Echo-Planar Imaging of ghosting artifacts often seen leaved echo-plana - PDF document

Echo-Planar Imaging of ghosting artifacts often seen leaved echo-planar images is presented. artifacts result phase and amplitude lines of phase-encoding direction, and timing misregistrations from often mea- sured using ghosting through From the expressions describing ghosting criteria were for reducing to be estimating these Mathematical Description experiment, where echo-time shifting during acquisition echo misalignment occurs to system filters an amplitude normalized k-space, k-space, is multiplied by an an [I1 The modulation function, function, could, for example, result from T, decay or periodic motion phase-encoding scheme as well angle. A representative example modulation function, was chosen to investigate modulation. Although the amplitude artifacts may more complicated modulations, representative function is ghosting artifacts that result result gives f [k,I = f[k,I . ",I F"n,I = F[nyl *,HTn,I 121 where F'[n,] is the circular convolution convolution and the modulation kernel, ghost artifacts The modulation function depicted Simple amplitude discontinuities in the is denoted phase-encoding steps. h[ky] can be simplified simplified shown here the amount amount shown in Fig. 2, is defined defined N for any integer integer + G,[n,I [51 I dkyl = For a k-space data set that contains steps, the the is where C;,[n,l = DFT((g[k,l ~ g[k, - n,])(AA/2)) is de- fined as the ghost kernel, and is calculated in Appendix Appendix sin2(Tnjn,,/Ng [ sin( rn,/ N,) m=-n, 2n, Figures 3a-3d plots the magnitude of the ghost kernel, IG,[n,]l, normalized by AA and image intensity (N,, see Eq. [5]). Note that the m even terms are zero, meaning that the spacing between the image kernel and the m = ghosts is FOVI2n,, while the spacing between shows the terms to computer simulation was written ghosts resulting that contain Figs. 4e-4h represent im- with the image. Likewise are seen weaker ghosts modulation is required achieve moderate the number impinge into becomes very high, the ghosts become then the ghosts appear image, giving shows this effect for time delays phase discontinuities, is natural extension vious section. use Discon tin similar approach can to describe ghost arti- stant-phase modulations phase-encoding direc- Constant-phase shifts echoes can from field susceptibility, as well as receiver-phase Position in Phase Encoding Encoding normalized by AA and image intensity represent the even values GR4SE imaging, also cause following analysis phase modula- a representative modulation function discontinuity can can = g[kv]e’A4’/z + g[k, - n,]e-”+” [71 The N,-point DFT of h[kJ takes the form where the image kernel is ghost kernel This result is is for amplitude modulation, except jAAl2 is replaced small, then are interchange- tional result is that the amplitude phase discontinuity cos(A+/2), unlike with amplitude modulation, decrement is seen. simulation was written show the phase discontinuities. that contain constant phase discontinuities same phase modulations Fourier transform readout direction, the phase discontinuity between successive not an integer value thorough description ghost artifacts sentative examples tude and phase discontinui- time delays, was presented. allowable phase discon- misalignment can Artifact Acceptability many possible can be established reduction. These vary for desired in- age. For dependent on Simulated magnitude no amplitude discontinuity, with by theory. that results results ny] = sin (2yx)1( - 1)"J The image kernel is simulation was written time delays. that contain time time shifts the sinusoidal readout (horizontal) Figures 8a-8d, axial that arise shows an with time delay corrections, 1-shot, 4-shot, 64-shot images with no time The time delay is approx- morphological features, anatomical brain heart image, a higher that are These ghosts are indexed most likely to ment measurements. phase discontinuities istrations is is reasonable, it assumes that that only residual mod- ulation remains Ideally, ghost artifacts be reduced noise level. as the standard deviation discontinuities in the says that the er- ror in estimating a phase dis- ghosts below an n, shot ghost-to-noise ratio phase discontinuity phase discontinuity is Time Delays magnitude images Images (e)-(h) Ghost and we wish artifact to level as ghost-to-noise ratio reduced below below can be signal-to-noise ratio the upper ghosts below ghost-to-noise ratio maximum ampli- discontinuity is 4%. similar analysis can be be it is Time shifts point will cause one will cause phase wrapping. assumed that time delays can be corrected to less ghosting artifacts time delays are greatest at minimized here. can be be that N,Axan, sin(.rr/Zn,) S,rrSNR S% [181 Multiplying both sides the bandwidth readout direction is is where t,, = sT is the maximum allowable delay to an ni object for which the image. For for an image For n, discussed previously, stringent are required changes are on the ghost arti- will be affected by ghost. Measure- Motion, system instabili- physiological fluc- to fluctuate between Postprocessing corrections reference-scan measure- ments made leave considerable ghosting are treated treated and 1121 can be Simulated magnitude a signal change a signal be greater containing ghosts can affected by with the aid diagrams a probability dis- a region are present, standard deviation, is the pixels averaged in the goal is signal change ghosting, several possibilities arise. the corruption is constant through detected will is the ghost-intensity fluc- fluc- to describe the m = 21 ghosts caused by phase offsets, normalizing for image intensity (Ny), and assuming sin(A$/P:) = A412 I211 where oG is the standard deviation the standard phase disconti- modeled here as a Gaussian This means a signal measurement is the minimum can be detected certainty is The value particular experiment 128 axial interleaved brain images that demonstrate by time time delay correction, and shot, and Ghosting Artifacts Gaussian distributions and non-activated are often shifts between successive as part exam. Various described previously two echoes are opposite polarity readout gradients phase encoding. and Fourier transform both, the is subtracted. the time (k-space) domain will be seen phase rolls quency (spatial) domain. Constant-phase echoes will be seen. will cancel, phase-shift esti- regressed to determine any time-delay When reference scans are two echoes, limited may require efficient estimators to make following analysis assumes that the were collected same manner been ignored. calculated using (20-22). Extend- detection (23), time-delay estimation noise is calculated calculated TBW SNR S, S, Equation [23] is time delay between homogeneous rectangular pixel dimensions signal-to-noise ratio per pixel this equation, time delay can be improved directions. Since readout direction, have its is usually prevent aliasing in the however, is not optimal ghosting artifact, as also be noted that that neither phase direction phase-encoding steps any hearing that increasing per pixel improves computer simulations were performed to with the theoretical lower [23]). Complex Gaussian noise was opposite phase The phase each point these points regressed to time shift the slope The standard deviation 100 trials is plotted agreement exists those predicted [23] to be written that this [23] as residual time delay equation can can and rearrangement for a gives This expression is the minimum ghost-to-noise ratio time delay, expression is implies that ghosting artifact be reduced longest axis p hase-encoding ghost artifact is smaller object for delay, reducing the minimum ghost-to-noise ratio. a profile orientation improves time-delay estimate, readout direc- tion. This orientation, however, not always ]Extending from Smith (26), the standard constant-phase shift noise is and has for large a reference echo can (SNR) for homogeneous rectangular one sample a profile readout direc- phase extends then this Monte Carlo simulations like those described vious section were performed phase shift SNR, for simulated results are plotted plotted which uses all points along the profile in the readout direction for av- there is excellent agreement ulated and error from estimation method phase-offset es- is minimized object's long phase-encoding direction. [30] as residual phase offset after after This expression is ghost-to-noise ratio phase discon- homogeneous square that this implies that phase estimates are best with the object's long phase-encoding direction. thorough mathematical description ghost artifacts was presented. Expressions phase discon- as those Summary for Discontinuities, and amplitude of noise ratio, the text. Ghost to to = sin(T)--- 2 mn, 1 td 5 __ Phase Time delay n, sin(d2n;) BW S,n SNR istrations due to echo-time delays, were derived. The the amplitude are positioned these expressions, were presented artifact levels are summarized bounds on time delays constant-phase discontinui- were calculated that used two reference echoes. Excellent agreement was found between and the error performance tors, indicating that these are optimal suring time delays analytical expressions time delays phase discontinuities with the relate ghost artifact low levels, efficient estimators are used. This has portant implications small changes The minimum time delays are third column ghosting artifacts that is seen also been that cause will allow determination the minimum culations about ghost-to-noise ratio to the readout directions has on the minimum achievable ghosting. both time delays axis along phase-encoding direction, is avoided. however, that time delays is is oriented the readout direction direction )This means that way to time delays is make reference with the in lhe readout direction and then This is only gradient configurations. commonly used ence scans take a time during clinical examination. examination. can be written written [A2 AA 2 G,[n,] = -(I - where the DFT of g[k,] is, Ny/2-1 G[n,] = 2 g[ky]e-j~nn~k~/N~ [A31 kV=-Ny12 Expanding - NV/ 2 +n,- 1 - N,/ 2 t 3n, - 1 G[n,] = 2 e-j2nn?kdNy + c e--j2nnvkv/Nv k,= -N,/ 2 +2n, kv=-Nv/2 - Nv/ 2 + Sn, - 1 + e-12~nykdNy k,= - N,/ 2 + 4 n, N,l 2 - n,- 1 [A41 where lii determines the periodicity of the modulation. solution using using is zero, unless ny = N,m/2ni where in is any integer, allowing be expressed as a delta functions, that delta functions is determined using l'H6pital's is even. even. can be written or if we limit ny to the interval -(NJ2) 5 ny 5 (N,/2) - 1, since was assume assume is periodic periodic can be simplified to and summarizing, G[ny] can be written as n,-1 sin( rrnlnyI N,) sin(nn,lNy) --_ m=-n, Substitution of Eq. [All] into Eq. [A21 determines the ghost kernel It is important to note that the term is since the amplitude amplitude is also zero all other BOUND CALCULATIONS time-delay estimation noise can the time summation is were collected denominator can can is the DFT of s(iT). This assumes s(iT) is peri- is band-limited. Expanding Expanding ej2mkt/NxT 1 Nxi2-1 Nx s(t) = - c k=-Nx/2 and since Therefore k=-N,/2 For a centered homogeneous rectangular with di- image voxel projection is can be simplified The numerator numerator is the variance on the noise in the time domain, and can be converted to the frequency domain as the standard domain. Substituting Eq. [BlO] [BlO] and not- ing that the image SNR equals AIw, and readout band- per pixel The authors thank the echo planar non-equidistan! k-space blood oxygenation. 9868-9872 (1990). with echo P. Koretsky, arterial water. D. G. A. C. Warach, Qualitative cerebral blood flow echo planar frequency. 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