High‐dimensionality undersampled patch‐based reconstruction (HD‐PROST) for accelerated multi‐contrast MRI

Abstract

Purpose To develop a new high‐dimensionality undersampled patch‐based reconstruction (HD‐PROST) for highly accelerated 2D and 3D multi‐contrast MRI. Methods HD‐PROST jointly reconstructs multi‐contrast MR images by exploiting the highly redundant information, on a local and non‐local scale, and the strong correlation shared between the multiple contrast images. This is achieved by enforcing multi‐dimensional low‐rank in the undersampled images. 2D magnetic resonance fingerprinting (MRF) phantom and in vivo brain acquisitions were performed to evaluate the performance of HD‐PROST for highly accelerated simultaneous T 1 and T 2 mapping. Additional in vivo experiments for reconstructing multiple undersampled 3D magnetization transfer (MT)‐weighted images were conducted to illustrate the impact of HD‐PROST for high‐resolution multi‐contrast 3D imaging. Results In the 2D MRF phantom study, HD‐PROST provided accurate and precise estimation of the T 1 and T 2 values in comparison to gold standard spin echo acquisitions. HD‐PROST achieved good quality maps for the in vivo 2D MRF experiments in comparison to conventional low‐rank inversion reconstruction. T 1 and T 2 values of white matter and gray matter were in good agreement with those reported in the literature for MRF acquisitions with reduced number of time point images (500 time point images, ~2.5 s scan time). For in vivo MT‐weighted 3D acquisitions (6 different contrasts), HD‐PROST achieved similar image quality than the fully sampled reference image for an undersampling factor of 6.5‐fold. Conclusion HD‐PROST enables multi‐contrast 2D and 3D MR images in a short acquisition time without compromising image quality. Ultimately, this technique may increase the potential of conventional parameter mapping.

Water–fat Dixon cardiac magnetic resonance fingerprinting

“…The singular images x estimated with this method can still present remaining undersampling artefacts and lead to noisy parametric maps. HD‐PROST reconstruction proposes to further exploit local (within a patch), non‐local (between patches in a neighborhood), and spectral (between contrasts) redundancies through high‐order low‐rank regularization . HD‐PROST reconstructs the multi‐contrast Dixon‐cMRF singular images x i for each echo i , by jointly solvingwhere P b (·) is the operator that assembles a third order tensor for the patch centered on voxel b by concatenating the K most similar patches along the non‐local similarity dimension (similar patches within a neighborhood), and the R contrasts reconstructed along the spectral dimension (singular images), whereas λ is the corresponding parameter promoting low‐rank regularization.…”

Free‐running 3D whole heart myocardial T1 mapping with isotropic spatial resolution

“…After data selection, the highly undersampled 3D radial data is reconstructed over multiple T 1 contrasts by combining a dictionary‐based low‐rank inversion to efficiently reduce the number of T 1 contrasts to be reconstructed with a recently proposed high‐dimensionality 3D patch‐based undersampled reconstruction (HD‐PROST), exploiting local (within a patch), non‐local (between similar patches), and contrast redundancies . The reconstruction for the proposed technique can be formulated as the following unconstrained Lagrangianwhere ||·|| F and ||·|| * denote the Frobenius norm and nuclear norm respectively; I is the compressed T 1 image series to be reconstructed ; is the encoding operator, with S being sensitivity maps, F being Fourier transform, U r being the low‐rank operator obtained by truncating the singular value decomposition (SVD) of a dictionary generated by Bloch simulation, A being the convolutional gridding operator, transforming Cartesian data back to 3D radial, and D being the non‐Cartesian density compensation function; K is the undersampled data; P p (·) is the patch selection operator at pixel p of a 3D multi‐contrast image set. This operator selects patches on local (patch for a given pixel location and contrast), non‐local (similar patches within a neighborhood for a given contrast) and contrast (patches from all the contrasts) scales and is a 3D tensor built by the selected patches centered at pixel p ; T represents the denoised multi‐contrast images constructed by folding and aggregating the tensors for each pixel p (see the step 2 below); Y is the Augmented Lagrangian multiplier; λ is the sparsity‐promoting regularization parameter and µ is the penalty parameter.…”

“…The details to solve the above equation can be found in Bustin et al Generally speaking, is obtained by thresholding the singular values obtained via high‐order singular value decomposition of the 3D tensor built by the patches selected from the multi‐contrast images. The thresholding parameter is defined by .…”

“…The regularization parameter λ of HD‐PROST was optimized by visual inspection of the reconstruction quality on 1 subject and used for all other data set. For the patch‐based denoising step in HD‐PROST, the following parameters were used: patch size = 5 × 5 × 5; search window = 10 × 10 × 10; patch offset = 3; number of selected similar patches = 15. The number of ADMM iterations was set to 5.…”

“…With obtained I and Y from step 1 and step 3 separately, the second step is to minimize the following equation regarding to the high order tensor  p The details to solve the above equation can be found in Bustin et al 21 Generally speaking,  p is obtained by thresholding the singular values obtained via high-order singular value decomposition of the 3D tensor built by the patches selected from the multi-contrast images. The thresholding parameter is defined by .…”