatio-temporal image reconstruction for dynamic PET

In tomographic imaging, dynamic images are typically obtained by reconstructing the frames of a time sequence independently, one by one. A disadvantage of this frame-by-frame reconstruction approach is that it fails to account. For temporal correlations in the signal. Ideally, one should treat the entire image sequence as a single spatio-temporal signal. However, the resulting reconstruction task becomes computationally intensive. Fortunately, as the authors show in this paper, the spatio-temporal reconstruction problem call be greatly simplified by first applying a temporal Karhunen-Loeve (KL) transformation to the imaging equation. The authors show that if the regularization operator is chosen to be separable into space and time components, penalized weighted least squares reconstruction of the entire image sequence is approximately equivalent to frame-by-frame reconstruction in the space-KL domain. By this approach, spatio-temporal reconstruction can be achieved at reasonable computational cost. One can achieve further computational savings by discarding high-order KL components to avoid reconstructing them. Performance of the method is demonstrated through statistical evaluations of the bias-variance tradeoff obtained by computer simulation reconstruction     

Analysis of dynamic magnetic resonance images

Dynamic magnetic resonance (MR) imaging with contrast agents is a very promising technique for studying tissue perfusion in vivo. A temporal series of magnetic resonance images of the same slice are acquired following the injection of a contrast agent into the blood stream. The image intensity depends on the local concentration of the contrast agent, so that tissue perfusion can be studied by the image series. A new method of analyzing such series is described here. Nonparametric linear regression is used for modeling the image intensity along the series on a pixel by pixel basis. After modeling, some relevant quantities describing the time series are obtained and displayed as images. Due to its flexibility, this approach is preferred to parametric modeling when pathology is present since this can induce a wide spread of patterns for the pixel image intensity along time. Results of the application of the method to series of dynamic magnetic resonance images from ischaemic rat brains after the injection of the susceptibility agent Sprodiamide Inj. (Dy-DTPA-BMA) are shown and compared to results from a related known method.     

Performance analysis of a new real-time elastographic time constant estimator

New elastographic techniques such as poroelastography and viscoelasticity imaging aim at imaging the temporal mechanical behavior of tissues. These techniques usually involve the use of curve fitting methods being applied to noisy data to estimate new elastographic parameters. As of today, however, current elastographic implementations of poroelastography and viscoelasticity imaging methods are in general too slow and not optimized for clinical applications. Furthermore, image quality performance of these new elastographic techniques is still largely unknown due to a paucity of data and the lack of systematic studies that analyze their performance limitations. In this paper, we propose a new elastographic time constant (TC) estimator, which is based on the use of the least square error (LSE) curve-fitting method and the Levenberg-Marquardt (LM) optimization rule as applied to noisy elastographic data obtained from a material in a creep-type experiment. The algorithm is executed on a massively parallel general purpose graphics processing unit (GPGPU) to achieve real-time performance. The estimator's performance is analyzed using simulations. Experimental results obtained from poroelastic phantoms are presented as a proof of principle of the new estimator's technical applicability on real experimental data. The results of this study demonstrate that the newly proposed elastographic estimator can produce highly accurate and sensitive elastographic TC estimates in real-time and at high signal-to-noise ratios.     

Diffusion basis functions decomposition for estimating white matter intravoxel fiber geometry

In this paper, we present a new formulation for recovering the fiber tract geometry within a voxel from diffusion weighted magnetic resonance imaging (MRI) data, in the presence of single or multiple neuronal fibers. To this end, we define a discrete set of diffusion basis functions. The intravoxel information is recovered at voxels containing fiber crossings or bifurcations via the use of a linear combination of the above mentioned basis functions. Then, the parametric representation of the intravoxel fiber geometry is a discrete mixture of Gaussians. Our synthetic experiments depict several advantages by using this discrete schema: the approach uses a small number of diffusion weighted images (23) and relatively small b values (1250 s/mm2), i.e., the intravoxel information can be inferred at a fraction of the acquisition time required for datasets involving a large number of diffusion gradient orientations. Moreover our method is robust in the presence of more than two fibers within a voxel, improving the state-of-the-art of such parametric models. We present two algorithmic solutions to our formulation: by solving a linear program or by minimizing a quadratic cost function (both with non-negativity constraints). Such minimizations are efficiently achieved with standard iterative deterministic algorithms. Finally, we present results of applying the algorithms to synthetic as well as real data.     

基于时空连续约束的4D脑图像分割模型

纵向分析脑解剖结构的变化可以预测脑组织的生长或萎缩状态,为临床治疗和科学研究提供必要的依据.但由于成像设备或模式不同以及成像时间间隔较长,3D的分割方法得到的结果无法体现脑组织在时间维上缓慢变化的特征.针对这一问题,提出一种基于时空约束的4D脑图像水平集分割模型.该模型包含了由全局以及局部信息组成的数据拟合项、空间平滑项以及时间平滑项.其中数据拟合项体现了各个时间点的图像灰度信息,空间和时间平滑项则能保证分割结果在时空维上体现其缓慢变化的特性.实验结果表明本文方法既能保证准确的分割结果又能保证空间维以及时间维上的连续性.     

Blind deconvolution of medical ultrasound images: a parametric inverse filtering approach.

The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a "hybridization" of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the "hybrid" approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolutioh algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used.     

Spectral analysis of motor unit action potentials

The statistical processing of electromyographic signal examination performed in the time domain ensures mostly correct classification of pathology; however, because of an ambiguity of most temporal parameter definitions, a diagnosis can include a significant error that strongly depends on the neurologist's experience. Then, selected temporal parameters are determined for each run, and their mean values are calculated. In the final stage, these mean values are compared with a standard and, including additional clinical information, a diagnosis is given. An inconvenience of this procedure is high time consumption that arises from the necessity of determination of many parameters. Additionally, an ambiguity in determination of basic temporal parameters can cause doubts when parameters found by the physician are compared with standard parameters determined in other research centers. In this paper, we present a definition for spectral discriminant that directly enables a unique diagnosis to be made. An essential advantage of the suggested discriminant is a precise and algorithmically realized definition that enables an objective comparison of examination results obtained by physicians with different experiences or working in different research centers. A suggestion of the standard for selected muscle based on a population of 70 healthy cases is presented in the Results section.     

合成孔径雷达参数化成像技术进展

传统合成孔径雷达(SAR)成像可视为点目标散射模型约束下数据空间到图像空间的映射。然而,真实目标多为延展目标,与传统线性成像处理中的点目标散射模型存在失配,会导致SAR图像表征失真。常见的现象是使延展目标多呈现为孤立强点,阻碍了基于SAR图像的目标辨识等应用。SAR参数化成像技术是为解决上述模型失配问题而诞生的一种非线性成像方法,特点是兼顾点目标和延展目标的散射模型。具体来说,是通过利用不同类别目标的回波或图像的相位与幅度特征对观测角度的敏感性,辨识目标类型,反演目标散射参数,进而根据目标散射的参数化模型,重建目标图像的技术。在对延展目标成像时,可获得比传统线性成像方法更好的图像质量。该文主要介绍了线型延展目标的参数化成像技术,对应真实场景中的孤立强点和连续边缘,深入讨论了基于回波域、图像域的参数化成像技术和试验结果,展望了未来SAR参数化成像技术的发展趋势。      

Detection and visualization method of dynamic state transition for biological spatio-temporal imaging data

In the statistical analysis of functional brain imaging data, regression analysis and cross correlation analysis between time series data on each grid point have been widely used. The results can be graphically represented as an activation map on an anatomical image, but only activation signal, whose temporal pattern resembles the predefined reference function, can be detected. In the present study, we propose a fusion method comprising innovation approach in time series analysis and statistical test. Autoregressive (AR) models were fitted to time series data of each pixel for the range sufficiently before or after the state transition. Then, the remaining time series data were filtered using these AR parameters to obtain its innovation (filter output). The proposed method could extract brain neural activation as a phase transition of dynamics in the system without employing external information such as the reference function. The activation could be detected as temporal transitions of statistical test values. We evaluated this method by applying to optical imaging data obtained from the mammalian brain and the cardiac sino-atrial node (SAN), and demonstrated that our method can precisely detect spatio-temporal activation profiles in the brain or SAN.     

Analyse de la parole par les méthodes de modélisation paramétrique

This paper provides a survey of recent speech analysis techniques. After stressing the value of a precise and accurate analysis technique in most of speech processing applications, the basic parameter extraction methods are critically summarized. Attention is then focused on parametric modelling methods as applied to speech analysis. After a restatement of the linear prediction principles and associated fast algorithms, the three following topics are examined in some depth : ? global analysis methods on short time windows, with variable frequency resolution, and with additive noise; ? global analysis by multipulse techniques ; ? time evolving methods where a time varying parametric model is adjusted to model the transitions between quasistationnary periods; ? time adaptive sequential methods using fast (Kaiman, Cholesky…) algorithms along with a synchronous detection of temporal events.     

Parametric interaction in electron beam waves—A system function characterization

In this paper we develop a technique for characterizing parametric interaction in electron beam waves in terms of a system transfer function. We consider systems in which the parametric interaction is described by a matrix equation of the form (∂/∂t + uo∂/∂z)a = -iH a where a is a state vector of the system and H is the matrix characterizing the interaction. Solutions in the time domain can be expressed in the form a(z, t) = M(z, t) a(O, t - z/uo) where M (a matrix) is called the system function in the time domain. Solutions in the frequency domain can be expressed in the form â(z, ω) = ∫ M(z, ω - ω')â(O, ω')dω' where â(z, ω) is the Fourier transform of a(z, t) and M(z, ω) is the transform of M(z, t). Solutions for parametric interaction in transverse beam waves are worked out for two cases: In Case I we derive the well-known result that describes the behavior of a single pump wave, electron beam parametric amplifier. In Case II we consider a parametric interaction involving two pump waves in which an infinite number of frequencies are parametrically coupled.     

Aberrations in temporal imaging

Recent advances in temporal imaging allow construction of systems that can expand or compress arbitrary waveforms in time, while maintaining the shape of their envelope profile with subpicosecond resolution. The process is analogous to imaging in space, with the quadratic spectral phase introduced by narrow-band dispersion performing the time-domain role of paraxial diffraction and quadratic temporal phase modulation acting as a time lens. Higher order phase terms in the dispersive networks and the time lens modulation introduce aberrations into the system. The effect each aberration has on the final temporal image varies depending on the system configuration and where the source is located in the system. A theoretical and experimental study of aberration effects is presented     

Direct reconstruction of kinetic parameter images from dynamic PET data

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.