Gregory Lemberskiy^{1,2}, Steven Baete^{1}, Jelle Veraart^{1}, Timothy M. Shepherd^{1}, Els Fieremans^{1}, and Dmitry S Novikov^{1}

^{1}New York University School of Medicine, New York, NY, United States, ^{2}Microstructure Imaging INC, New York, NY, United States

We develop random matrix theory (RMT)-based MRI image reconstruction able to increase SNR by up to 10-fold, and to radically increase resolution for routine clinical acquisitions. RMT offers an objective criterion for separating signal from noise across all coils, voxels and MRI contrasts, by utilizing the redundancy in MRI measurements. We demonstrate RMT on a 0.8x0.8x0.8 mm^{3} neuro exam that includes a series of
multiple T2w, T1w, diffusion, and fMRI images on a 3T clinical scanner. RMT can serve as a paradigm for reconstructing multiple contrasts, enhancing image quality for low-field scanners, increasing MR value, and improving biomarker precision.

RMT identifies

Contrary to previous approaches

The distribution (1) relies on uncorrelated noise. Hence, we apply RMT after coil noise decorrelation and phase-unwinding, and before k-space filling, since standard k-space filling techniques

**Diffusion at different resolutions**(Fig.1-3): A 3-slice brain slab from a 31 y/o female volunteer was acquired with different isotropic resolutions [0.8,0.9,1.0,1.5,2.0] mm (original SNR = [2.5,3.1,4.0,7.9,14.9] at $$$b=0$$$), $$$T_R=3$$$s,$$$\,T_E=132$$$ms, with 8 $$$b$$$-shells [0,250,500,1000,2000,3000,4000,5000] along [1,6,6,12,20,30,30,40] directions, respectively. Scan time was 7min per resolution.

**Multimodal protocol at $$$0.8\times0.8\times0.8$$$mm resolution**(Fig.4-5): A 5-slice segment of the brain from a 28 y/o male volunteer with various contrasts was acquired through the hand knob of the precentral gyrus, using GRAPPA^{10 }$$$R=2$$$, pFourier 6/8 with POCS (original SNR 3.31 at $$$b=0$$$). Total scan time was 12:30. There were $$$N_m=256$$$ total measurements [70 SE diffusion ($$$10 b = 0, 20 b = 1000, 40 b = 2000$$$), 13 SE IR images for $$$T_1$$$ mapping ($$$T_R=4000\,$$$ms, $$$T_E=77$$$, $$$BW = 1125.2$$$ Hz/pix, $$$T_I=[33-2000]$$$), 13 SE images for $$$T_2$$$ mapping ($$$T_R=4000$$$,$$$\,T_E=[80-200]$$$), and 160 GE images for a right index finger tapping fMRI ($$$T_R=1000$$$ms, $$$T_E=39$$$ms, FA$$$=62^\circ$$$, using 8 on/off 20s epochs). The standard protocol at 2.4 mm resolution was generated by using 1/3 of the k-space in each dimension.

All images were aligned using TOPUP

Fig.2: RMT recovers high-$$$b$$$ diffusion images from under the noise floor, down to $$$0.8\times0.8\times0.8$$$ voxels, yielding at least $$$5\times$$$ noise reduction.

Fig.3: RMT provides up to $$$10\times$$$ precision increase for mean diffusivity. Moreover, RMT successfully removes the noise-floor bias in both MD and RK, where mean values at high and low match.

Fig.4: RMT increases temporal SNR over $$$5\times$$$ for task-fMRI, enabling unprecedented $$$0.8\times0.8\times0.8$$$ voxels at 3T. The fMRI time-courses (normalized by their mean values) show clear noise reduction, with the full-protocol RMT reconstruction yielding the highest gain in precision.

Fig.5: RMT reaches its fullest potential on a multimodal neuro protocol, where information is shared between contrasts. Indeed, the number $$$P$$$ of information-carrying components outside of the distribution (1) after full-protocol-RMT is notably smaller than the sum of $$$P$$$ from RMT on individual modalities (fMRI, diffusion, etc).

- By objectively identifying the low-rank structure
^{12,21-25}across all MRI contrasts/voxels/coils, RMT reconstruction unlocks an untapped $$$\sim10\times$$$ SNR reserve, essentially for free. - RMT prompts acquiring all clinically necessary contrasts with the same highest possible resolution and jointly denoise all of them, whereby each measurement alone would drown in noise.
- RMT is complementary to hardware improvements (high field, multi-coils, strong gradients). It can further improve image quality for low-field scanners reducing cost and increasing MRI value.
- RMT has potential to enhance the performance of modern acquisitions and reconstruction algorithms, and increase accuracy and precision of imaging biomarkers lowering sample sizes for human studies.
- RMT reveals information content of MRI, and serves as a paradigm to combine multiple contrasts, without relying on priors or training data.

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