Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals

Barkhuijsen, H.; Beer, R. de; Ormondt, D. van

doi:10.1016/0022-2364(87)90023-0

Cited by 238 publications

(239 citation statements)

References 3 publications

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“…Let F be the (N × N) unitary matrix corresponding to the DFT, and let K be the (M × N) projection matrix which shortens an N-element vector to its first M elements. Then [8] and [9] where † denotes the Hermitian transpose; F † corresponds to the IDFT and K † corresponds to zero-filling.…”

Section: Minimum L 1 -Norm Reconstructionmentioning

confidence: 99%

“…Re-writing Eq. [9] in operator notation, [10] where trunc(x) = zerofill(shorten(x)) is the operation of setting the elements x M , ..., x N-1 to zero. Now we are in a position to see the unexpected relationship between the gradient of Q and the operations of IST.…”

Section: Relationship Of Ist To Minimum L 1 -Norm Reconstructionmentioning

confidence: 99%

“…Procedures adopted from fields outside of NMR have proven to be superior to the discrete Fourier transform (DFT) [1,2]; examples include maximum entropy (MaxEnt) [3,4] and minimum-area [5] reconstruction, maximum likelihood reconstruction (MLM) [6,7], and matrix methods such as LPSVD [8] and HSVD [9]. A method that is conceptually simpler and easier to implement than these methods is iterative thresholding [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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NMR data processing using iterative thresholding and minimum l1-norm reconstruction

Stern¹,

Donoho

Hoch

2007

Journal of Magnetic Resonance

128

118

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Iterative thresholding algorithms have a long history of application to signal processing. Although they are intuitive and easy to implement, their development was heuristic and mainly ad hoc. Using a special form of the thresholding operation, called soft thresholding, we show that the fixed point of iterative thresholding is equivalent to minimum l 1 -norm reconstruction. We illustrate the method for spectrum analysis of a time series. This result helps to explain the success of these methods and illuminates connections with maximum entropy and minimum area methods, while also showing that there are more efficient routes to the same result. The power of the l 1 -norm and related functionals as regularizers of solutions to underdetermined systems will likely find numerous useful applications in NMR.

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Section: Minimum L 1 -Norm Reconstructionmentioning

confidence: 99%

Section: Relationship Of Ist To Minimum L 1 -Norm Reconstructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

NMR data processing using iterative thresholding and minimum l1-norm reconstruction

Stern¹,

Donoho

Hoch

2007

Journal of Magnetic Resonance

128

118

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“…After finding the uncompensated gradient eddy currents EC 0 () at various delay times , a Levenberg-Marquardt least-squares fitting routine is used to estimate the three exponential constants to be used for fitting subsequent FIDs. The initial values of the time constants may be obtained using the space-state singular value decomposition method (18). Once the three exponential constants are found, these values are downloaded to the preemphasis unit and held constant for the remainder of the procedure.…”

Section: Methodsmentioning

confidence: 99%

Automatic gradient preemphasis adjustment: A 15‐minute journey to improved diffusion‐weighted echo‐planar imaging

Schmithorst

Dardzinski

2001

Magnetic Resonance in Med

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Image distortion caused by gradient eddy currents is a major problem in the use of diffusion tensor imaging (DTI), as using the uncorrected images for calculation of apparent diffusion coefficient (ADC) and diffusion anisotropy will result in areas of artificially increased anisotropy and ADC at the edge of the images, as well as decreased spatial resolution and accuracy in ADC computations overall. This distortion may be substantially reduced by careful adjustment of the gradient preemphasis unit. A completely automatic method of adjusting the preemphasis unit is proposed which finds the optimal settings for all three gradient directions in approximately 15 min by estimating the magnitudes of the eddy currents at various delay times after a test gradient. The pixel shifts in a 64 ؋ 128 echo-planar diffusion-weighted image with a diffusion gradient strength of 30 mT/m were reduced to less than 0. Geometric distortion resulting from gradient eddy currents is a major source of image artifacts in diffusion-weighted echo-planar imaging (DW-EPI). Depending on the direction of the diffusion gradient relative to the image plane, the distortion will consist of shearing, stretching, or shift in the phase-encoding direction. Because the diffusionweighted images are misaligned relative to images acquired without diffusion gradients, computed parameter maps such as apparent diffusion coefficient (ADC) or diffusion anisotropy maps will suffer from degraded resolution, lower accuracy, and visible areas of artificially increased ADC and anisotropy around the edges of the object. While the use of actively shielded gradients has greatly reduced the magnitude of eddy currents, significant distortion often still remains in DW-EPI images, which becomes more severe at higher field strengths.Methods proposed for distortion correction include: postacquisition image warping (1,2), modifications of the DW-EPI pulse sequence (3-5), acquisition of calibration scans (6 -10), and gradient preemphasis calibration (11). Gradient preemphasis calibration offers the significant advantage of eliminating the need for time-consuming image postprocessing, thereby allowing the use of diffusionweighted imaging (DWI) and diffusion tensor imaging (DTI) in clinical settings. Additionally, by minimizing image distortion associated with gradient eddy currents during the image acquisition, postprocessing to remove any remaining distortion should result in near-perfect coregistration of the diffusion-weighted images.Very accurate preemphasis and B 0 corrections are necessary to adequately correct for all image distortions in DW-EPI. For a typical 3 Tesla DW-EPI single-shot acquisition time of 60 ms and a field of view (FOV) of 20 cm, 10 cm from the isocenter, a gradient eddy current of 4 T/m, or a B 0 offset of 0.4 T, will produce an image shift of one pixel. The pixel shift is equal to the number of revolutions of dephasing over the acquisition time according to the Fourier shift theorem. For a typical diffusion gradient strength of 40 mT/m, the preemphasis...

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“…In the method called HSVD, 47,46 an estimate of the matrix Q is obtained by solving eqn (12) in an LS sense. The eigenvalues of the latter matrix are the estimates ẑ k , k = 1, …, K, of the signal poles.…”

Section: Quantitation Algorithmsmentioning

confidence: 99%

MR spectroscopy quantitation: a review of time‐domain methods

et al. 2001

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In this article an overview of time-domain quantitation methods is given. Advantages of processing the data in the measurement domain are discussed. The basic underlying principles of the methods are outlined and from them the situations under which these algorithms perform well are derived. Also an overview of methods to preprocess the data is given. In that respect, signal-to-noise and/or resolution enhancement, the removal of unwanted components and corrections for model imperfections are discussed.

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Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals

Cited by 238 publications

References 3 publications

NMR data processing using iterative thresholding and minimum l1-norm reconstruction

NMR data processing using iterative thresholding and minimum l1-norm reconstruction

Automatic gradient preemphasis adjustment: A 15‐minute journey to improved diffusion‐weighted echo‐planar imaging

MR spectroscopy quantitation: a review of time‐domain methods

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