United States Patent [191 [11] Patent Number: 4,950,991 Zur [45] Date of Patent: Aug

United States Patent [191 [11] Patent Number: 4,950,991 Zur [45] Date of Patent: Aug. 21, 1990

[54] REDUCTION OF TRUNCATION CAUSED ARTIFACTS OTHER PUBLICATIONS [75] Inventor: Yuval Zur, Herzliya, Israel R. Bracewell, “The Fourier Transform and its Applica tion”, McGraw-Hill Book Co. (1965), pp. 209-211. [73] Assignee: Elscint Ltd., Haifa, Israel Primary Examiner-Hezron E. Williams [21] Appl. No.: 359,488 Assistant Examiner——Kevin D. O’Shea Attorney, Agent, or Firm-Sandler, Greenblum & [22] Filed: May 31, 1989 Bernstein [30] Foreign Application Priority Data [5 7] ABSTRACT May 31, 1988 [IL] Israel ...... 86570 The Gibb’s artifact in magnetic resonance images is [51] Int. Cl.5 , ...... G01R 33/20 reduced by asymmetrically sampling acquired F.I.D. [52] US. Cl...... 324/307; 324/312 signals to obtain data, time domain ?ltering the obtained [58] Field of Search 324/307, 311, 312, 309; data with a ?lter that reduces overshoot, degrades reso 375/104; 364/413, 13, 574, 724, 726 lution but increases SNR. Then obtaining symmetrical data by complex conjugating the time domain ?ltered [56] References Cited data which improves the resolution, compresses the US. PATENT DOCUMENTS overshoot, but decreases SNR. Processing the symmet 4300096 11/1981 Harrison etal ...... 324/309 ii°ni data i° °biain images with insigni?cant Gibb’s 4,535,460 11/1935 Wedel, Jr...... 375/104 artifacts 4,614,907 9/1986 Nagayama ...... 324/312 4,780,675 10/1988 DeMeester et a]...... 324/312 14 Claims, 2 Drawing Sheets

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FIG. 6 (a) FIG. 6 (b) FIG. 6 (C) 4,950,991 1 2 ously used imaging methods, said method comprising REDUCTION OF TRUNCATION CAUSED the steps of: ARTIFACI' S (a) acquiring free-induction decay (FID) signals; (b) asymmetrically sampling the acquired signals to FIELD OF THE INVENTION obtain data; This invention is concerned with the magnetic reso (c) multiplying the obtained data by an optimized ?lter nance imaging (MRI) and more particularly with the in the time domain to provide time domain ?ltered minimization of Gibbs artifacts in images obtained using data, which: MRI systems. (1) reduces the overshoot, 10 (2) degrades the resolution, and BACKGROUND OF THE INVENTION (3) increases the SNR, Sampling is time limited. The ?nite sampling time (d) obtaining symmetrical data by complex conjugating results in artifacts caused by what is known as “the the time domain ?ltered data which: Gibbs Phenomenon”. The representation in the image (1) increases the amount of data and consequently domain near a discontinuity, for example, includes an improves the resolution. “oscillatory overshoot” which is approximately 9% of (2) compresses overshoot causing the ringing artifact; the magnitude of the signal at the discontinuity. An and artifact due to the Gibbs phenomen appears as “ring (3) decreases the signal-to-noise ratio (SNR); ing” in the image. The ringing is often referred to as (e) Fourier transforming the symmetrical data to obtain “Gibbs artifact”. See the book entitled “The Fourier the image data; and Transform and its Applictions” by R. Bracewell, pub (f) processing the image data to obtain an image with lished by McGraw-Hill Book Co. (1965) pp. 209 et seq. substantially no ringing artifact and with resolution If more sampling points are taken, the amplitude and signal-to-noise ratio comparable to images ob remains 9%, but the overshoot is compressed towards tained using symmetrical sampling. the edge of the discontinuity which reduces the artifact 25 As used herein FID signals may includes echo sig and accordingly improves the spatial resolution. While nals. Also it should be understood that the ?ltering can taking more sampling points improves spatial resoltion, occur after the complex conjugation step (of the ac it requires time which reduces throughput. Also, as is quired data) or that the Fourier transforming step can well known, the signal-to-noise ratio (SNR) is propor occur before the complex conjugating step within the tional to the inverse of the square root of N where N is the number of sampling points. Accordingly, to obtain scope of the invention. In addition, while invention can enough sampling points to effectively reduce the Gibbs be applied in either the phase encoding or frequency artifact not only reduces throughput, but also reduces encoding direction maximum bene?ts (time saving) the SNR of the image to the point where the improved occur when the invention is applied in the phase encod resolution may be obscured by noise. 35 ing direction. A multiplicative filter in the time domain can effec BRIEF DESCRIPTION OF THE DRAWINGS tively reduce the overshoot and increase the SNR. However, such a ?lter reduces the resolution of the The above mentioned and other features and objects image. The reduction in resolution occurs because a of the present invention will be best undertood when time domain ?lter that reduces the overshoot also in 40 considered in the light of the following description of a creases the transition width of the function. The spatial broad aspect of the present invention taken in conjunc resolution; i.e. the smallest size detectable, is propor tion with the accompanying drawings, wherein: tional to the transition width; so that, an increased tran FIG. 1 illustrates Gibbs overshoot in a frequency sition width means the smallest size detectable in signal obtained from a Fourier transformed truncated creases. 45 time signal; In magnetic resonance imaging there are many in FIG. 2 illustrates the Gibbs overshoot in the fre stances, for example, for thoracic images when an image quency signal obtained from the Fourier transformed of 256 X 256 is not required. In fact many times an image and truncated time signal when more sampling points providing less resolution, but improved SNR and acqui are used than were used in FIG. 1; sition time would be preferred. Until now the lower FIG. 3 shows the Gibbs overshoot in a frequency resolution images have not been used because of the signal obtained from a Fourier transformed multiplica Gibbs artifact, which obscures the image and especially tively ?ltered time signal; an image with less resolution. Therefore, what is re FIG. 4 illustrates a preferred type of ?lter for use in quired is a reduction of the Gibbs artifact without ad the inventive system. versely effecting the resolution, the SNR or the scan FIG. 5 shows an MRI system and components for time. carrying out the inventive Gibbs artifact reduction, and Accordingly, it is an object of the present invention FIG. 6 illustrates at: to effectively and substantially reduce the ringing arti (a) prior art symmetrical sampling, fact in the display image while substantially maintaining (b) asymmetrical sampling, and a given resolution and the signal-to-noise ratio of the (c) asymmetrically sampled data after complex conju ?nal display image without increasing the scan time. gation. BRIEF DESCRIPTION OF THE INVENTION GENERAL DESCRIPTION According to the present invention a method of re In FIG. 1, the drawing shows a typical FID signal 11 ducing ringing artifacts is provided; the method accom 65 acquired in the time domain. As indicated by the styl plishes the scan without increasing the scan time while ized “F”, the time domain signal which in a preferred reducing the ringing artifacts and maintaining the sig embodiment is an echo signal, is Fourier transformed nal-to-noise ratio and the resolution obtained by previ into the frequency domain signal 12. Note that the time 4,950,991 3 4 domain signal does not go from minus in?nity to plus particularly a radio frequency (RF) coil (not shown) is in?nity, but instead is truncated as indicated by lines 13 located within the large magnet 22. In the transmitting and 14 de?ning the limites of the time domain signal 11. mode a transmitter 29 applies RF pulses through a du The truncation of the time domain signal results in the plexer circuit 31 to the RF coil. The transmitter 29 Gibbs effect overshoot 16 that appears in the frequency receives the pulses through a modulator 32. The modu domain signal 12. This overshoot causes the Gibbs arti lator may be used to modulate a radio frequency from a fact; i.e., a blurring or ringing artifact to appear in the radio frequency generator 33 with a modulating signal image. from the modulating generator 34 to shape the RF FIG. 2 shows the effect on the Gibb’s overshoot of pulse. The RF pulse applied to the RF coil of the mag sampling a greatly increased number of points. Sam net system tips the spins ?rst through 90 degrees and pling the greatly increased number of points, narrows subsequently through 180 degrees in a regular spin echo or compresses the frequency displacement of the over sequence, for example. shoot. This reduces the ringing artifact effect of the During the application of the RF pulses, a slice select overshoot. However, the throughout time and the sig ing gradient pulse G2 is applied. Subsequently, a phase nal-to-noise ratio suffer due to the increased number of 15 encoding pulse Gy is applied. During the receipt of a sampling points even though the image resolution im signal, a read or view gradient pulse G2 is applied. proves. In the prior art the Gibbs effect precluded ac quiring images with fewer sampling points because of In the receive cycle, the echo is received as indicated the resulting disasterous ringing artifacts which ob by signals shown at 36 in FIG. 6(b). The signal 36 is an scured the images. asymmetrically sampled signal. The receipt of the signal occurs during the-application of read gradient pulse 39. FIG. 3 shows the effect on the Fourier transformed signal of a time domain spatial ?lter. Here note that the The distinction between a normal or symmetrically signal 17 has a sharply reduced Gibbs overshoot ‘18. sampled received signal and an asymmetrically sampled However, the line 19 which de?nes the edge of the signal is best shown by comparing FIGS. 6(a) and 6(b). signal is now biased rather than being substantially per 25 FIG. 6(a) shows the signal 36 as normally sampled. pendicular. In actual practice the line 19 is transformed Therein the same number of samples (M/2) are taken on from having a transitional width D of one pixel to hav each side of the peak of the received signal. Thus, if M ing a transitional width D much larger than the one is 128, for example, 64 samples are taken on each side of pixel. In a preferred embodiment, the transitional width the center of the signal peak, along the O ordinate. D may vary up to three times the original one pixel 30 FIG. 6(b) shows an example of asymmetric sampling. width. It is apparent from FIG. 3 that since the transi Therein (M/2)(l +R) samples are shown as being taken ' tional width is greatly increased over the transitional on one side of the center of the signal. The other side of with of FIG. 2, for example, the size of smallest detail the center of the signal provides (M/2)(1—R) samples that can be discerned; i.e., the resolution (in pixels or where R<0.7 or 45 sam The ?lter is shown in FIG. 4 as a window 20. While ples. Further, as shown in FIG. 6(0) after complex con a Kaiser type window is shown it should be understood jugation, the number of samples totals 166 which of that other functions could be used. An important char course increases the resolution and reduces the SNR acteristic is that substantially only the center of the 40 without effecting the scan time. acquired data passes through the window and the over Returning to the explanation of FIG. 5, the received shoot is attenuated. signal is demodulated in the demodulator 32 which The magnetic resonance imaging (MRI) system 21 receives both the received signal and a signal from the shown in FIG. 5 is equipped to minimize or reduce modulating generator 34. The signal from the demodu signi?cantly the Gibbs artifact without any signi?cant 45 lator is converted into digital signals by analog to digital adverse effects on SNR, resolution or imaging time. converter 43. The asymmetric sampling is generally The MRI system 21 comprises the usual magnet 22 used done in one direction. It could be done in either the time to provide the large static magnetic ?eld that aligns the or in the phase encoding directions. More time is saved “spins” in the patient placed within the bore of the if the eccentric sampling is done in the phase encoding magnet. 50 direction. ' The magnet and system and under the control of the .The complete acquired data, for example, comprises control processor shown at 23. The control processor is data in a 128x128 matrix obtained by acquiring and not shown attached to the component parts of the MRI digitizing signal 36. Complex congjugation is used to system 21 to avoid a plethora of lines in the drawing generate data for a 128x166 matrix, for example. The that would add more confusion than enlightenment. It is complex conjugator is shown as unit 44. The output of understood and well known that the control-processor the complex conjugator is sent through a multiplicative 23 provides the timing and control signals for the MRI ?lter, such as a Kaiser ?lter 46 to aid in the removal of system 21. the Gibbs artifacts. The output of the Kaiser ?lter is Associated with large static magnet are gradient ?eld _ Fourier transformed by Fourier transform operator 47. generators shown for generating X, Y, and Z gradient 60 In practice the Fourier transforming and/or the ?l ?elds used for locating the sources of the received sig tering can be accomplished prior to complex conjuga nals. In greater detail the X gradient ?eld generator Gx tion within the scope of this invention. Further, in prac is shown at 24, the Y gradient ?eld generator Gy is tice the ?lter parameters are selected to optimize the shown at 26 and the Z gradient ?eld generator G2 is reduction of the Gibbs artifact and to retain substani shown at 27. The large static magnetic ?eld generator tally the same resolution, SNR (and scan time) by also Ho is shown at 28. taking into account the improvement to resolution and Means are provided for perturbing (i.e. “tipping”) the the impairment of SNR caused by the complex conjuga spins aligned by the large static magnetic ?eld. More tion step. 4,950,991 5 6 The resolution obtained by the inventive imaging, a is a free parameter of the ?lter, the other parame that is, for example, by the asymmetric sampling, multi— ters can be computed once a is selected; for a Kai plicative ?ltering, and complex conjugation as com ser ?lter: pared to the resolution with symmetrical sampling ob tained using the same number of sampling points is A is the ?lter attenuation of the Gibbs overshoot in given by: decidbels,

D RES = m A _ 7.95 D = 14.36 A > 21 where: 0.9222 A < 21 D is the transition width (in pixels or mm) after multi plicative ?ltering (see FIG. 3), and n = 1,2,3 . .. R is the sampling asymmetry (see FIG. 6). 15 By determining a, D, A o'F from the ?lter selected, Before ?ltering the transition width is one pixel. In the following type of table can be generated: symmetrical sampling as opposed to asymmetrical sam pling, R is zero. In practice the number of sampling TABLE I points is N without complex conjugation. After com Transition Attenuation Alpha Sigma Width plex conjugation there are 2M sampling points where Adb a crF D 2M=N(1+R) and N<2M. Note that the ?lter de 22 0.663 0.966 0.978 grades the resolution, but the complex conjugation 23 0.929 0.938 1.048 improves the resolution. Consequently, the resolution 24 1.143 0.913 1.118 does not change signi?cantly during the processing 25 1.333 0.890 1.187 25 26 1.506 0.869 1.257 which reduces the Gibbs artifact. 27 1.669 0.850 1.327 The SNR obtained by the unique imaging described 28 1.821 0.832 1.396 herein compared to the SNR normally obtained is given 29 1.973 0.816 1.466 by: 30 2.117 0.802 1.536 31 2.256 0.788 1.605 30 By way of example, if the overshoot is to be attenu ated by 6db (which means A=27db) then a: 1.669, UP is 0.850 and D= 1.327. where: In our example with R=0.3, the resolution would 35 R is the selected sampling asymmetry, which is then be 1.327/ 1.3 or approximately 1 and the compara chosen to effect the best compromise, and tive SNR would then be (IF is the RMS noise reduction due to the multiplica tive ?lter. With symmetric sampling R is zero and the SNR is 40 Thus, a Kaiser ?lter would cut the overshoot in half, one. Therefore, the asymmetric sampling degrades the while substantially maintaining the resolution and the SNR. The ?lter on the other hand improves the SNR. SNR. Consequently, the SNR does not change signi?cantly Attenuating the overshoot by 10 db, which means during the processing to reduce the Gibbs artifact. that A=31, a=2.256, o-F=0.788 and D: 1.605 would Assume 2M points are sampled after conjugation. 45 provide a comparative resolution of 1.24 and a compar The ?lter multiplies every point by ?lter function ?c; ative SNR of 0.9207—-a slightly decreased comparative where: —M§k§M and the point fk=o is normalized resolution and a better comparative SNR. In addition, to 1. Then: the asymmetry can be selectively varied to add to the control of the resolution and the SNR. The'following 1'M 50 table shows sample variations in the comparative reso (rt-2 = lution and SNR’obtainable by selecting the R to be 0.30, 0.33 or 0.27 and the attenuation to be 27 or 31 db: As an example where the Kaiser ?lter is applied (see TABLE II the book entitled “Digital Filters”, 2nd ed. by R. W. III LII Comparative Hamming, published by Prentice Hall Inc. (1983): R Adb Resolution Comparative Asymmetry Attenuation RES SNR 0.30 27 1.021 0.8536 0.33 27 0.9557 0.8340 0.27 27 1.045 0.8745 0.30 31 1.24 0.9207 0.33 31 1.206 0.8996 where: 0.27 31 1.264 0.9432 I0 is a function given by Thus, the parameters of the ?lter can be chosen to 2 65 effect a compromise between the resolution, the ringing artifact and the SNR all without taking additional scan time. Ideally the parameters are chosen so that the deg radation of neither the resolution nor the SNR are sig 4,950,991 7 8 ni?cant while the Gibbs artifact is substantially reduced conjugation by an optimized ?lter comprises ultilizing a and the scan time remains the same. Kaiser ?lter. It should be understood that in the prior art even 7. The method of claim 3 including the step of multi when the resolution is maximized, where the Gibbs plying data acquired by the asymmetrically sampling artifact prevails, then the artifact often prevents proper step by an optimized ?lter to obtain ?ltered data, com diagnoses through the use of the image. Lesions, for plex conjugating the ?ltered data, and Fourier trans example, are often too badly “smeared” to be discern forming the complex conjugated ?lter data to obtain ible. image data. Thus methods and equipment are provided for mini 8. A system for reducing Gibbs artifacts in images mizing the Gibbs artifact without having to pay with acquired using magnetic resonance imaging (MRI) sys added scan time, worse resolution or lower SNR. tems, said system comprising: While the invention has been described using speci?c (a) means for acquiring MRI signals, embodiments, it should be understood that these em (b) means for sampling the acquired signals to obtain bodiments are described by way of example only and data, should not be interpreted as limitations on the scope of 15 (c) means for increasing the amount of data to im the invention which is de?ned by thhe accompanying prove the resolution, compress overshoot causing claims. Gibbs artifacts, but decrease signal-to-noise ratio What is claimed is: (SNR) of a subsequent image, 1. A method fo reducing Gibbs artifacts in images ((1) means for operating on the increased data to de acquired using magnetic resonance imaging (MRI) sys crease the overshoot, tems, said method comprising the steps of: (e) means for processing the increased data with de (a) acquiring MRI signals, creased overshoot to obtain the subsequent images (b) sampling the acquired signals to obtain data, with very little Gibbs artifact and with resolution (0) increasing the amount of data to improve the and SNR comparable to images obtained through resolution, compress overshoot causing Gibbs arti 25 normal operations. facts but decrease the signal-to-noise ratio (SNR) 9. The system for reducing Gibbs artifacts of claim 8 of the subsequent image, wherein the means for sampling the acquired signals to obtain data comprises means for asymmetrically sam (d) operating on the increased data to decrease the pling the acquired signals to obtain data. overshoot, 30 10. The system of claim 9 wherein the means for (e) processing the increased data with decreased increasing the amount of data comprises means for com overshoot to obtain the subsequent images with plex conjugating the data obtained by asymmetrically very little Gibbs artifact and with resolution and sampling the acquired signals. SNR comparable to images obtained through nor 11. The system of claim 10 wherein the means for mal operations. 35 operating on the increased data to decrease the over 2. The method of reducing Gibbs artifacts of claim 1 shoot comprises means for multiplying the increased wherein the step of sampling the acquired signals to data obtained using the complex conjugation by an obtain data comprises asymmetrically sampling the optimized ?lter. acquired signals to obtain data. 12. The system of claim 11 wherein the means for 3. The method of claim 2 wherein said step of increas 40 processing the increased data with the decreased over ing the amount of data comprises complex conjugating shoot includes means for Fourier transforming the data the data obtained by asymmetrically sampling the ac obtained from the ?lter to obtain image data. quired signals. . - 13. The system of claim 11 wherein the means multi 4. The method of claim 3 wherein the step of operat plying the increased data obtained using the complex ing on the increased data to decrease the overshoot 45 conjugating by an optimized ?lter comprises a Kaiser comprises multiplying the increased data obtained using ?lter. ' ' the complex conjugation by an optimized ?lter. 14. The system of claim 9, including means for multi 5. The method of claim 4 wherein the step of process plying the data acquired by the means for asymmertri ing the increased data with the decreased overshoot cally sampling data by an optimized ?lter to provide includes the step of Fourier transforming the data ob ?ltered data, means for complex conjugating the ?l tained from the ?lter to obtain image data. tered data and means for Fourier transforming the com 6. The method of claim 4 wherein the step of multi plex conjugated ?ltered data to provid image data. plying the increased data obtained using the complex 3 # * * i