From 3d0832d1a1c4b27ed833d8c66600ca37e55f3dee Mon Sep 17 00:00:00 2001 From: Alba Collocott Date: Sun, 19 Oct 2025 09:48:51 +0200 Subject: [PATCH] Add The Constrained Optimization Problem In Eq --- The-Constrained-Optimization-Problem-In-Eq.md | 7 +++++++ 1 file changed, 7 insertions(+) create mode 100644 The-Constrained-Optimization-Problem-In-Eq.md diff --git a/The-Constrained-Optimization-Problem-In-Eq.md b/The-Constrained-Optimization-Problem-In-Eq.md new file mode 100644 index 0000000..b10b141 --- /dev/null +++ b/The-Constrained-Optimization-Problem-In-Eq.md @@ -0,0 +1,7 @@ +
Issue date 2021 May. To achieve extremely accelerated sub-millimeter decision T2-weighted functional MRI at 7T by developing a 3-dimensional gradient and spin echo imaging (GRASE) with internal-quantity choice and [BloodVitals SPO2](http://polyamory.wiki/index.php?title=Journal_Of_Diabetes_Science_And_Technology) variable flip angles (VFA). GRASE imaging has disadvantages in that 1) ok-space modulation causes T2 blurring by limiting the number of slices and [BloodVitals device](https://gitlab.digineers.nl/torri45x34384/painless-spo2-testing1564/issues/9) 2) a VFA scheme results in partial success with substantial SNR loss. In this work, accelerated GRASE with managed T2 blurring is developed to improve a point spread operate (PSF) and temporal signal-to-noise ratio (tSNR) with numerous slices. Numerical and experimental studies have been performed to validate the effectiveness of the proposed methodology over regular and VFA GRASE (R- and V-GRASE). The proposed methodology, while attaining 0.8mm isotropic decision, purposeful MRI in comparison with R- and V-GRASE improves the spatial extent of the excited volume as much as 36 slices with 52% to 68% full width at half most (FWHM) reduction in PSF but roughly 2- to 3-fold mean tSNR improvement, thus resulting in greater Bold activations.
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We efficiently demonstrated the feasibility of the proposed methodology in T2-weighted useful MRI. The proposed method is particularly promising for cortical layer-specific purposeful MRI. Because the introduction of blood oxygen stage dependent (Bold) contrast (1, 2), functional MRI (fMRI) has become one of the mostly used methodologies for neuroscience. 6-9), by which Bold effects originating from larger diameter draining veins may be considerably distant from the precise sites of neuronal exercise. To simultaneously achieve excessive spatial decision while mitigating geometric distortion inside a single acquisition, inner-volume choice approaches have been utilized (9-13). These approaches use slab selective excitation and refocusing RF pulses to excite voxels inside their intersection, [Blood Vitals](http://cloud4.co.kr/bbs/board.php?bo_table=data&wr_id=597838) and restrict the field-of-view (FOV), during which the required number of section-encoding (PE) steps are decreased at the identical resolution so that the EPI echo train length turns into shorter alongside the phase encoding path. Nevertheless, the utility of the inner-volume based mostly SE-EPI has been restricted to a flat piece of cortex with anisotropic decision for overlaying minimally curved gray matter area (9-11). This makes it challenging to seek out functions beyond major visual areas notably within the case of requiring isotropic high resolutions in different cortical areas.
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3D gradient and spin echo imaging (GRASE) with inner-volume choice, which applies a number of refocusing RF pulses interleaved with EPI echo trains along side SE-EPI, alleviates this problem by permitting for prolonged volume imaging with excessive isotropic resolution (12-14). One major concern of using GRASE is image blurring with a large level unfold function (PSF) in the partition route because of the T2 filtering effect over the refocusing pulse prepare (15, [monitor oxygen saturation](http://ksmart.or.kr/bbs/board.php?bo_table=free&wr_id=1986396) 16). To cut back the picture blurring, a variable flip angle (VFA) scheme (17, 18) has been integrated into the GRASE sequence. The VFA systematically modulates the refocusing flip angles with the intention to maintain the sign power all through the echo practice (19), thus increasing the Bold sign changes in the presence of T1-T2 combined contrasts (20, 21). Despite these advantages, VFA GRASE still leads to important loss of temporal SNR (tSNR) due to lowered refocusing flip angles. Accelerated acquisition in GRASE is an interesting imaging possibility to reduce both refocusing pulse and [BloodVitals SPO2](https://git.vekus.ru/lakeshaolney27) EPI prepare size at the identical time.
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In this context, accelerated GRASE coupled with picture reconstruction techniques holds great potential for both reducing image blurring or improving spatial volume alongside each partition and section encoding directions. By exploiting multi-coil redundancy in indicators, parallel imaging has been successfully applied to all anatomy of the body and [BloodVitals SPO2](http://49.232.247.99:1040/forum.php?mod=viewthread&tid=1238) works for each 2D and [BloodVitals wearable](http://kpoong.com/bbs/board.php?bo_table=free&wr_id=133681) 3D acquisitions (22-25). Kemper et al (19) explored a combination of VFA GRASE with parallel imaging to increase quantity protection. However, the limited FOV, localized by only some receiver coils, potentially causes excessive geometric factor (g-issue) values because of in poor health-conditioning of the inverse drawback by together with the large number of coils that are distant from the area of interest, thus making it challenging to realize detailed sign analysis. 2) signal variations between the same phase encoding (PE) traces throughout time introduce picture distortions during reconstruction with temporal regularization. To handle these points, Bold activation needs to be separately evaluated for each spatial and temporal traits. A time-series of fMRI photographs was then reconstructed below the framework of strong principal element analysis (ok-t RPCA) (37-40) which may resolve possibly correlated data from unknown partially correlated photographs for reduction of serial correlations.
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