Obtaining sparse distributions in 2D inverse problems

Reci, Andi; Sederman, Andrew J.; Gladden, Lynn F.

doi:10.1016/j.jmr.2017.05.010

Cited by 27 publications

(22 citation statements)

References 66 publications

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“…An important factor is that NTGV regularization is a two-parameter regularization technique, as opposed to TV regularization and NN regularization which For completeness, the 3D T 2 maps obtained from the T 2 -weighted images are now considered. Each pixel in the 3D image is assigned a T 2 distribution by using L 1 regularization [43] to convert the decay of the pixel intensity into a T 2 distribution. As this step is not the focus of the paper, only an example is presented; the optimisation of the L 1 regularization technique is not considered.…”

Section: Resultsmentioning

confidence: 99%

Accelerating the estimation of 3D spatially resolved T2 distributions

Reci

Kort

Sederman

et al. 2018

Journal of Magnetic Resonance

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Obtaining quantitative, 3D spatially-resolved T distributions (T maps) from magnetic resonance data is of importance in both medical and porous media applications. Due to the long acquisition time, there is considerable interest in accelerating the experiments by applying undersampling schemes during the acquisition and developing reconstruction techniques for obtaining the 3D T maps from the undersampled data. A multi-echo spin echo pulse sequence is used in this work to acquire the undersampled data according to two different sampling patterns: a conventional coherent sampling pattern where the same set of lines in k-space is sampled for all equally-spaced echoes in the echo train, and a proposed incoherent sampling pattern where an independent set of k-space lines is sampled for each echo. The conventional reconstruction technique of total variation regularization is compared to the more recent techniques of nuclear norm regularization and Nuclear Total Generalized Variation (NTGV) regularization. It is shown that best reconstructions are obtained when the data acquired using an incoherent sampling scheme are processed using NTGV regularization. Using an incoherent sampling pattern and NTGV regularization as the reconstruction technique, quantitative results are obtained at sampling percentages as low as 3.1% of k-space, corresponding to a 32-fold decrease in the acquisition time, compared to a fully sampled dataset.

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Section: Resultsmentioning

confidence: 99%

Accelerating the estimation of 3D spatially resolved T2 distributions

Reci

Kort

Sederman

et al. 2018

Journal of Magnetic Resonance

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“…Most regularization methods employ the ℓ 2 norm, ie Tikhonov regularization 52 with p = 2, and L is the identity matrix 12,16,17,22,25 ; however, there are cases where the ℓ 1 norm is preferable. [53][54][55] The regularization term forces neighboring points in f α ð Þ…”

Section: And the Kernel Matrix Asmentioning

confidence: 99%

Multidimensional correlation MRI

Benjamini

Basser

2020

NMR in Biomedicine

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Multidimensional correlation spectroscopy is emerging as a novel MRI modality that is well suited for microstructure and microdynamic imaging studies, especially of biological specimens. Conventional MRI methods only provide voxel‐averaged and mostly macroscopically averaged information; these methods cannot disentangle intra‐voxel heterogeneity on the basis of both water mobility and local chemical interactions. By correlating multiple MR contrast mechanisms and processing the data in an integrated manner, correlation spectroscopy is able to resolve the distribution of water populations according to their chemical and physical interactions with the environment. The use of a non‐parametric, phenomenological representation of the multidimensional MR signal makes no assumptions about tissue structure, thereby allowing the study of microscopic structure and composition of complex heterogeneous biological systems. However, until recently, vast data requirements have confined these types of measurement to non‐localized NMR applications and prevented them from being widely and successfully used in conjunction with imaging. Recent groundbreaking advancements have allowed this powerful NMR methodology to be migrated to MRI, initiating its emergence as a promising imaging approach. This review is not intended to cover the entire field of multidimensional MR; instead, it focuses on pioneering imaging applications and the challenges involved. In addition, the background and motivation that have led to multidimensional correlation MR development are discussed, along with the basic underlying mathematical concepts. The goal of the present work is to provide the reader with a fundamental understanding of the techniques developed and their potential benefits, and to provide guidance to help refine future applications of this technology.

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“…To date, the L1 regularization problem Equation (A10) in NMR data inversion has been solved by a one-step iterative algorithm whose solution is only affected by the solution of the previous step at each iteration, such as the IST algorithm and the primal-dual hybrid gradient algorithm [26,27]. To improve the inversion speed, we used a TIST algorithm [28,39] to solve the objective function Equation (A10).…”

Section: Appendix Amentioning

confidence: 99%

Nuclear Magnetic Resonance T1–T2 Spectra in Heavy Oil Reservoirs

et al. 2019

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Low-field nuclear magnetic resonance (NMR) has been widely used in the petroleum industry for reservoir evaluation. Fluid properties and petrophysical parameters can be determined from NMR spectra, obtained from processing echo data measured from the NMR tool. The more accurate NMR spectra are, the higher the reliability of reservoir evaluation based on NMR logging is. The purpose of this paper is to obtain more precise T1–T2 spectra in heavy oil reservoirs, with focus on the T1–T2 data acquisition and inversion. To this end, four inversion algorithms were tested on synthetic T1–T2 data, their precision was evaluated and the optimal inversion algorithm was selected. Then, the sensitivity to various acquisition parameters (wait time and echo spacing) was evaluated with T1–T2 experiments using a disordered accumulation of glass beads with a diameter of 45 μm saturated with heavy oil and distilled water. Finally, the sensitivity to various inversion parameters (convergence tolerance, maximum number of iterations and regularization parameter) was evaluated using the optimal inversion algorithm. The results showed that the inverted T1–T2 spectra loss some relaxation information when the number of echo train is less than 7. The peak of the heavy oil signal gradually moves along the direction of increase in the T2 and the intensity of the heavy oil signal gradually decreases with increasing echo spacing. The echo spacing should be as small as possible for T1–T2 measurements in heavy oil reservoirs on the premise that the NMR instrument operates normally. A convergence tolerance that is too large or a maximum number of iterations that is too small may result in exiting the iteration prematurely during the inversion. A convergence tolerance of 1 × 10−7 and a maximum number of iterations of 30,000 are recommended for the inversion of the T1–T2 spectra. An appropriate regularization parameter is an important factor for obtaining accurate T1–T2 spectra from the optimal inversion algorithm.

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Obtaining sparse distributions in 2D inverse problems

Cited by 27 publications

References 66 publications

Accelerating the estimation of 3D spatially resolved T2 distributions

Accelerating the estimation of 3D spatially resolved T2 distributions

Multidimensional correlation MRI

Nuclear Magnetic Resonance T1–T2 Spectra in Heavy Oil Reservoirs

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