Reflectivity function reconstruction using the frequency deconvolution technique

Deconvolution of ultrasonic echo signals improves resolution and quality of ultrasonic images. A frequency deconvolution algorithm depends on the Fast Fourier transform is proposed for ultrasonic data. The stability of the algorithm and the influence of the truncation effect on the deconvoluted results were investigated with respect to the duration time of reflectivity function reconstruction and the signal to noise ratio. Reliability of the separation of reconstructing the reflectivity of a biological tissue is estimated by frequency deconvolution of the echo ultrasound signals.     

Evaluation of deconvolution modelling applied to numerical combustion

A possible modelling approach in the large eddy simulation (LES) of reactive flows is to deconvolve resolved scalars. Indeed, by inverting the LES filter, scalars such as mass fractions are reconstructed. This information can be used to close budget terms of filtered species balance equations, such as the filtered reaction rate. Being ill-posed in the mathematical sense, the problem is very sensitive to any numerical perturbation. The objective of the present study is to assess the ability of this kind of methodology to capture the chemical structure of premixed flames. For that purpose, three deconvolution methods are tested on a one-dimensional filtered laminar premixed flame configuration: the approximate deconvolution method based on Van Cittert iterative deconvolution, a Taylor decomposition-based method, and the regularised deconvolution method based on the minimisation of a quadratic criterion. These methods are then extended to the reconstruction of subgrid scale profiles. Two methodologies are proposed: the first one relies on subgrid scale interpolation of deconvolved profiles and the second uses parametric functions to describe small scales. Conducted tests analyse the ability of the method to capture the chemical filtered flame structure and front propagation speed. Results show that the deconvolution model should include information about small scales in order to regularise the filter inversion. a priori and a posteriori tests showed that the filtered flame propagation speed and structure cannot be captured if the filter size is too large.     

Rapid MR imaging by sensitivity profile indexing and deconvolution reconstruction (SPID)

A new parallel MR imaging technique, which uses localized information from the elements of a multi-coil array to accelerate imaging, is described. The technique offers an alternative reconstruction approach to currently available techniques (e.g., SMASH and SENSE). Following a partial k-space data acquisition, image reconstruction in this approach proceeds in two steps: first, fitting the measured coil sensitivities to a set of partially localized target functions, a blurred intermediate image of the studied object is produced. Blurring is obtained in a systematic manner, forming images of the studied object convolved with a known convolution kernel. Full spatial resolution is then recovered by deconvolution of the blurred images with the known kernel function. The technique offers flexibility in the arrangement of the acquired signal data k-lines, and a mechanism for controlling reconstruction quality through the convolution the deconvolution procedure. The technique was validated in phantom and in vivo imaging experiments demonstrating high time reduction factors.     

基于目标和点扩展函数联合估计的点源目标图像近视解卷积

在传统的基于波前探测的解卷积方法中,由波前探测得到的点扩展函数被认为是精确的,并用维纳滤波进行复原,但是点扩展函数不可避免地存在误差,所以最终的复原目标图像质量不佳.为了解决该难题,提出了基于目标和点扩展函数联合估计的图像近视解卷积算法.它运用了点扩展函数和目标的先验信息,对点扩展函数和目标进行了规整和进一步约束,从而得到更优的恢复图像质量.对该方法的原理和实现过程进行了阐述,并将其运用于室内点源目标数据中.实验结果证明,与维纳滤波方法相比,该方法使图像恢复的效果得到明显改善.     

Self-deconvolution for shift-and-add imaging

A shift-and-add (SAA) method is used to restore atmospherically degraded images. The operation of the SAA method is simple, but the deconvolution method of SAA images remains to be developed, especially for extended objects. We propose to deconvolve a SAA image of an extended object by use of a self-deconvolving data reconstruction algorithm (SeDDaRA). Computer simulations show the effectiveness of the SeDDaRA to SAA images. It is also shown that use of the SAA method after each data frame is self-deconvolved leads to a better reconstruction.     

Force reconstruction: analysis and regularization of a deconvolution problem

The reconstruction of force is considered by means of indirect measurements. This necessitates taking measurements from the impacted structure and then to deconvolve those signals from the impulse response function. More precisely, the purpose of the work described here is to analyze a deconvolution technique and to solve the problems which occur. Thus, it is highlighted that the associated deconvolution problem depends on the location of the measurement points: is it possible or not to reconstruct the impact force versus the location of this point. Numerical predictions are compared and validated with experiment. But, the deconvolution is a well-known ill-posed problem: the results are often unstable. This is why it is necessary to regularize the problem, which consists of adding a condition to the solution which does not appear in the initial problem. Some regularization methods are presented. Nevertheless, they necessitate the determination of a parameter; the difficulty is to calculate an appropriate value of this regularization parameter. The methods are successfully used to recover an experimental force.     

Image reconstruction by scanning a crystal with an electron-beam-produced grating of atomic lens focuses

When atomic rows in a crystal layer are used to focus a beam from an electron microscope, the intensity distribution behind the crystal represents a grating of narrow peaks with diameters from 0.03 to 0.04 nm in the first Fourier plane. A scheme of scanning transmission electron microscopy (STEM) with such a grating is simulated that makes it possible to reconstruct the transmission function of an object from the signal recorded. The reconstruction quality depends on the type and amount of distortions. Distortions due to the following two factors are simulated: random noise imposed on the signal detected in the experiment and the lack of information about the wave incident on the object because of uncertainty involved in the width of the electron beam striking the focusing crystal. The range of distortions within which the object can be reconstructed with a tolerable quality is determined.     

Reconstruction of ultrasonic fields by deconvolving the hydrophone aperture effects. I. Theory and simulation

In many ultrasound applications-especially in the area of medical diagnostics-conventional sensors and particularly piezoelectric hydrophones do not comply with the requirements for "point detectors". It therefore suggests itself to develop methods, which allow ultrasonic fields to be reconstructed from the spatially averaged measurement values with the necessary spatial resolution. In this publication, this task will be treated as an inverse problem. It will be shown by simulations that it is possible with the aid of reconstruction methods to invert the aperture effects of the sensor. Three different reconstruction methods are tested: (1) Wiener's method furnishes the best approximation of the field to be reconstructed in the sense of the minimum mean square error. (2) The power spectral equalization method is based on equalization between the spatial power spectral densities of the field to be reconstructed and that of its estimated value. (3) With the maximum a-posteriori method, the maximum a-posteriori probability density function for the reconstructed field is searched. The results of this paper show that the quality of reconstruction depends on the signal-to-noise ratio (SNR) and the spatial frequency bandwidth of the sound field investigated. Good quality reconstructions were obtained at correlation coefficients larger than 0.995 and an SNR of at least 40 dB. In general, the quality of reconstruction decreases with decreasing SNR and is unacceptable at SNR = 20 dB. The quality also decreases with decreasing axial distance from the source that is with increasing spectral frequency bandwidth.     

Parallel-quadrature phase-shifting digital holographic microscopy using polarization beam splitter

We present a digital holography microscopy technique based on a parallel-quadrature phase-shifting method. Two π/2 phase-shifted holograms are recorded simultaneously using polarization phase-shifting principle, slightly off-axis recording geometry, and two identical CCD sensors. The parallel phase-shifting is realized by combining circularly polarized object beam with a 45° degree polarized reference beam through a polarizing beam splitter. DC term is eliminated by subtracting the two holograms from each other and the object information is reconstructed after selecting the frequency spectrum of the real image. Both amplitude and phase object reconstruction results are presented. Simultaneous recording eliminates phase errors caused by mechanical vibrations and air turbulences. The slightly off-axis recording geometry with phase-shifting allows a much larger dimension of the spatial filter for reconstruction of the object information. This leads to better reconstruction capability than traditional off-axis holography.     

Signal-to-noise ratio and frequency analysis of continuous loop averaging deconvolution (CLAD) of overlapping evoked potentials

In this study, a frequency domain formulation of continuous loop averaging deconvolution (CLAD) of overlapping evoked potentials is developed and applied for the extraction of transient responses from recordings obtained at high stimulation rates. This formulation allows for a faster execution of CLAD by using fast Fourier transform algorithms. The frequency characteristics of the deconvolution filter depends exclusively on the stimulus sequence and determines whether the noncoherent noise is amplified or attenuated in different frequencies. A formula for calculating the signal-to-noise ratio (SNR) achieved by the deconvolution process is developed. The newly developed theory and the methodology is applied to the extraction of the auditory brainstem and middle latency responses using various sequences. The effects of the sequence used and the number of sweeps averaged in ongoing acquisition on SNR are examined by using single sweep recordings. The results verify the deconvolution theory and the methodology and show its limitations. Depending on the frequency characteristics of the sequence, the deconvolution process can amplify or attenuate the EEG noise. Proper selection of the stimulus sequence can increase the SNR enhancement obtained with conventional averaging.     

光学扫描全息术研究进展

光学成像技术极大地拓展了人类的视觉极限,提高了人们观察和理解现实世界的能力。越多地获得目标的光学信息,对其的认识越充分。数字全息术是一种可以将样本的三维信息以二维全息图的形式编码记录下来的一种成像技术。通过获得由携带物体信息的物光波和参考光波叠加产生的干涉图案,可以以数字化的方式实现多种重建模态,例如图像恢复、相位成像和切片成像等。光学扫描全息术是一种独特的数字全息成像技术,通过主动式二维化扫描对三维物体进行成像,其完整的波前信息可以被单像素探测器记录,并基于光外差检测进行信号解调,从而恢复出复数全息图。对光学扫描全息术的最新进展进行介绍。首先,基于双光瞳成像系统,通过特殊的硬件和算法设计,提高光学成像系统的性能,如提高空间分辨率、缩短扫描时间。其次,基于计算成像原理,通过改进和优化全息像重建算法,实现高质量的图像恢复,主要涉及切片成像和三维成像等重建模态。第三,介绍光学扫描全息术的其他研究方向,并讨论该领域未来可能的发展方向。     

Phase retrieval using an aperture-array filter under partially coherent illumination

Recently we have proposed a deterministic phase retrieval method using an aperture-array filter to reconstruct a complex-valued object from a single diffraction intensity pattern. We describe here the effect of quasi-monochromatic partially coherent illumination on the object reconstruction by the phase retrieval method, and then present the method of eliminating the effect of the partially coherent illumination from the diffraction intensity pattern via a simple Fourier deconvolution operation provided that the complex degree of spatial coherence of the illuminating beam is known. The usefulness of this method is shown in computer-simulated examples of the object reconstructions under Gaussian Schell-model partially coherent illumination.     

时域反卷积算法用于提高超声反射CT成像分辨率

超声反射CT成像通常采用反射回波的包络作为投影,按一定算法进行重建,以实现对物体内某一截面的成像。由于超声换能器的发射脉冲具有一定宽度,这样,被检测物体内相距较近的缺陷回波信号将产生混叠,使得重建像中难以区分各相距较近的缺陷。针对这一问题,本文应用时域反卷积（TDD）算法对缺陷回波信号进行预处理,再进行图像重建,理论和实验结果表明,成像分辨率得到提高,图像质量明显改善。     

Phase diversity imaging through atmospheric turbulence

A method of phase diversity imaging is applied to reconstruct an overly extended object from stellar speckle images. The reconstruction algorithm is based on the iterative blind deconvolution method and the Gerchberg-Saxon phase retrieval procedure. Computer simulations for reconstructing solar granulations are conducted. The simulation results exhibit the effectiveness of the phase diversity method for high-resolution solar imaging.     

Holographic method of deconvolution and analytic continuation

In this paper a method of analytic continuation for gaining spatial frequency components of an object filtered by an optical system, based on the Taylor series and the series of orthogonal polynomials, is proposed in connection with the holographic method of deconvolution. An analysis of the efficiency of this method is carried out in terms of information theory and improving terms are explicitly calculated. Some simple realizations of the present theory are also proposed. Higher frequency components of the object reconstructed with the help of this method will permit to observe greater details of the restored object.This work was partly done during a stay of the author at the University of Florence.The author thanks Profs G. W. Stroke, G. Toraldo di Francia and B. Havelka for interesting discussions and fruitful comments. A financial support of Ministero degli Affari Esteri in Rome during the stay of the author at the University of Florence is acknowledged, too.     

Two-dimensional imaging by the continuous-wave EPR

To be able to perform a two-dimensional study of free radical distribution by the continuous-wave electron paramagnetic resonance method in the X-band, special coils producing a magnetic gradient of 8 G/mm have been designed and constructed. The EPR spectra recorded for this gradient were subjected to the procedure of deconvolution in order to elicit information on the concentration of the radical distribution. The data obtained were used as the source file of the program reconstructing the image. The reconstruction was based on the iterative simultaneous algebraic reconstruction technique (Andersen A.H., Kak A.C.: Ultrason. Imag. 6, 81–94, 1984). The quality of the generated images depends on the angle of the sample axis to the gradient direction set by a goniometer and on the deconvolution procedures applied. The first tests on artificially generated phantoms indicated a dependence of the obtained images on the magnetic field gradients applied. The determined spatial distribution of radicals has confirmed their uniform distribution in the sample. The preliminary tests were performed for diphenyl-picrylhydrazyl. Having proved the reliability of the method, analogous measurements were also performed for plyphenylene sulphide PPS-V1 and indicated a homogeneous distribution of radicals in the whole volume of the sample. The images obtained confirmed the uniform distribution of the radicals.     

LEED and AES studies of the initial growth of Ge epilayers on GaAs(100)

The initial stages of growth of epitaxial Ge overlayers on the GaAs(100) surface have been studied by LEED and AES on overlayers from 0.1 monolayers (ML) to 10 ML in thickness. It is found that a coverage of about 0.2 ML converts the initial clean surface reconstruction into a single domain (1 × 2) reconstruction with a surface atomic geometry very similar to that of clean Ge. Further growth does not significantly change the arrangement of atoms at the surface. Growth from 1 to 4 ML proceeds by a double layer growth mechanism which maintains the single (1 × 2) domain. Auger measurements indicate that the growing surface has a $\text{1}\text{2}$ ML As enrichment, and that the interface is not abrupt, but has a mixed GeGa or GeAs transition layer.     

环状干涉条纹成像技术的实验研究

 从傅里叶分析的角度来讨论环状干涉条纹成像的处理过程，并报道二维连续散射目标的成像实验。激光干涉条纹成像是利用激光源在空域形成的干涉条纹同目标间的相对运动来提取目标的图像信息。对利用环状干涉条纹的激光干涉成像，其机理常用全息理论来解释。     

Improvement of the optical image reconstruction based on multiplexed quantum ghost images

Ghost imaging allows one to obtain information on an object from the spatial correlation function between photons propagating through or reflected from the object and photons of the reference arm. In this case, detection in the object arm is performed over the entire aperture of the beam and, therefore, it does not give information on the object. The reference beam does not interact with the object, but is recorded with a scanning point detector or a CCD array permitting the measurement of the spatial correlation function of photons in two arms. The use of multimode entangled quantum light beams by illuminating the object by one beam and orienting other beams to reference arms makes it possible to obtain simultaneously several ghost images (GIs). Cross correlations of multiplexed GIs (MGIs) are determined by eighth-order field correlation functions. A special algorithm is developed for calculating higher-order correlations of Bose operators. The presence of GI cross correlations is used for improving the quality of the reconstructed object’s image by their processing using the measurement reduction method. An example of the computer simulation of the image reconstruction by MGIs formed in the field of four-frequency entangled quantum states is considered. It is found that in this case the reduced GI has a signal-to-noise ratio several times higher than that of GIs.     

Application of acoustic reflection tomography to sonar imaging

Computer-aided tomography is a technique for providing a two-dimensional cross-sectional view of a three-dimensional object through the digital processing of many one-dimensional views (or projections) taken at different look directions. In acoustic reflection tomography, insonifying the object and then recording the backscattered signal provides the projection information for a given look direction (or aspect angle). Processing the projection information for all possible aspect angles enables an image to be reconstructed that represents the two-dimensional spatial distribution of the object's acoustic reflectivity function when projected on the imaging plane. The shape of an idealized object, which is an elliptical cylinder, is reconstructed by applying standard backprojection, Radon transform inversion (using both convolution and filtered backprojections), and direct Fourier inversion to simulated projection data. The relative merits of the various reconstruction algorithms are assessed and the resulting shape estimates compared. For bandpass sonar data, however, the wave number components of the acoustic reflectivity function that are outside the passband are absent. This leads to the consideration of image reconstruction for bandpass data. Tomographic image reconstruction is applied to real data collected with an ultra-wideband sonar transducer to form high-resolution acoustic images of various underwater objects when the sonar and object are widely separated.