MR imaging with phase encoding of intermolecular multiple quantum coherences

Novel 2D and 3D pulse sequences producing images through the phase encoding of intermolecular multiple quantum coherences (i-MQCs) are presented. The signal acquired with these sequences is free from intermolecular zero quantum coherences (i-ZQCs) which are not phase encoded and additional phase cycling eliminates artifacts. Phase encoding during the n-quantum evolution period provides n times the resolution expected from equivalent phase encoding of the reconverted single quantum coherences. These sequences have potential applications for producing i-MQC images of biological tissues as well as nonbiological materials with substantial amounts of water.     

Unequally spaced four levels phase encoding in holographic data storage

Holographic data storage system is a candidate for the information recording due to its large storage capacity and high transfer rate. We propose an unequally spaced four levels phase encoding in the holographic data storage system here. Compared with two levels or three levels phase encoding, four levels phase encoding effectively improves the code rate. While more phase levels can further improve code rate, it also puts higher demand for the camera to differentiate the resulting smaller grayscale difference. Unequally spaced quaternary level phases eliminates the ambiguity of pixels with same phase difference relative to reference light compared to equally spaced quaternary levels. Corresponding encoding pattern design with phase pairs as the data element and decoding method were developed. Our encoding improves the code rate up to 0.875, which is 1.75 times of the conventional amplitude method with an error rate of 0.13 % according to our simulation results.     

Hadamard encoding with surface coils for high SNR MR spectroscopy.

The advantages of Hadamard over phase encoding in magnetic resonance spectroscopy (MRS) applied with surface coils in the direction perpendicular to the coil are demonstrated experimentally. With the recently introduced, time-shifted adiabatic pulses, the application of Hadamard encoding with surface coils results with almost ideal point spread function for pixels up to a distance of a radius from the coil. Comparison to phase encoding with equal region of interest size shows the significant advantage of Hadamard encoding in slice sharpness, overlapping, and spatial contamination. In addition, since there is no aliasing in Hadamard space, the total experimental time for the same region of interest is much shorter. We conclude that the hybrid of Hadamard encoding in the direction perpendicular to the coil and phase encoding in other directions is the method of choice to obtain reliable high signal to noise ratio MRS in vivo.     

In-plane flow velocity quantification along the phase encoding axis in MRI

In-plane flow quantification in MRI offers the potential for assessing vessel patency, and both volume flow rate and flow velocity. These techniques will have definite future impact on MR angiography. The method used in this paper employs motion artifact suppression technique (MAST) gradients to refocus spins travelling along any of the three imaging axes while encoding the velocity component along the phase encoding axis. This method has several advantages over in-plane flow quantification along the read axis. Primarily, flow voids due to complete spin dephasing can be eliminated (or reduced), wider velocity limits can be measured, and gradients can be designed which are sensitive to only velocity along the phase axis with no additional effect from higher order derivatives, or motion along the read axis. Flow phantom studies, carried out on 19 mm inside diameter glass tubes, have produced accurate results for flow rates ranging from 0.6 gallons per minute (GPM) to 2.5 GPM, corresponding to a mean velocity range from 13.2 cm/sec to 55.3 cm/sec. Reynolds numbers varied from 2,700 to 11,500. Errors were less than or equal to 8% over the range of flow rates studied.     

匹配滤波器映射编码方法研究

在Vander Lugt 相关器中,预先制作的匹配滤波器是系统能否得到较好的相关识别结果的关键。通常使用的迂回相位匹配滤波器编码法数据利用率不高,相关效果有进一步改进的空间。对基于最小欧几里德距离的映射编码法进行了研究,利用空间光调制器的振幅与相位调制特性进行滤波器编码,通过仿真实验分析了匹配滤波函数幅度因子对相关结果的影响,并与迂回相位编码法的相关结果进行了对比分析。从仿真结果可以看出:匹配滤波函数幅度因子越大,相关峰值越高;当幅度因子达到103时,相关峰值达到最大值;此时,映射编码法的相关峰值接近于迂回相位编码法的2倍。因此映射编码法比迂回相位编码法更有利于相关峰的判别。     

Analysis of phase encoding for optical encryption

A phase encoded image is encrypted using the double random phase encoding technique, (DRPE). The effects of using a variable dynamic range of phase distribution during phase encoding (pre-encryption) are examined. We begin by phase encoding the input image using the full phase range, from −π to π. We perform numerically perfect encryption and we then introduce errors into the decrypting phase-keys in the form of a pseudo-random distribution (position and phase) of incorrect pixels values. By quantifying the resulting error in the attempted decryptions, for increasing amounts of error in the decrypting phase-keys, we examine the effects of reducing the phase range to, +/− (π − Δ). In this way we attempt to improve the phase encoding procedure for use with the DRPE technique. When the pixel values calculated, during an attempted decryption, fall outside the phase range used to phase encode the assigned input image, we examine different methods of redistributing the value of that pixel to an assigned value within the allowed phase range. The effects of the phase quantisation used in the keys are also examined.     

波前相位编码体光栅选择性衍射的理论分析

阐述了波前相位复用技术记录和再现体全息光栅的原理;运用波耦合理论,从衍射波的一阶微分方程推导出多重体光栅对随机波前相位的选择性衍射;构造了一个复随机过程函数,并利用其相关函数得到了随机波前相位编码体光栅实现无串扰再现的充分必要条件;给出了理论上分析多重体光栅对随机波前相位选择性衍射的一种方法.     

用于光学图象加密的分数傅里叶变换双相位编码

作者提出了一种用于图象加密的基于分数傅里叶变换的双相位编码技术.该方法由于密钥比传统的编码技术增加两重,因而其安全性有所改进.     

MR angiography with pulsatile flow.

To achieve acceptable scan times, current multiple thin slice and 3D MR angiography (MRA) methods usually are based on continuous data acquisition, without ECG-synchronization. The purpose of this work is to study consequences of pulsatile blood flow for the 2D inflow method. Arterial blood flow and blood signal intensity versus cardiac phase were studied by a 2D phase based method with retrospective cardiac synchronization. Such studies were performed in different parts of the body and with different excitation flip angles. As expected, a clear relation between intensity enhancement and time dependent flow can be demonstrated. The raw data of these multiphase studies was used to simulate alternative inflow MRA data acquisition strategies to improve image quality, without the excessive increase in scan time implied by standard cardiac triggering. The alternatives investigated were data collection during part of the cardiac cycle and cardiac-ordered phase encoding. Simulation results indicate that the best results are obtained by a combination of both strategies. This method was implemented on Philips Gyroscan systems to compare it with standard nontriggered 2D inflow in practical MRA studies. For highly pulsatile flow, much better MR angiograms were obtained in this way.     

Estimating Spatial Resolution of In Vivo MR Images Using Spatial Modulation of Magnetization

Spatial Modulation of Magnetization is shown to provide a means of estimating perceived spatial resolution directly in vivo. On the first magnetic resonance system tested, resolution in conventional spin echo images was found to be stability limited in the phase encoding direction and voxel limited (via the Nyquist sampling theorem) in the frequency encoding direction both in vitro and in vivo. As the voxel size approaches half the stripe separation, fringes of resolved and unresolved stripes are formed across the image. This phenomenon is explained and described mathematically. On a second magnetic resonance scanner, resolution in the phase encoding direction of fast spin echo images with centrically ordered phase encoding is shown to be voxel limited in substances with long T₂, with poorer resolution in substances with short T₂. Resolution in fast spin echo images with linearly ordered phase encoding was shown to be voxel limited in the phase encoding direction.     

Free control of far-field scattering angle of transmission terahertz wave using multilayer split-ring resonators’ metasurfaces

To enhance transmission efficiency of Pancharatnam–Berry (PB) phase metasurfaces, multilayer splitring resonators were proposed to develop encoding sequences. As per the generalized Snell’s law, the deflection angle of the PB phase encoding metasurfaces depends on the metasurface period’s size. Therefore, it is impossible to design an infinitesimal metasurface unit; consequently, the continuous transmission scattering angle cannot be obtained. In digital signal processing, this study introduces the Fourier convolution principle on encoding metasurface sequences to freely control the transmitted scattering angles. Both addition and subtraction operations between two different encoding sequences were then performed to achieve the continuous variation of the scattering angle. Furthermore, we established that the Fourier convolution principle can be applied to the checkerboard coded metasurfaces.     

Double image encryption based on phase-amplitude hybrid encoding and iterative phase encoding in fractional Fourier transform domains

A new method for double image encryption is proposed that is based on amplitude-phase hybrid encoding and iterative random phase encoding in fractional Fourier transform (FrFT) domains. In the iterative random phase encoding operation, a binary random matrix is defined to encode two original images to a single complex-valued image, which is then converted into a stationary white noise image by the iterative phase encoding with FrFTs. Compared with the previous schemes that uses fully phase encoding, the proposed method reduces the difference between two original images in key space and sensitivity to the FrFT orders. The primitive images can be retrieved exactly by applying correct keys with initial conditions of chaotic system, the pixel scrambling operation and the FrFT orders. Computer simulations demonstrate that the encryption method has impressively high security level and certain robustness against data loss and noise interference.     

Beyond k-space: spectral localization using higher order gradients

Chemical shift imaging (CSI) often suffers from the inconvenient shape of its spatial response function (SRF), which affects both localization and signal-to-noise ratio. Replacing the magnetic field gradients for phase encoding by higher order magnetic fields allows a better adjustment of the SRF to the structures in the sample. We combined this principle with the SLOOP (spectral localization with optimal pointspread function) technique to simultaneously obtain spectra from several arbitrarily shaped compartments within a sample. Linear combinations of the fields of the shim coils are used to generate the pulsed fields for phase encoding. Their shapes are matched to the given sample geometry by numerical optimization. Using this method, spectra from a phantom were obtained that show a higher signal-to-noise ratio and a strongly reduced contamination compared to an equivalent CSI experiment.     

Optimization of spoiler gradients in flash MRI

The FLASH technique for fast magnetic resonance (MR) imaging often employs strong magnetic field gradients, called spoiler gradients, to dephase the transverse magnetization after it has been measured. Otherwise, image artifacts can develop. The effectiveness of spoiler gradients at suppressing these artifacts was evaluated experimentally on two-dimensional MR images of a uniform phantom and patients. It was informative to compare the magnetization immediately before the RF excitation in each phase encoding step. Only spoiler gradients in the slice selection direction were effective. Spoiler gradients that decreased steadily from a large amplitude in the first phase encoding step to zero in the last minimized the transverse magnetization and suppressed the image artifact, without changing the image contrast.     

Image encryption algorithm based on the random local phase encoding in gyrator transform domains

A random local phase encoding method is presented for encrypting a secret image. Some random polygons are introduced to control the local regions of random phase encoding. The data located in the random polygon is encoded by random phase encoding. The random phase data is the main key in this encryption method. The different random phases calculated by using a monotonous function are employed. The random data defining random polygon serves as an additional key for enhancing the security of the image encryption scheme. Numerical simulations are given for demonstrating the performance of the proposed encryption approach.     

Fast imaging with the MMME sequence

The multiple-modulation-multiple-echo sequence, previously used for rapid measurement of diffusion, is extended to a method for single shot imaging. Removing the gradient switching requirement during the application of RF pulses by a constant frequency encoding gradient can shorten experiment time for ultrafast imaging. However, having the gradient on during the pulses gives rise to echo shape variations from off-resonance effects, which make the image reconstruction difficult. In this paper, we propose a simple method to deconvolve the echo shape variation from the true one-dimensional image. This method is extended to two-dimensional imaging by adding phase encoding gradients between echoes during the acquisition period to phase encode each echo separately. Slice selection is achieved by a frequency selective pulse at the beginning of the sequence. Imaging speed is mainly limited by the phase encoding gradients' switching times and echo overlap when echo spacing is very short. This technique can produce a single-shot image of sub-millimeter resolution in 5 ms.     

Image encryption by using local random phase encoding in fractional Fourier transform domains

Based on fractional Fourier transform, an image encryption algorithm is proposed and researched. A local random phase encoding is introduced into this algorithm. The data at the local area of complex function is converted by fractional Fourier transform. The local random phase encoding is performed many times. Moreover only one set of random phase data is used in image encryption process. Compare to double random phase encoding, the parameter defining local area can be regarded as the additional key to increase the security of the encryption scheme. Some numerical simulations are achieved to demonstrate the performance of the image encryption scheme.     

相位编码光学加密算法的扩散及混淆特性分析

为了阐明相位编码光学加密算法的扩散及混淆特性,基于傅里叶变换位移定理,从分组密码设计准则出发,以双随机相位光学加密算法为研究对象,分析了采用单个随机相位模板的2 f系统的扩散和混淆特性。将单随机相位加密过程分解为2个相互关联的过程,结果表明,傅里叶变换在加密算法中引入了混淆操作,而傅里叶变换结合随机相位模板实现了扩散操作。通过数值模拟对上述理论分析进行了验证,引入信息熵来评价加密图像的统计分布特性,进一步分析了菲涅尔域及分数阶傅里叶变换域随机相位加密算法的扩散混淆特性。研究表明,单随机相位加密和双随机相位加密图像的信息熵分布为7.038和7.157,而随机振幅加密图像信息熵为4.521。因而,随机相位加密算法比随机振幅加密算法能实现对信息更好地扩散。     

Two-dimensional shift-orthogonal random-interleaving phase-code multiplexing for holographic data storage

A novel phase encoding technology for phase-code multiplexing in holographic data storage (HDS) system called two-dimensional shift-orthogonal random-interleaving (2-D SORI) phase encoding is proposed. Compared with the traditional one-dimensional orthogonal phase-code multiplexing methods, the 2-D method is less sensitive to the variations of the diffraction amplitude and to the phase error of the phase mask. Phase masks for the 2-D SORI phase-code multiplexing can be generated by shifting an elaborately designed phase plate at a certain step, which can avoid the use of a high-cost phase spatial light modulator for the generation of multiple orthogonal phase masks. The cross-talk arising from the systematic phase defects of the static phase modulator is eliminated by the shift operation of the phase plate. Phase codes are interleaved under a predetermined random mapping rule to prevent unauthorized users from accessing the data and eliminate the Bragg degeneration cross-talk. A 2-D SORI phase plate with the size of 5.12 mm × 10.24 mm is designed and fabricated, from which 128 orthogonal phase patterns are generated. The feasibility of the 2-D SORI phase-code multiplexing method for HDS is experimentally demonstrated.     

Single-point imaging with a variable phase encoding interval

A modified single-point imaging (SPI) technique using a variable phase encoding interval is proposed. This method is based on the minimization of the phase encoding interval for further signal-to-noise ratio (SNR) optimization. This is particularly beneficial when the maximum gradient amplitude limits an optimal phase encoding interval, and the resulting SNR suffers from T(2)-related signal attenuation. Theoretical calculation of the SNR and simulation of the point spread function (PSF) for the different experimental parameters are presented. Experiments using a rubber sample (T(2)* approximately 73 micros) and a tooth (bi-exponential relaxation: T(2,1)*=111 micros and T(2,1)*=872 micros) showed a significant increase in SNR (>3 and >2, respectively) when compared with images acquired with conventional SPI.