W.A. Edelstein. Intrinsic signal to noise ratio in nmr imaging. Magnetic Resonance in Medicine, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....= s #p,n,i ( # p,n,i , where the additive measurement error # p,n,i has a Gaussian distribution with (possibly unknown) variance # . In MR imaging, the source of this noise is thermally generated, randomly fluctuating noise currents in the body which are picked up by the receiving antenna, [36] so it is correct to assume that the measurement errors are Gaussian and independent. It is convenient to group the ideal projection and measurement samples in the different ways defined below. First group the samples by rows: y p,n = y p,n,1 , y p,n,W ] s #p,n ( s #p,n,1 ( ....

W. A. Edelstein, G. H. Glover, C. J. Hardy, and R. W. Redington, "The intrinsic signal-to-noise ratio in NMR Imaging," Magnetic Resonance in Medicine, vol. 3, pp. 606--18, 1986.

....antenna length and field of view increase while noise resistance decreases. With proper design, insulation can improve both the safety and SNR of internal loopless MRI receivers. II. METHODOLOGY The signal to noise ratio for MR receivers can be objectively compared by finding the intrinsic SNR [4]. Using the reciprocity principle, this intrinsic SNR is: 4FrR where co is the Larmor frequency, g is the magnetic permeability of the sample, Mo is the total transverse nuclear magnetic moment in a 1 ml sample, H is the right hand circularly polarized component of the magnetic field ....

W. A. Edelstein, G. H. Glover, C. J. Hardy, and R. W. Redington, "The intrinsic signal-to-noise ratio in NMR imaging," Magn Reson Med, vol. 3, pp. 604-18., 1986.

....of x ray and gamma rays, by considering the e ects of both quantum noise and object variability. A pioneer work is reported in reference [19] on the speckle statistics in medical ultrasound images in which the rst order and the second order statistics received intensive treatment. References [21, 26] study the intrinsic signal to noise ratio and noise power spectrum for MR imaging, both object variability and thermal noise are considered and evaluated theoretically. Reference [24] conducts a comparative work for evaluating several statistical approaches in MR imaging, in which intensive real ....

W. A. Edelstein, G. H. Glover, and R. W. Redington, \The intrinsic signal-to-noise ratio in NMR imaging," Magn. Reson. Med. 3, pp. 604-618, 1986.

....I denote indicator functions for the fieldof view and the ROI respectively (see Fig. 3) The contrast of the MRI image is given by where Under the assumptions that the MRI scanner has spaceinvariant Gaussian point spread function and that the measurement noise is additive zero mean white Gaussian [26] we have the following representation for the MRI measurements I (5) where I (6) 7) and in (6) the 2 D convolution is denoted by Note that the full width half max (FWHM) spatial resolution of the MRI scanner is proportional to the width of the symmetric (2D) Gaussian shaped point spread ....

W. A. Edelstein, G. H. Glover, C. J. Hardy, and R. W. Redington, "Intrinsic signal to noise ratio in NMR imaging," Magn. Reson. Medicine, vol. 3, pp. 606--618, 1986.

.... order 1 (30) For an arrangement of K coils, the coefficients, C n , are given by C n = Gamma K X k=1 I k R Gamma(n 1) k sin k P 1 n 1 (cos k ) 17] The field at the origin, B r = B z (R = 0) can be written as B r = 2 K X k=1 I k a 2 k (a 2 k z 2 k ) 3=2 : [18] The coil sizes, positions, and currents are chosen so the first N Gamma 1 coefficients are zero, C 1 = C 2 = Delta Delta Delta = CN Gamma1 = 0. We refer to the index of the first nonzero coefficient, N , as the order of the field. The resulting magnetic field magnitude varies as R N . ....

....these large coils bulky, but most of the magnetic field energy is wasted. The energy stored in the imaging volume is only about (0:2=2) 3 = 0:1 of the total energy. This makes it difficult to implement this design. For example, assume the coil cross sectional area is A = 20 cm 2 . Using Eq. [18], the current required to operate at 1 MHz is I = 26,000 Amp turns. The total power dissipation given by Eq. 1] is 74 kW, so the power supply is likely to be very expensive. The coils would also be very difficult to move since the windings alone would weigh 112 kg (246 lbs) apiece. Cooling might ....

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W. Edelstein, G. Glover, C. Hardy, and R. Redington, The Intrinsic Signalto -Noise Ratio in NMR Imaging. Magn. Reson. Med. 3, 604--618 (1986).

....the ROI R , respectively (see Fig. 3) The contrast of the MRI image is given by CROI Gamma CBG , where CROI ; CBG 0. Under the assumptions that the MRI scanner has space invariant Gaussian point spread function H(x; y) and that the measurement noise is additive zero mean white Gaussian [26] with power spectrum density oe 2 n , we have the following representation for the MRI measurements YM (x; y) I s (x; y) x; y) 8(x; y) 2 R f (5) where I s (x; y) I H ) x; y) 6) H(x; y) 1 2 oe 2 s exp Gamma x 2 y 2 2oe 2 s (7) CSPL REPORT ....

W. A. Edelstein, G. H. Glover, C. J. Hardy, and R. W. Redington, "Intrinsic signal to noise ratio in NMR imaging," Magnetic Resonance in Medicine, vol. 3, pp. 606--618, 1986.

....by interest in high resolution (spatial and or temporal) MRI for applications such as angiography, functional MRI, and myocardial perfusion imaging. The relevance of this problem is also attested to by the fact that low SNR is the subject of a large number of papers in the MRI literature, e.g. [2, 3, 4, 5, 6, 7, 8, 9, 10]. Hence, we are interested in studying noise reduction methods for MRI. Magnetic resonance (MR) image reconstruction data are commonly modeled by the Rician distribution [7, 5] and we assume this model throughout the paper, unless otherwise noted. The Rician model is widely accepted in the MRI ....

....Im denote the real and imaginary components of the data. The measurements can be decomposed into a signal and noise component Y ( S( N( where S( is the signal of interest and N( is a complex Gaussian white noise. The noise is primarily due to thermal noises in the patient [3, 4, 8, 14]. 3 The measurement space is also commonly referred to as k space in the literature [7] The most common reconstruction technique in MRI is to compute the inverse discrete Fourier transform (DFT) of the raw data Y [7, 11] Let y denote the inverse DFT of Y . Due to phase errors which are ....

W. A. Edelstein, G. Glover, C. Hardy, and R. Redington, "The intrinsic signal-to-noise ratio in NMR imaging," Magn. Reson. Med., vol. 3, pp. 604--618, 1986.

....(2) where yn ( P k a nk k r n and a nk are the elements of system matrix, r n is the acquisition background radiation term, j represents the equivalence due to a term independent of . We assume that the MRI has additive electrical noise, which can be modeled as white Gaussian noise[7], and different regions have different intensities. If MRI is segmented using simple pixel by pixel thresholds, then the log likelihood for l k given l k is: L( ljl) P p k=1 log P ( l k jl k ) where P ( l k jl k ) is the probability of assigning the label l k to the kth pixel ....

W.A. Edelstein, G.H. Clover, C.J. Hardy, and R.W. Redington, "The Intrinsic Signal to Noise Ratio in NMR Imaging", Magnetic Resonance in Medicine, Vol. 3, pp. 606-618, 1986.

.... ; x; y) 2 IR 2 : 4) Function s (x; y) r (x; y) k(x; y) is the smoothed image resulting from the convolution operation (which approximates the finite resolution of the physical system) The point response k(x; y) is approximated by a 2D symmetric Gaussian hill of variance oe 2 s as in [6]; i.e. k(x; y) 1 2 oe 2 s exp Gamma(x 2 y 2 ) 2oe 2 s : 5) 2.3. Fisher Information and C R Bound The Cramer Rao bound gives an expression for the minimum mean squared error or, equivalently, covariance of any estimator of parameter vector . In the unbiased case, where E[ ....

W.A. Edelstein. Intrinsic signal to noise ratio in nmr imaging. Magnetic Resonance in Medicine, 1986.

....( ffl p;n;i ; where the additive measurement error ffl p;n;i has a Gaussian distribution with (possibly unknown) variance oe 2 . In MR imaging, the source of this noise is thermally generated, randomly fluctuating noise currents in the body which are picked up by the receiving antenna, [36] so it is correct to assume that the measurement errors are Gaussian and independent. It is convenient to group the ideal projection and measurement samples in the different ways defined below. First group the samples by rows: y p;n 4 = y p;n;1 ; y p;n;W ] 0 ; s p;n ( 4 = s p ....

W. A. Edelstein, G. H. Glover, C. J. Hardy, and R. W. Redington, "The intrinsic signal-to-noise ratio in NMR Imaging," Magnetic Resonance in Medicine, vol. 3, pp. 606--618, 1986.

....boundary. Side information is extracted from the MRI image using ML estimation of [4] i.e. argmax ln f(YM ; 2) We model the MRI scanner as a linear, spatially shift invariant system with a symmetric Gaussian 2D impulse response h(x; y) and with additive white Gaussian noise [5]. These system and noise models lead to the following Gaussian model for MRI image YM : YM = I( H N (3) where matrix I( is the true MRI image containing boundary , H contains samples of h(x; y) at pixel centers, N contains IID white noise, and operator denotes 2D matrix convolution. ....

W.A. Edelstein. Intrinsic signal to noise ratio in NMR imaging. Magnetic Resonance in Medicine, 1986.

....common assumptions about the magnetic resonance imaging system: it is linear and spatially invariant, its point spread function is Gaussian, and the source of noise is additive thermal noise introduced solely by the electronic instrumentation. This noise is well modeled by white Gaussian noise [4]. Under this model, the magnetic resonance image I corresponding to a proton spin density I true is I(x; y) I true (x; y) G(x; y) N (x; y) 1) where the point spread function G is given by G(x; y) 1 p 2 oe s e Gamma(x 2 y 2 ) 2 oe 2 s ; N is a zero mean spatial white noise ....

W.A. Edelstein. Intrinsic signal to noise ratio in NMR imaging. Magnetic Resonance in Medicine, 1986.

....the ROI R , respectively (see Fig. 3) The contrast of the MRI image is given by CROI Gamma CBG , where CROI ; CBG 0. Under the assumptions that the MRI scanner has space invariant Gaussian point spread function H(x; y) and that the measurement noise is additive zero mean white Gaussian [26] we have the following representation for the MRI measurements YM (x; y) I s (x; y) x; y) 8(x; y) 2 R f (5) where I s (x; y) I H ) x; y) 6) H(x; y) 1 2 oe 2 s exp Gamma x 2 y 2 2oe 2 s (7) and in (6) the 2 dimensional convolution is denoted by ....

W. A. Edelstein, G. H. Glover, C. J. Hardy, and R. W. Redington, "Intrinsic signal to noise ratio in NMR imaging," Magnetic Resonance in Medicine, vol. 3, pp. 606--618, 1986.

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W.A. Edelstein. Intrinsic signal to noise ratio in nmr imaging. Magnetic Resonance in Medicine, 1986.

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W. A. Edelstein, G. Glover, C. Hardy, and R. Redington. The intrinsic signal-to-noise ratio in NMR imaging. Magn. Reson. Med., 3:604--618, 1986.

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