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Correlation between k ‐space sampling pattern and MTF in compressed sensing MRSI
Author(s) -
Heikal A. A.,
Wachowicz K.,
Fallone B. G.
Publication year - 2016
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.4962930
Subject(s) - undersampling , sampling (signal processing) , optical transfer function , imaging phantom , compressed sensing , nyquist frequency , computer science , physics , optics , algorithm , artificial intelligence , computer vision , detector , filter (signal processing)
Purpose To investigate the relationship between the k ‐space sampling patterns used for compressed sensing MR spectroscopic imaging (CS‐MRSI) and the modulation transfer function (MTF) of the metabolite maps. This relationship may allow the desired frequency content of the metabolite maps to be quantitatively tailored when designing an undersampling pattern. Methods Simulations of a phantom were used to calculate the MTF of Nyquist sampled (NS) 32 × 32 MRSI, and four‐times undersampled CS‐MRSI reconstructions. The dependence of the CS‐MTF on the k ‐space sampling pattern was evaluated for three sets of k ‐space sampling patterns generated using different probability distribution functions (PDFs). CS‐MTFs were also evaluated for three more sets of patterns generated using a modified algorithm where the sampling ratios are constrained to adhere to PDFs. Results Strong visual correlation as well as high R 2 was found between the MTF of CS‐MRSI and the product of the frequency‐dependant sampling ratio and the NS 32 × 32 MTF. Also, PDF‐constrained sampling patterns led to higher reproducibility of the CS‐MTF, and stronger correlations to the above‐mentioned product. Conclusions The relationship established in this work provides the user with a theoretical solution for the MTF of CS MRSI that is both predictable and customizable to the user's needs.