Spatial Encoding Technique Research Articles

A method for longitudinal relaxation time measurement in inhomogeneous fields

The spin-lattice relaxation time (T1) plays a crucial role in the study of spin dynamics, signal optimization and data quantification. However, the measurement of chemical shift-specific T1 constants is hampered by the magnetic field inhomogeneity due to poorly shimmed external magnetic fields or intrinsic magnetic susceptibility heterogeneity in samples. In this study, we present a new protocol to determine chemical shift-specific T1 constants in inhomogeneous fields. Based on intermolecular double-quantum coherences, the new method can resolve overlapped peaks in inhomogeneous fields. The measurement results are in consistent with the measurements in homogeneous fields using the conventional method. Since spatial encoding technique is involved, the experimental time for the new method is very close to that for the conventional method. With the aid of T1 knowledge, some concealed information can be exploited by T1 weighting experiments.

An objective method to identify optimum clip-limit and histogram specification of contrast limited adaptive histogram equalization for MR images

In contrast limited adaptive histogram equalization (CLAHE), the selection of tile size, clip-limit and the distribution which specify desired shape of the histogram of image tiles is paramount, as it critically influences the quality of the enhanced image. The optimal value of these parameters devolves on the generic of the image to be enhanced and usually they are selected empirically. In this paper, the degradation of intensity, textural and geometric features of the medical image with respect to the variation in clip-limit and specified histogram shape is analyzed. The statistical indices used to quantify the feature degradation are Absolute Mean Brightness Error (AMBE), Absolute Deviation in Entropy (ADE), Peak Signal to Noise Ratio (PSNR), Variance Ratio (VR), Structural Similarity Index Matrix (SSIM) and Saturation Evaluation Index (SEI). The images used for the analysis are axial plane MR images of magnetic resonance spectroscopy (MRS), under gradient recalled echo (GRE), diffusion weighted imaging (DWI) 1000b Array Spatial Sensitivity Encoding Technique (ASSET), T2 Fluid Attenuation Inversion Recovery (FLAIR) and T1 Fast Spin-Echo Contrast Enhanced (FS-ECE) series of pre-operative Glioblastoma-edema complex. The experimental analysis was performed using Matlab®. Results show that for MR images the exponential histogram specification with a clip-limit of 0.01 is found to be optimum. At optimum clip-limit, the mean of SSIM exhibited by the Rayleigh, uniform and exponential histogram specification were found to be 0.7477, 0.7946 and 0.8457, for ten sets of MR images and mean of variance ratio are 1.242, 2.0316 and 1.7711, respectively.

Two-Dimensional J-Resolved NMR Analyses of Fish and Its Products via Spatially Encoded Intermolecular Double-Quantum Coherences

Nuclear magnetic resonance (NMR) spectroscopy provides a powerful tool for food analyses due to its high-throughput information related to component analyses and its non-invasive property without altering detected samples. Current liquid NMR approaches, however, are subject to the influence of field inhomogeneity in direct measurements of biological foods, generally resorting to techniques of tissue extractions or magic-angle spin to eliminate the inhomogeneity. Therefore, we propose an NMR approach based on intermolecular double-quantum coherences (iDQCs) and spatial encoding technique to fast recover high-resolution two-dimensional (2D) J-resolved spectra in inhomogeneous fields. Inheriting from the immunity to field inhomogeneity of iDQCs and the enhancement in acquisition efficiency of the spatial encoding technique, the proposed method can resist the field inhomogeneity in biological foods without superfluous pretreatments and time-consuming shimming procedures, and yield satisfactory 2D J-resolved information for analyses within minutes. Fish and its products, which are closely related to human daily life, capture extensive attentions with the rapid development of the aquaculture. At first, experiments on cod liver oils are implemented in a purposely deshimmed magnetic field to demonstrate the feasibility of the proposed approach. Then, caviars and an intact fish are tested to further show the applicability of the proposed approach for direct measurements on intact biological food samples. Herein, the proposed method may constitute an effective technique in analyzing fish and its products.

Feasibility of Ultrafast Intermolecular Single-Quantum Coherence Spectroscopy in Analysis of Viscous-Liquid Foods

A newly developed nuclear magnetic resonance (NMR) technique, ultrafast intermolecular single-quantum coherence (UF iSQC) spectroscopy, demonstrated its potentials to obtain spectra of viscous-liquid samples in deuterium-free environment. UF iSQC not only inherits the advantage of ultrafast acquisition efficiency of spatial encoding but also keeps the intrinsic merit of immunity of iSQC in inhomogeneous magnetic field. In the present study, UF iSQC spectroscopy is used for the direct analysis of three typical viscous-liquid foods, namely, honey, yogurt, and tomato sauce, and its feasibility is verified by ultrafast acquisition of NMR spectra of these viscous-liquid foods. UF iSQC spectroscopy presents an advantageous alternative to directly detect most components of these samples in favorable spectral information within 1 min, thus saving the trouble of complicated sample pretreatments and tedious shimming processes. Due to the immunity to field inhomogeneity, the UF iSQC technique can be a proper supplement to dilution, extraction NMR, and magic angle spinning. In addition, in comparison with the conventional iSQC method, the acquisition time of the proposed method is greatly reduced due to the introduction of the spatial encoding technique. The lower sensitivity and resolution of UF iSOC spectra than those of dilutions acquired by the conventional NMR method could be improved by some newly developed strategies. Results obtained here demonstrate the potential application of the UF iSQC spectroscopy in the quality control of food.

Improving spectral resolution in spatial encoding dimension of single-scan nuclear magnetic resonance 2D spin echo correlated spectroscopy

The spatial encoding technique can be used to accelerate the acquisition of multi-dimensional nuclear magnetic resonance spectra. However, with this technique, we have to make trade-offs between the spectral width and the resolution in the spatial encoding dimension (F1 dimension), resulting in the difficulty of covering large spectral widths while preserving acceptable resolutions for spatial encoding spectra. In this study, a selective shifting method is proposed to overcome the aforementioned drawback. This method is capable of narrowing spectral widths and improving spectral resolutions in spatial encoding dimensions by selectively shifting certain peaks in spectra of the ultrafast version of spin echo correlated spectroscopy (UFSECSY). This method can also serve as a powerful tool to obtain high-resolution correlated spectra in inhomogeneous magnetic fields for its resistance to any inhomogeneity in the F1 dimension inherited from UFSECSY. Theoretical derivations and experiments have been carried out to demonstrate performances of the proposed method. Results show that the spectral width in spatial encoding dimension can be reduced by shortening distances between cross peaks and axial peaks with the proposed method and the expected resolution improvement can be achieved. Finally, the shifting-absent spectrum can be recovered readily by post-processing.

Spatial phase encoding exploiting the Bloch–Siegert shift effect

The present work introduces an alternative to the conventional B0-gradient spatial phase encoding technique. By applying far off-resonant radiofrequency (RF) pulses, a spatially dependent phase shift is introduced to the on-resonant transverse magnetization. This so-called Bloch-Siegert (BS) phase shift has been recently used for B1(+)-mapping. The current work presents the theoretical background for the BS spatial encoding technique (BS-SET) using RF-gradients. Since the BS-gradient leads to nonlinear encoding, an adapted reconstruction method was developed to obtain undistorted images. To replace conventional phase encoding gradients, BS-SET was implemented in a two-dimensional (2D) spin echo sequence on a 0.5 T portable MR scanner. A 2D spin echo (SE) measurement imaged along a single dimension using the BS-SET was compared to a conventional SE 2D measurement. The proposed reconstruction method yielded undistorted images. BS-gradients were demonstrated as a feasible option for spatial phase encoding. Furthermore, undistorted BS-SET images could be obtained using the proposed reconstruction method.

Ultrafast acquisition of localized two-dimensional magnetic resonance correlated spectra of inhomogeneous biological tissues with resolution improvements

Long acquisition time and strict requests of homogeneous magnetic fields restrain wide applications of localized 2D magnetic resonance spectroscopy. Here, a pulse sequence utilizing the spatial encoding technique and spin echo is proposed to obtain localized 2D correlated spectra with resolution improvements under inhomogeneous fields within greatly reduced times. The localized correlated spectrum of pig marrow obtained with the proposed scheme retained more information compared to the conventional spectrum. The method proposed herein offers important perspectives for fast in vivo analyses of metabolites in living inhomogeneous organisms and in situ characterization of intermediates of inhomogeneous chemical reaction systems.

Multichannel Spatial Encoding and Extraction for Low-Noise Laser Applications

A multichannel spatial encoding and extraction technique is demonstrated for laser-based experimental applications. The technique makes use of a multichannel beam chopper to encode spatial information onto the transverse profile of a laser beam. Lock-in detection is subsequently employed in a parallel processing algorithm to extract the encoded experimental spatial information. The technique is demonstrated with an optical system incorporating ten parallel frequency channels.

Parallel imaging enhanced MR colonography using a phantom model

To compare various Array Spatial and Sensitivity Encoding Technique (ASSET)-enhanced T2W SSFSE (single shot fast spin echo) and T1-weighted (T1W) 3D SPGR (spoiled gradient recalled echo) sequences for polyp detection and image quality at MR colonography (MRC) in a phantom model. Limitations of MRC using standard 3D SPGR T1W imaging include the long breath-hold required to cover the entire colon within one acquisition and the relatively low spatial resolution due to the long acquisition time. Parallel imaging using ASSET-enhanced T2W SSFSE and 3D T1W SPGR imaging results in much shorter imaging times, which allows for increased spatial resolution. Using two porcine colon phantoms each with eight simulated 3-10-mm "polyps," baseline reference sequences acquired without ASSET (6-mm slices and readout bandwidth [BW] 62 kHz) were compared with 11 SSFSE and 8 SPGR sequences acquired with 2-fold ASSET acceleration. ASSET-enhanced SSFSE and SPGR sequences comprised BW/matrix combinations ranging from 20-62 kHz/256-352x256, respectively, with slice thicknesses adjusted from 3.0 to 4.5 mm to maintain a 23-26-second acquisition time and 30 cm slab thickness. Two experienced radiologists viewed the datasets in a randomized, blinded fashion. Compared to reference sequences, ASSET-enhanced SSFSE and SPGR sequences facilitated better polyp detection and had similar overall image quality and per-phantom specificity. The two best ASSET-enhanced SSFSE (3 and 4.5 mm slices, each with BW of 62.5 kHz and 352x256 matrices) and three best ASSET-enhanced SPGR BW/slice thickness/matrix combinations of 31 kHz/4.4 msec/192x256; 62/3.4/192x256; and 62/4.0/192x256, respectively, permitted detection of all polyps>or=5 mm. Parallel imaging using ASSET-enhanced T2W SSFSE and T1W 3D SPGR improves the ability to detect significant colon polyps in an MRC phantom model.

Fast magnetic resonance force microscopy with Hadamard encoding

We present a spatial encoding technique for magnetic resonance force microscopy that allows for a much enhanced image acquisition rate. The technique uses multiplexing, based on spatial Hadamard encoding, to acquire several slices of the image simultaneously and at an undiminished signal-to-noise ratio. We demonstrate an improvement in imaging time by a factor of 7.6, and further advances can be expected.

Signed-negabinary-arithmetic-based optical computing by use of a single liquid-crystal-display panel.

Based on the negabinary number representation, parallel one-step arithmetic operations (that is, addition and subtraction), logical operations, and matrix-vector multiplication on data have been optically implemented, by use of a two-dimensional spatial-encoding technique. For addition and subtraction, one of the operands in decimal form is converted into the unsigned negabinary form, whereas the other decimal number is represented in the signed negabinary form. The result of operation is obtained in the mixed negabinary form and is converted back into decimal. Matrix-vector multiplication for unsigned negabinary numbers is achieved through the convolution technique. Both of the operands for logical operation are converted to their signed negabinary forms. All operations are implemented by use of a unique optical architecture. The use of a single liquid-crystal-display panel to spatially encode the input data, operational kernels, and decoding masks have simplified the architecture as well as reduced the cost and complexity.

Classified one-step high-radix signed-digit arithmetic units

High-radix number systems enable higher information storage density, less complexity, fewer system components, and fewer cascaded gates and operations. A simple one-step fully parallel high-radix signed-digit arithmetic is proposed for parallel optical computing based on new joint spatial encodings. This reduces hardware requirements and improves throughput by reducing the space-bandwidth product needed. The high-radix signed-digit arithmetic operations are based on classifying the neighboring input digit pairs into various groups to reduce the computation rules. A new joint spatial encoding technique is developed to present both the operands and the computation rules. This technique increases the spatial bandwidth product (SBWP) of the spatial light modulators (SLMs) of the system. An optical implementation of the proposed high-radix signed-digit arithmetic operations is also presented. It is shown that our one-step trinary signed-digit (TSD) and quarternary signed-digit (QSD) arithmetic units are much simpler and better than all previously reported high-radix signed-digit techniques.

Optical implementation of programmable logic neural networks

Optical implementation of a purely digital type neural net of programmable logic neural networks, which is based on optical spatial encoding and decoding technique, is proposed. The optical system is simple and easy to be built. The simulated experimental results are also given.

Classified one‐step modified signed‐digit arithmetic and its optical implementation

Based on the two-step modified signed-digit (MSD) algorithm, we present a one-step algorithm for the parallel addition and subtraction of two MSD numbers. This algorithm is reached by classifying the three neighboring digit pairs into 10 groups and then making a decision on the groups. It has only a look-up truth table, and can be further formulated by eight computation rules. A joint spatial encoding technique is developed to represent both the input data and the computation rules. Furthermore, an optical correlation architecture is suggested to implement the MSD adder in parallel. An experimental demonstration is also given. (C) 1996 Society of Photo-Optical instrumentation Engineers.

Non-Commutative Affine Geometry and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets

Abstract. Magnetic Resonance Imaging (MRI) is one of the most significant advances in medical imaging in this century. The multiplanar capability and high-resolution imaging are unmatched by any other current clinical imaging technique. The physical and mathematical principles on which this non-invasive imaging technology is based are as complex as the computer-controlled synergy of the MRI scanner organization. The MRI scanner is a quantum electrodynamical (QED) device, the components of which implement and detect the wavelet interference and resonance phenomena which underly the symplectic MRI filter-bank processing. Notice the fact that QED has approved the semi-classical approach to quantum holography. In this paper, a semi-classical QED treatment of the basic MRI system organization is presented, with deep roots in the Keppler phase triangulation procedure of physical astronomy and in the symplectically invariant symbol calculus of pseudodifferential operators. It is based on non-commutative geometry of affine transvections and non-commutative Fourier analysis. This allows for modeling the interference patterns of phase coherent wavelets by distributional harmonic analysis on the Heisenberg nilpotent Lie group G of quantum mechanics. Geometric quantization yields the tomographic slices by the planar coadjoint orbit stratification O v,v ≠ 0, of the unitary dual Ĝ of the Heisenberg group G. The resonance of affine wavelets is treated by harmonic analysis on the affine solvable Lie group GA(ℝ), which is intrinsically operating on non-trivial blocks of G. It allows the acquisition of the coordinates of high-resolution tomographic scans within the tomographic slices by the Lauterbur spatial encoding technique of quantum holography.

Measuring 3-D location and shape parameters of cylinders by a spatial encoding technique

We are concerned with the problem of estimation of true cylinder radius, height, location, and orientation. We present mathematical models for measuring these location and shape parameters using a spatial encoding technique. A crucial step in the proposed method is to convert the estimation problem with complex curved stripe patterns to an equivalent, but simpler, estimation problem with line stripe patterns. The notions of silhouette edges and virtual plane are introduced. Various projective geometry techniques are applied to derive the cylinder location and shape parameters. The actual experiment apparatus is set up to employ the developed mathematical models to measure the cylinder geometric parameters. Description of the image-processing tasks for extracting perceived curved stripes and stripe endpoints is given. Sensitivity analysis and proper measures are taken to consider the effects of the uncertainties of stripe endpoints and silhouette edge locations on the measurement. Experiments have confirmed that our measurement method yields quite good results for different cylinders under various measurement environment conditions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optical space-variant logic-gate array based on spatial encoding technique

A new optical logic operation technique is proposed that is based on spatial encoding and superposition of a decoding mask with the coded input patterns. Sixteen logical functions of two logical variables can be realized. In the present method, a space-variant logic operation is realized, that is, different logical operations are performed in parallel. The new method is the space-variant extention of the optical shadow-casting logic of Tanida and Ichioka, which is based on a space-invariant logic-gate array. Simple examples are given.

Progress report on archival storage of color films utilizing a white-light processing technique

The authors report a spatial encoding technique such that the moire fringe pattern inherently existing with the retrieved image can be avoided. To improve the diffraction efficiency of the film, they have introduced a bleaching process so that the step of obtaining a positive encoded transparency can be eliminated. Instead of restricting the encoding processing to the linear region of the T-E curve, they allow encoding in the linear region of the D-E curve, so that a broader range of encoding exposure can be utilized. Experimental results indicate that excellent color fidelity, high signal to noise ratio, and good resolution of the reproduced color images can be obtained.

Scanning technique for coherent processors

In certain linear coherent processing techniques a temporal signal is spatially encoded on an amplitude transmittance that serves as the processor input. In this paper a technique is presented whereby the temporal signal is alternately used to amplitude- and/or phase-modulate a raster scan of the processor's input plane. Using the temporal integrating and summing properties of a hologram placed in the processor's output plane, one can then regain the identical processor output that would have arisen from the spatial encoding technique. Preliminary experimental results are presented along with the theory of the input scanning technique.