Uncertainty quantification for sparse Fourier recovery

One of the most prominent methods for uncertainty quantification in high-dimen-sional statistics is the desparsified LASSO that relies on unconstrained $\ell_1$-minimization. The majority of initial works focused on real (sub-)Gaussian designs. However, in many applications, such as magnetic resonance imaging (MRI), the measurement process possesses a certain structure due to the nature of the problem. The measurement operator in MRI can be described by a subsampled Fourier matrix. The purpose of this work is to extend the uncertainty quantification process using the desparsified LASSO to design matrices originating from a bounded orthonormal system, which naturally generalizes the subsampled Fourier case and also allows for the treatment of the case where the sparsity basis is not the standard basis. In particular we construct honest confidence intervals for every pixel of an MR image that is sparse in the standard basis provided the number of measurements satisfies $n \gtrsim\max\{ s\log^2 s\log p, s \log^2 p \}$ or that is sparse with respect to the Haar Wavelet basis provided a slightly larger number of measurements

A Plug-and-Play Approach To Multiparametric Quantitative MRI:Image Reconstruction Using Pre-Trained Deep Denoisers

Current spatiotemporal deep learning approaches to Magnetic Resonance Fingerprinting (MRF) build artefact-removal models customised to a particular k-space subsampling pattern which is used for fast (compressed) acquisition. This may not be useful when the acquisition process is unknown during training of the deep learning model and/or changes during testing time. This paper proposes an iterative deep learning plug-and-play reconstruction approach to MRF which is adaptive to the forward acquisition process. Spatiotemporal image priors are learned by an image denoiser i.e. a Convolutional Neural Network (CNN), trained to remove generic white gaussian noise (not a particular subsampling artefact) from data. This CNN denoiser is then used as a data-driven shrinkage operator within the iterative reconstruction algorithm. This algorithm with the same denoiser model is then tested on two simulated acquisition processes with distinct subsampling patterns. The results show consistent de-aliasing performance against both acquisition schemes and accurate mapping of tissues' quantitative bio-properties. Software available: https://github.com/ketanfatania/QMRI-PnP-Recon-PO

Geometry of Deep Learning for Magnetic Resonance Fingerprinting

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy storage and computation requirements of a dictionary-matching (DM) step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. In this paper we study a deep learning approach to address these shortcomings. Coupled with a dimensionality reduction first layer, the proposed MRF-Net is able to reconstruct quantitative maps by saving more than 60 times in memory and computations required for a DM baseline. Fine-grid manifold enumeration i.e. the MRF dictionary is only used for training the network and not during image reconstruction. We show that the MRF-Net provides a piece-wise affine approximation to the Bloch response manifold projection and that rather than memorizing the dictionary, the network efficiently clusters this manifold and learns a set of hierarchical matched-filters for affine regression of the NMR characteristics in each segment

Multi-shot Echo Planar Imaging for accelerated Cartesian MR Fingerprinting: An alternative to conventional spiral MR Fingerprinting.

PURPOSE: To develop an accelerated Cartesian MRF implementation using a multi-shot EPI sequence for rapid simultaneous quantification of T1 and T2 parameters. METHODS: The proposed Cartesian MRF method involved the acquisition of highly subsampled MR images using a 16-shot EPI readout. A linearly varying flip angle train was used for rapid, simultaneous T1 and T2 quantification. The results were compared to a conventional spiral MRF implementation. The acquisition time per slice was 8s and this method was validated on two different phantoms and three healthy volunteer brains in vivo. RESULTS: Joint T1 and T2 estimations using the 16-shot EPI readout are in good agreement with the spiral implementation using the same acquisition parameters (<4% deviation for T1 and <6% deviation for T2). The T1 and T2 values also agree with the conventional values previously reported in the literature. The visual qualities of fine brain structures in the multi-parametric maps generated by multi-shot EPI-MRF and Spiral-MRF implementations were comparable. CONCLUSION: The multi-shot EPI-MRF method generated accurate quantitative multi-parametric maps similar to conventional Spiral-MRF. This multi-shot approach achieved considerable k-space subsampling and comparatively short TRs in a similar manner to spirals and therefore provides an alternative for performing MRF using an accelerated Cartesian readout; thereby increasing the potential usability of MRF.The research leading to these results has received funding from the European Commission H2020 Framework Programme (H2020- MSCAITN- 2014), number 642685 MacSeNet, the Engineering and Physical Sciences Research Council (EPSRC) platform Compressed Quantitative MRI grant, number EP/M019802/1 and the Scottish Research Partnership in Engineering (SRPe) award, number SRPe PECRE1718/ 17