Optical On-Line Running Reconstruction of MR-Images in the Phase-Scrambling Fourier-Imaging Technique

Optical on-line running reconstruction of MR-imagesin the phase-scrambling Fourier-imaging technique

Satoshi Ito and Yoshifumi Yamada

Recently, the use of magnetic-resonance–guided navigation to improve the safety and effectiveness ofsurgical procedures has shown great promise. The purpose of the present study was to develop anddemonstrate an imaging strategy that allows surgeons to continue operating without delays caused byimaging. The phase-scrambling Fourier-imaging technique has two prominent characteristics: local-ized image reconstruction and holographic image reconstruction. The combination of these character-istics allows images to be observed even during the data-acquisition period, because the acquired signalis converted into a hologram and the image is reconstructed instantly in the coherent optical image-processing system. Experimental studies have shown that the phase-scrambling Fourier-imaging tech-nique enables the motion of objects to be imaged more quickly than the standard fast imaging. Theproposed running reconstruction strategy can be easily implemented in the well-established magnetic-resonance imaging equipment that is currently in use. © 2002 Optical Society of America

OCIS codes: 100.3010, 170.3010.

1. Introduction

Interventional magnetic resonance imaging �iMRI� isan emerging application in which both diagnostic andtherapeutic procedures are performed under MR im-age guidance. Real-time or near-real-time image re-construction are required for most iMRI proceduresperformed under MR image guidance. Several stud-ies concerning real-time or near-real-time reconstruc-tion of MR images have concentrated on the couplingof the ultra-fast imaging technique1 and methods offaster reconstruction.2–5 However, these ap-proaches have required specific hardware for imple-menting the fluoroscopic acquisitions, and growingconcern has arisen regarding radio frequency powerdeposition in the patient’s body associated with usinghigh-field MRI.

The purpose of the present study was to demon-strate the utility of fast reconstruction methods inwhich the imaging object can be more safely moni-tored at a repetition time �TR� interval by use ofwell-established MR fast-imaging techniques, such

The authors are with Utsunomia University, Departmentof Information Science, Faculty of Engineering, 7-1-2 Yoto,Utsunomia 321-8585, Japan. S. Ito’s e-mail address is [email protected].

Received 5 July 2001; revised manuscript received 13 March2002.

0003-6935�02�265527-11$15.00�0© 2002 Optical Society of America

1

as FLASH MRI.6 The imaging strategy, a phase-scrambling Fourier-imaging technique �PSFT�,7,8 isbased on conventional two-dimensional Fourier-transform imaging methods, except for the use of aquadratic field during phase encoding. The use of aquadratic field in the Fourier imaging reveals twoprominent features in PSFT. The first is localizedimage reconstruction. In PSFT a localized imagecan be obtained from a segmented signal by settingthe imaging parameter properly. This feature alsoimplies the relative insensitivity to the motion of thesubjects, which is important in iMRI procedures.The second feature is that MR images can be recon-structed using a very fast optical imaging system.9,10

Because the equation of the nuclear magnetic reso-nance �NMR� signal is similar to the diffraction equa-tion in the light or sound wave in principle, MRimages can be reconstructed by a hologram producedby the NMR signals. We have demonstrated exper-imentally that the quality of images reconstructedusing the hologram produced by the signal obtainedin PSFT was fairly improved when compared withthe signal obtained in Fourier imaging, and the im-ages can be reconstructed very rapidly by an electri-cally writable liquid-crystal spatial light modulator�LC-SLM�.11 A simulation experiment involving thereal-time reconstruction was also performed in orderto examine the feasibility of applying this techniqueas an image-reconstruction tool for the real-time re-construction of MR images.12,13

This paper describes a new rapid-imaging strategy

0 September 2002 � Vol. 41, No. 26 � APPLIED OPTICS 5527

that combines localized image reconstruction and veryfast optical image reconstruction in PSFT and thendemonstrate the utility of that imaging during iMRI.In the proposed imaging method, whenever an NMRecho signal is acquired, the image on the focal plane isupdated instantaneously. Because the image is up-dated in a TR interval during the signal-acquisitionperiod, the orientation or location of the subject �devic-es� can be monitored more quickly than is possible withthe conventional fast-imaging technique. Feasibilitystudies of the proposed imaging method were per-formed using a 0.0192T MRI scanner. Because thesignal-to-noise �SN� ratio of images obtained using theultra-low field MRI scanner were quite small, experi-ments were performed with a moving phantom.

2. Nuclear Magnetic Resonance Echo Signal in thePhase-Scrambling Fourier-Imaging Technique

In conventional Fourier-transform–based imagingmethods, the NMR signal is proportional to the Fou-rier transform of the spin density distribution of sub-jects, having a large amplitude near the zero-spatialfrequency to which all spins contribute. Thereforethe dynamic range of the signal becomes very largeand introduces significant quantization noise in theanalog-to-digital conversion when the bit number ofthe analog-to-digital converter is small. The PSFTwas proposed as a modified version of the Fourier-transform imaging technique to reduce quantizationerrors by reducing the dynamic range of the NMRsignal.7,8

In the PSFT a nonlinear field gradient for the spinphase scrambling is added to the pulse sequence of aconventional Fourier-transform imaging technique insynchronization with the magnetic field gradient forphase encoding. Figure 1 shows the pulse sequenceof the PSFT in which the xy plane is imaged using thequadratic magnetic field as the nonlinear magneticfield gradient, and the slice selection field gradient Gzalong the z axis. Letting the time from the inversionof the read-out linear field gradient Gx be t, and letting

tx � t � txr, the center of acquisition in the read-outdirection tx is set zero. Then, the NMR echo signal�gradient echo signal� is represented as

v��Gx tx, �Gy ty� � exp��j�b0x�ty � 2txr � tx��

� � ��

�� x, y�exp��j�b�� x2

� y2�� exp��j��Gx tx x

� Gy ty y��dxdy, (1)

where ��x, y� is the spin density distribution of the xyplane, and b and � are the coefficient and impressingtime, respectively, of the quadratic magnetic fieldgradient. Gx and Gy are the coefficients of the linearfield gradients in the x and y directions, respectively,ty is the impressing time of Gy, txr is the inversiontime of Gx, b0x is a homogeneous field added in timetx, and � is the magnetogyric ratio.

Using the variable transformations kx � �Gxtx andky � �Gyty, and rearranging Eq. �1�, we obtain thefollowing form:

v�kx, ky� � exp��j�0�exp��j�0xkx�

� � ��

�� x, y�exp��j�b�� x2

� y2�� exp��j�kx x � ky y��dxdy, (2)

where �0 is the constant phase shift �b0x�ty � 2txr�and �0x is b0x�Gx.

In Eq. �2� because the spin phase on the xy planeshifts in proportion to the square of the distance fromthe center, the NMR signal, which takes the valueproportional to the Fourier transformation of ��x,y�exp��j�b��x2 � y2��, does not take a large value atthe origin of the k space, and the dynamic range is notenlarged. Experimental results using two-dimensional Fourier imaging have obtained a reduc-tion of up to 25 dB in peak-signal intensity.7 Imagereconstruction is performed easily by obtaining theabsolute value of the inverse Fourier transform ofv�kx, ky�.

3. Localized Image Reconstruction inPhase-Scrambling Fourier-Imaging Technique

Equation �2� can be rewritten by using the variablesubstitutions �0x� � 2b0x�b��Gx, x� � �kx�2�b� andy� � �ky�2�b� to obtain

v� x�, y�� exp��j�0�exp��j�0x�x��

� exp� j�b�� x�2 � y�2��

� � ��

�� x, y�exp�j�b�� x� � x�2

� � y� � y�2� dxdy. (3)

Equation �3� contains a Fresnel integral equation inwhich the variables x� and y� correspond to the coor-dinates on the diffracted wave front. Because the

Fig. 1. Pulse sequence for PSFT. The pulse sequence is repeatedwith an appropriate repetition time �TR�. The quadratic fieldgradient is applied for a fixed time � to produce a nonlinear phasescrambling in the x and y directions. The gradient echo signalappearing at the reversal of Gx is sampled as the data.

5528 APPLIED OPTICS � Vol. 41, No. 26 � 10 September 2002

Fresnel region is defined as a region close to the objectin optics, the intensity of the diffracted wave front onthe hologram resembles the distribution of the object,depending on the distance between the object and thescreen. When a photosensitive material is placedclose to the object during the hologram recording, alocalized image of the object is reconstructed from asegmented hologram corresponding to the region inwhich the wave front is recorded.

Like the Fresnel hologram in optics, the NMR sig-nal in the PSFT has the characteristics of localizedimage reconstruction. Let us discuss the case inwhich the k-space signal in Eq. �2� is restricted in anarea, the center of which is located on kn and thewidth of which is 2kw for the phase encoding direction�Fig. 2�. This segmented signal is represented asEq. �4� in which v�x�, y�� is multiplied by the rectan-gular function. The reconstructed image from thissegmented signal ��n�x, y� is obtained by taking theinverse Fourier transformation of the signal

��n� x, y� � ��1�v�kx, ky�rect�ky � kn

kw�� , (4)

where rect��ky � kn��kw�� indicates the rectangularfunction, the center of which is located on kn, and thewidth of which is 2kw. By the variable substitutionky� � ky � kn, Eq. �4� can be written as Eq. �5�,

��n� x, y� � ��1�v�kx, ky� � kn�rect�ky�

kw�� . (5)

Rewriting Eq. �5� using Eq. �2�, we obtain the fol-lowing equation by the variable substitution yn� ��kn��2�b��,

��n� x, y� � �� x, y�exp��j�b�� x2 � y2��

� exp��jkn y� � sinc�kw y�,

� exp��j�b�yn2�� x, y�exp��j�b� x2 � � y

� yn��2 � � sinc�kw y�, (6)

where yn� � �kn��2�b��.The function in brackets � � on the right-hand side

oscillates very rapidly at a high range of �y � y��.Therefore the information of ��x, y� in the range of�y � y�� beyond a certain limit may be lost as a resultof averaging by the convolution with the sinc func-tion, and the value of Eq. �6� may become zero at ahigh range of y�. Let yw� be the limit within whichthe information of ��x, y� is not lost by the convolu-tion. Then yw� can be roughly estimated as the pointat which the phase change of exp��j�b�y2� in themain lobe of the convolved sinc function 2��kw isequal to 2�.14

�2�

kw��

� y��b�� y � yn��

2��y�yw�

� 2�. (7)

From Eq. �7�, we have yw� as

yw� kw

2�b�, (8)

and the imaging region is

yn� � yw� � y � yn� � yw�. (9)

From Eq. �9�, yw� is roughly equal to the region inwhich the NMR signal exists in the x� � y� coordinatein Eq. �3�. This indicates that the localized image canbe reconstructed from a segmented signal, correspond-ing to the signal distribution in the x� � y� domain.Letting the sampling step for the ky coordinate be �kyand substituting variables in Eq. �8� as yc� � 0 andkw � N�ky�2, the maximum region over which theimage is adequately reconstructed, ymax�, is given by

ymax� �N�ky

4�b�. (10)

Let the field of view be ymax, where ymax is defined interms of �ky as

ymax �2�

�ky� N�y. (11)

Here �y indicates the spatial resolution. The condi-tion of ymax� � ymax�2, equalizing the image-reconstructed region in Eq. �10� using the field-of-view area in Eq. �11�, yields the following:

�ky � �4�b��

Nor �y � � �

�b�N. (12)

Fig. 2. In PSFT a localized image can be obtained from a seg-mented signal by setting the imaging parameter properly: �a�imaging object; �b� k-space signal is restricted in the area, thecenter of which is located on kn and the width of which is 2kw forthe phase encoding direction; �c� image reconstructed from thesegmented signal shown in �b�; the reconstructed area yw� isroughly equal to the segmented signal region in the x� � y� coor-dinate; �d� If the range of motion is small during the tw period asshown in �e�; �f � the image of the moving object becomes the sum ofall values for ��n�x, y� at time tn and the reconstructed image willappear as a diagnonally skewed object.


The condition of ymax� � ymax is not necessary in theimaging experiment. When the relation ymax� �ymax holds, the imaging object is reconstructed with-out loss of image. However, when the relation ymax�� ymax holds, the localized image is reconstructedwithout applying any region-selective pulse.14

Figure 3 shows the simulation results of localizedimage reconstruction. Figure 3�a� shows the real-part signal obtained in the PSFT, consisting of 128 �128 pixels, with the parameter �b� set as 2.45 rad�cm2 to meet the condition of Eq. �12� using �y � 0.1cm. Figure 3�b� is a reconstructed image using theentire signal in the k space, and Fig. 3�d� is a recon-structed image using the upper-half region in thesignal space, as shown in Fig. 3�c�. Remarkably,almost the entire upper-half of the object is imagedwithout significant artifacts or blurring caused bysignal truncation.

4. Running Reconstruction of Magnetic ResonanceImages

Let us consider the case in which an object movescontinuously. If the range of motion is small duringthe TR period, the motion for a few phase-encodingsteps may be neglected and the object can be regardedas a still object during that period.

Suppose that the object is still during the period tw,as illustrated in Fig. 2�b�. Then the segmented sig-nal vn�kx, ky� is written as

�vn�kx, ky� � vn�kx, ky�rect�ky � kn

kw� , (13)

where kn � �Gyntw and kw � �Gytw. Here, the re-constructed image from the segmented signal, ��n�x,y�, is given as Eq. �14�,

��n� x, y� � exp��j�b�yn2��n� x, y�exp�j�b�� x2

� � y � yn�2� � sinc�kw y�, (14)

where yn � �kn�2�b� and �n�x, y� is the spin densitydistribution at the time when nth segmented signal isobtained. The reconstructed image by use of alldata in the k space obtained during Mtw, �mov�x, y�, isconsidered as the sum of all values for ��n�x, y�, asshown in Eq. �15�,

�mov� x, y� � �n�0

M

��n� x, y�. (15)

Equation �15� indicates that the reconstructed imagebecomes the sum of each localized image at time tn.Figure 2 illustrates a scheme by which the image isconstructed from strip images ��n�x, y�. When animaging object is moving in the horizontal direction,perpendicular to the phase-encoding direction, thereconstructed image will appear as a diagnonallyskewed object, as shown in Fig. 2�f �, because theimage will be the sum of the strip images, ��n�x, y�,which move in the horizontal direction as the phase-encoding step kn evolves.

By combining the localized image reconstructionand the very fast image-reconstruction method, a newsemi-dynamic imaging technique, referred to herein asthe running reconstruction of MR images, is realizedby reconstructing images during an interval of the TRperiod. The fast reconstruction must be performedwithin the TR period to keep up with the data-acquisition speed. The image reconstruction mightbe performed by use of a digital signal processor or ahigh-performance computer. In the present paper weadopt an optical image-processing system to performimage reconstruction and image display in less than 40msec, which is the TR period for present experiment.

5. Fast Image Reconstruction by Optical ImageProcessing

Because the equation of the NMR echo signal inPSFT is similar to the wave front in the optics, holo-graphic reconstruction of the MR image is possible byconverting the collected NMR signal into a hologramand reconstructing images in an optical image pro-cessing system. We have shown that the quality ofthe image obtained in the optical imaging system isdrastically improved by using PSFT,10,11 because thereduction of the signal dynamic range facilitates therecording of the signal into the hologram mediumthat has a smaller dynamic range than the NMRsignal in the standard Fourier-imaging technique.On-line reconstruction of MR images can be realizedby use of the electrically controlled hologram.

Image reconstruction and data acquisition can beexecuted in parallel by converting the collected NMRsignal into a line hologram soon after the data isacquired in the coherent optical-imaging system.The reconstructed image obtained in that system is

Fig. 3. �a� Shows the real-part of the computed echo signal ob-tained in PSFT consisting of 128 � 128 pixels, with the parametersof �b� set as 2.45 rad�cm2 to meet the condition of �y � �y�. �b�Shows the reconstructed image using the entire signal in k space,�c� is the signal filling the lower-half of the signal space with zerovalue, and �d� shows the reconstructed image using the signal �c�.Almost the entire upper-half of the object is imaged correspondingto the signal space.


always updated via the strip region, corresponding tothe acquired-signal region in x� � y� space. Thisimaging scheme allows visual feedback on the stripregion, in accordance with the phase-encoding step.

A. Principle of Holography

In the principle of holography, a reference light issuperimposed onto the object light, O�xi, yi�, scat-tered from an object.15 Assuming that the wavefront of the reference plane wave, R�xi, yi�, is parallelto the x axis, the intensity of the interferometricfringe, H�xi, yi�, is given by the following relation:

H� xi, yi�opt � �O� xi, yi� � R� xi, yi��2,

� �O� xi, yi��2 � �R0�2

� O� xi, yi� R0 exp� j�optxi�

� O*� xi, yi� R0 exp��j�optxi�, (16)

� �O� xi, yi��2 � �R0�2

� 2Re�O� xi, yi� R0 exp� j�optxi��, (17)

where the * indicates the complex-conjugate, R0 de-notes the light amplitude of the reference light, and�opt is a parameter determined by the wavelength ofthe light and the angle between the reference lightand the object light.

The first and second terms in Eq. �16� correspond tothe intensities of the object light and the referencelight, respectively, and the third and forth terms inEq. �16� and the third term in Eq. �17� contain theinformation of the object light and its conjugate light,respectively. In conventional off-axis Fourier-transform holography, the first and second term inEq. �17� is not used in the image formation, and so canbe replaced by a constant term K, given as

H� xi, yi�opt K � 2Re�O� xi, yi� R0 exp� j�optxi��.(18)

B. Lensless Fourier-Transform Hologram

In optical holography, a Fourier-transform type ho-logram can be produced without using Fourier-transform lenses by placing the point sourcereference light at the same distance as the object fromthe recording plate. This type of hologram is calleda lensless Fourier-transform hologram. The wavefront description of the lensless Fourier-transformhologram u�xi, yi� is written as �15�

u� xi, yi� �R0

��z�2 � ��

�O� x, y�

� exp�jk2z

� x2 � y2�� exp��j

kz

� xix � yiy�dxdy,

�R0

��z�2 ��O� x, y�exp�jk2z

� x2 � y2�� ,

(19)

where k is the wave number, � is the wavelength ofthe light, x and y are the coordinates of the objectplane, and z is the distance between the object andthe photographic plate that will be the hologram.

Comparing Eq. �2� and Eq. �19�, we see that v��kx,ky� corresponds to the object light O�xi, yi� andexp��j�0xkx�, giving an amplitude modulation tov��kx, ky�, corresponds to the illumination light by areference plane-wave light in the optical off-axis ho-lography. Therefore the NMR hologram is producedsimply by superimposing a constant K� on the realpart of the NMR signal v�kx, ky�

v�kx, ky� � exp��j�0xkx�v��kx, ky�, (20)

where

v��kx, ky� � exp��j�0� � ��

�� x, y�

� exp�j�b�� x2 � y2� �

� exp�j�kx x � ky y� dxdy. (21)

HNMR � K� � Re�v�kx, ky��, (22)

and the value of constant K� should be large enoughso that Eq. �22� is always positive, enabling the NMRhologram to be recorded on the recording material.

The reconstruction of the image from the NMRhologram is achieved by illuminating the hologramwith a plane-wave laser light and by taking the op-tical Fourier transformation of the light passingthrough the hologram by use of a convex lens. Thereconstructed images are obtained as symmetricalfirst-order diffraction images at both sides of the zero-order diffraction light on the focal plane.

Because the intensities of the reconstructing lightwave are detected, the square root of the output of theimage detected by the CCD must be used to obtain aquantity that is proportional to the amplitude of thedesired image.

6. Experiment

The gradient-echo imaging technique is used in thepresent experiments because the image contrast doesnot become low in the small-TR sequences, as in thecase of the spin-echo imaging technique. Imagingexperiments were performed using ultra-low field0.0192 T MRI. Figure 4 shows a schematic diagramof the experimental apparatus.

The transmitter-receiver coil, in which a phantomfor imaging is inserted, is cylindrical �6 cm � � 7 cm�.The spin-echo signal appearing upon the reversal ofGx �or Gy� is received by the cylindrical transmitter-receiver coil. The received NMR signal was ampli-fied �AMP� and converted to low frequency by meansof a phase-sensitive detector �PSD� prior to analog-to-digital conversion �ADC�.

Figure 5 shows the coil configuration used to gen-erate the quadratic field gradient.14 The long axis of


the coil system is aligned along the z direction, i.e.,the B0 direction. A rectangular prism coil generatesthe quadratic nonlinear field gradient shown in Eq.�23� having cylindrical contours extending in the zdirection when current is supplied in the directionshown by white arrows:

�B � b� x2 � y2�, (23)

where the coefficient of the quadratic term, b, is givenby Eq. �24� by letting the permeability of the space,�0, the distance from the z axis to each long segment,r0, and the ampere turns supplied to each long seg-ment, NI, are

b �2�0

2

�2B0 r04 �NI�2. (24)

Figure 6 shows a schematic diagram of the dataprocessing procedure used in the imaging experi-ments. In each phase-encoding step, an acquiredsignal corresponding to line data in k space is nor-malized to be shown in a gray-scale hologram andthen stored in a frame memory of the computer. Af-ter the video graphics array �VGA� signal scans theframe memory, the line hologram corresponding tothe line data in k space is updated on the LC-SLM.Because the optical computation is performed on theorder of ns, the image on the focal plane is updatedsoon after the hologram is refreshed. Because theupdate of the hologram on the LC-SLM is executedfrom the upper line to the lower line, corresponding tothe k-space data sampling, the reconstructed image isalso updated from the upper region to the lower re-gion. When the sequence is written so as to contin-uously loop to provide data, the reconstructed imageis also updated continuously for a moving object.

The hologram display used in the present experi-ment is a LC-SLM removed from a commerciallyavailable video projector �EPSON ELP3000�. Fig-ure 7 shows the outlook of the LC-SLM, and thespecifications of the LC-SLM are listed in Table 1.Figure 4 shows the optical setup for image formation.Taking the optical Fourier transformation of the lightpassed through the hologram, we obtain the recon-structed image as an amplitude image. A videotaperecording can be used to archive the semi-dynamicimaging session.

Motions, such as contraction, translation, and ro-tation were considered as the basic motion of pa-tients. Although in a clinical situation, the motionof patients will be complex, transitional images canbe estimated by combining the results of these mo-tions.

In all experiments, the data matrix and TR wereset to 128 � 128 and 40 msec, respectively. Thetotal acquisition time of one frame is 5.12 s.

A. Contraction

The contraction motion experiments were demon-strated by use of an elastic phantom having a diam-eter of 32 mm. The phantom is made of spongecontaining CuSO4 solution. In clinical situations,these motions are observed in the beating heart or inbreathing.

The direction of the contraction was set as the ver-tical direction on the image, corresponding to theread-out direction. The imaging parameters wereset as follows: �b� � 4.0 rad�cm2, �x � �y � 0.16cm. Figure 8 shows the reconstructed images, takenevery 0.5 s, while the phantom was being contracted.Although contraction of the phantom occurred uni-formly, shrinking is observed in the image from left toright.

Figure 8�c� shows the computer-reconstructed im-age obtained in the PSFT experiment. Comparingthe images �a� and �c�, the optically reconstructed

Fig. 4. Received NMR signal is amplified �AMP� and converted tolow frequency by means of a phase-sensitive detector �PSD� priorto analog-to-digital conversion �ADC�. The real-part of the NMRgradient echo signal is stored in the frame memory of the computeras hologram data and is sent to LC-SLM by the VGA video signal.The reconstruction of the image from the NMR hologram isachieved by taking the optical Fourier transformation of the lightpassing through the hologram illuminated by coherent laser light.The reconstructed images are obtained as the symmetrical first-order diffraction images at both sides of the zero-order diffractionlight on the focal plane.

Fig. 5. Coil configuration for generating the characteristic field.The long axis of the coil system is aligned along the z direction, i.e.,B0 direction. Rectangular prism coil generates a quadratic non-linear field gradient having cylindrical contours extending in the zdirection when current is supplied in the direction shown by whitearrows.


images had almost the same quality as the computer-reconstructed image. The computer-reconstructedimage obtained in the present experiment has highcontrast as well as low resolution and a low SN ratio,and may not be adequate for quality evaluation ofoptically reconstructed images. Image quality of op-

tically reconstructed images is described in greaterdetail in the Section 7.

Fig. 6. In each phase encoding step, the sampled echo signal corresponding to line data in k space is normalized to be shown in a gray-scalehologram and then stored in the frame memory of the computer. After the VGA signal scans the frame memory, the line hologramcorresponding to the line data in k space is updated on the LC-SLM. Because the optical computation is performed on the order of ns,the image on the focal plane is updated soon after the hologram is refreshed.

Fig. 7. Picture of the LC-SLM used in the experiments.

Table 1. Specifications of the LC-SLM

Parameter Characteristic

Display area 26.9 � 20.2 mmMode Twisted nematicNumber of pixels 640 � 480Pixel pitch 42 �m � 42 �mContrast ratio 1:200Control TFTa active matrixData source VGA,a NTSCa

aTFT, thin-film transistor; VGA, video graphics array; NTSC,National Television System Committee.

Fig. 8. �a� Shows the reconstructed images, taken every 0.5 s,while the phantom was being contracted. �b� Shows the phantomused in the experiments. The imaging parameters were set asfollows: �b� � 4.0 rad�cm2, �x � �y � 0.16 cm. Although thecontraction of the phantom occurred uniformly, shrinking is ob-served in the image from left to right. �c� Shows the computer-reconstructed image to compare the image quality with opticallyreconstructed images.


B. Translation

For the case in which the subject’s position changes ina stepwise manner, we moved a phantom from side toside over a certain time while acquiring the signal.The phantom used in the experiment is a half-roundhaving a diameter of 37 mm consisting of CuSO4solution and a three-circular plastic insert. The im-aging parameters were set as follows: �b� � 4.0rad�cm2, and the spatial resolutions were �x � �y �0.12 cm. Figure 9�a� shows the images, taken every0.7 sec, as the phantom shown in Fig. 9�b� was beingmoved in the phase-encoding direction from right toleft on the image. Because the hologram on the LC-SLM is updated from left to right on the image, thereconstructed image is updated in the same direction

in a manner such that the newer images are super-imposed onto the older image. A few artifacts arefound to be spread over the entire imaging regionowing to the motion or the effect of localized imagereconstruction.

C. Rotation

The rotating-motion experiments were performed us-ing a 32-mm-diameter circular phantom, consistingof CuSO4 solution and a two-circular plastic insert.The imaging parameters were set as follows: �b� �3.2 rad�cm2, �x � �y � 0.17 cm. The phase-encoding direction was set to the horizontal directionon the image. Figure 10�a� shows the reconstructedimage, taken every 0.4 s while the phantom shown in

Fig. 9. Reconstructed images of a phantom moving in the phase-encoding direction from right to left on the image. The phantom usedin the experiment is a half-round having a diameter of 37 mm consisting of CuSO4 solution and a three-circular plastic insert. Theimaging parameters were set as follows: �b� � 4.0 rad�cm2, and the spatial resolutions �x � �y � 0.12 cm. Because the hologram onthe LC-SLM is updated from left to right on the image, the reconstructed image is updated in the same direction in a manner such thatthe newer images are superimposed onto the older image. A few artifacts are found to be spread over the entire imaging region due tothe motion or the effect of localized image reconstruction.

Fig. 10. Reconstructed images of a phantom rotating in a clockwise direction. The imaging parameters were set as follows: �b� � 3.2rad�cm2, �x � �y � 0.17 cm. The phase encoding direction is set for the horizontal direction on the image. Although the transitionalimages, taken every 0.4 s, represent a blurring and degradation caused by motion, no defects or significant artifacts are observed on thetransitional images.


Fig. 10�b� was rotating in the clockwise direction.Although the image-updated region represents ablurring and degradation caused by motion, no de-fects or significant artifacts are observed on the tran-sitional images.

D. Simulation Experiment of Magnetic Resonance Biopsy

The on-line reconstruction system can partially re-flect the motion of the subject on the image, so thatthe surgeon can follow the motion even during dataacquisition, thus providing unique potential for semi-dynamic monitoring of interventional procedures.An example was demonstrated by imaging a needle-shaped phantom. The imaging parameters were setas in the rotation experiment. Device orientationand tip position are critical and are required to definethe device location for MR-guided interventional pro-cedures. Figure 11�a� shows the transient imagesfrom the video sequence while the needle-shapedphantom was being translated to another position ina stepwise manner, and Fig. 11�b� shows the tran-sient images while the angle between the needle-shaped phantom and the basement was varied.Because new information concerning the placementof the phantom is obtained while acquiring the signal,the surgeon can recognize the position or angle of theneedle earlier than when using images obtained viathe usual fast-imaging technique in which the oper-ator must wait N � TR periods to obtain an updatedimage.

7. Discussion

The sensitivity of MR imaging to motion and suscep-tibility normally requires that the operator using in-traoperative MRI cease surgical activity while imagedata sets are acquired. In contrast, the proposed

technique provides semi-dynamic image reconstruc-tion during data acquisition by combining the local-ized image-reconstruction property and very fastoptical reconstruction in the PSFT. The techniqueproposed herein can update images at an interval ofthe TR period, even though the updated region in theimage is small. The continuous-running reconstruc-tion allows the surgeon to operate without interrup-tion, which shortens the surgery. Imaging time canbe further reduced by acquiring an arbitrary partial-signal region for the phase-encoding direction, whenthe field of interest is restricted to a small region inthe field of view �FOV�. For instance, imaging onlythe region in which the tip of the needle is advancedsaves time. Images obtained in PSFT have fewermotion artifacts, with or without the sequence of run-ning reconstruction. In two-dimensional Fourier-transform imaging, shot-to-shot magnitude or phasefluctuations result in ghosting or blurring. PSFT isconsidered to be a cross between line scan imaging16

and Fourier-transform imaging, and images are notstrongly affected by field inhomogeneity or motion ofsubjects.

In contrast to conventional Fourier-transform im-aging methods, the present technique uses the qua-dratic field gradient for nonlinear phase scramblingto exploit the characteristic of localized image recon-struction. To generate a quadratic field gradient, weused a special coil in the experiment; however, phasescrambling can be most easily implemented by puls-ing the resistive shim coils that are already presenton a number of MRI systems. A quadratic field gra-dient can therefore be readily applied as a simplemeans of obtaining semi-dynamic images in the MRfast-imaging technique, the only additional require-ments being an extra waveform-generator channeland a suitable power supply for pulsing the shimcurrent.

To perform very fast image reconstruction, the ho-lographic image-reconstruction technique, i.e., apply-ing the similarity between the signal equation inPSFT and the wave-front equation, is used. Be-cause the optical image processing is considered to bean ideal for parallel information processing, imagereconstruction at a TR interval is performed, en-abling the semi-dynamic monitoring of an object.The holographic reconstruction requires that theFOV for the off-axis direction be at least twice aslarge as the image extent to avoid the superpositionof FOV between the real and conjugate images. In-creasing the FOV without reducing the spatial reso-lution means increasing the number of data collected.To suppress the increase in total data-acquisitiontime as a result of the increased number of data, theoff-axis direction is preferably set to the read-out di-rection in the imaging experiments. Recently, acommercially-available LC panel, supporting theSXGA standard of video signal and containing1280 � 1024 pixels, which is double the data matrixcurrently used in commercial MRI, has become avail-able. Thus if we use such a fine LC-SLM in the

Fig. 11. Reconstructed images of a needle-shaped phantom.The imaging parameters were set as in the rotation experiment.�a� Shows the transient images while the needle-shaped phantomwas being translated to another position in a stepwise manner, and�b� shows the transient images while the angle between the needle-shaped phantom and the basement was being varied.


experiments and set the off-axis direction as the read-out direction, the FOV requirement does not becomea concern.

However, optically reconstructed images must suf-fer from degradation due to the characteristics andimperfection of optical instruments or speckle noisesarising in the coherent optical-imaging system. Toevaluate the quality of the optically reconstructedimage in our system, experiments using a computer-generated hologram were performed. In generatingthe hologram from Eq. �2�, a high-SN ratio MR imageobtained via clinical MRI, shown in Fig. 12(a), wasused for spin density data. In the figure, �a� is theMRI transversal image having a matrix size of 128 �128 pixels. The imaging parameter that determinesthe phase modulation is set as Eq. �12�. Figure 12�b�is the optical image captured by a CCD camera. TheSN ratio appears to be decreased compared to theoriginal image Fig. 12�a�, however, the half-tone towhich the original image compared, is well repre-sented, and the image is reconstructed with a highreproducibility. The LC-SLM used in the experi-ment was a commercially available liquid-crystalpanel built in to the video projector, which has notonly amplitude modulation of the input light wavebut also phase modulation, which may degrade theimage quality. The image quality will be furtherimproved if the characteristics of the liquid-crystalpanel are improved by replacing the present model bya model better suited to the purpose, or by improvingthe fabrication technique of the liquid crystal panel.If the image reconstruction procedure is performedusing a high-performance computer that can performFourier transformation of data and display imageswithin the TR period, or if the operator allows imagesto be updated at an interval of several TR periods,then the reconstruction procedure can be replaced bycomputer-aided methods. The quality improvementin the holographic reconstructed image will be exam-ined in a future study.

8. Conclusions

A technique for continuously reconstructing imagesduring data acquisition in the MR fast-imaging tech-nique is presented and demonstrated. In contrast toconventional fast-imaging methods, the present tech-nique, which uses a quadratic field gradient for non-linear phase scrambling, can, in conjunction with veryfast optical image processing, update local images atan interval of the TR period. This optical on-line run-ning reconstruction appears feasible for image guid-ance of a variety of iMRI procedures and provides someimportant advantages over conventional Fourier-transform-based fast imaging. The proposed methodallows the surgeon to use surgical instruments withoutthe interruption associated with image acquisition.The proposed technique can be readily applied in well-established MRI equipped with the fast-imaging tech-nique by pulsing the resistive shim coils that arealready present on MRI systems.

This work was supported by a Grant-in-Aid forScientific Research �B� from the Ministry of Educa-tion, Science, Sports and Culture, Japan.

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Optical On-Line Running Reconstruction of MR-Images in the Phase-Scrambling Fourier-Imaging Technique