arXiv subjects

Charles Millard

Publications and source records attributed to Charles Millard.

6 recordsLinked to original sources

arXiv2026

Optimized Multi-Contrast Self-Supervised MRI Reconstruction using Learned k-space Partitioning

Objective: Deep Learning has shown promise in accelerating MRI by reconstructing high-quality images from under-sampled data. While recent work has leveraged multi-contrast information to improve reconstruction performance, these methods rely on supervised learning, which requires fully sampled k-space for training. One method, self-supervised learning via data undersampling (SSDU), enables direct training on under-sampled k-space by partitioning it into two sets, with a network mapping between the two. In this work, we improve MRI self-supervised MRI reconstruction with two modifications. Methods: We propose a multi-contrast self-supervised learning framework that jointly trains on multiple under-sampled contrasts without requiring fully sampled k-space data as a reference. Moreover, we learn an optimal self-supervised data partitioning for each contrast in an end-to-end manner, further enhancing reconstruction quality. Specifically, we learn an optimal partitioning probability distribution, which is sampled to generate a mask for partitioning. Results: Experiments on two publicly available multi-contrast MRI datasets demonstrate the improved reconstruction quality of our proposed self-supervised multi-contrast learned partitioning method compared to the current single-contrast self-supervised learning methods. We also demonstrate that learning the partitioning of k-space data further enhances the fidelity of reconstructions. Conclusion: Multi-contrast reconstruction combined with learned partitioning improves reconstruction fidelity over single-contrast self-supervised MRI reconstructions. Significance: Our method can facilitate higher image fidelity and/or accelerated MRI protocol times compared to previous self-supervised methods, and without requiring fully sampled k-space for training.

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arXiv2022

Clean self-supervised MRI reconstruction from noisy, sub-sampled training data with Robust SSDU

Most existing methods for Magnetic Resonance Imaging (MRI) reconstruction with deep learning use fully supervised training, which assumes that a high signal-to-noise ratio (SNR), fully sampled dataset is available for training. In many circumstances, however, such a dataset is highly impractical or even technically infeasible to acquire. Recently, a number of self-supervised methods for MR reconstruction have been proposed, which use sub-sampled data only. However, the majority of such methods, such as Self-Supervised Learning via Data Undersampling (SSDU), are susceptible to reconstruction errors arising from noise in the measured data. In response, we propose Robust SSDU, which provably recovers clean images from noisy, sub-sampled training data by simultaneously estimating missing k-space samples and denoising the available samples. Robust SSDU trains the reconstruction network to map from a further noisy and sub-sampled version of the data to the original, singly noisy and sub-sampled data, and applies an additive Noisier2Noise correction term at inference. We also present a related method, Noiser2Full, that recovers clean images when noisy, fully sampled data is available for training. Both proposed methods are applicable to any network architecture, straight-forward to implement and have similar computational cost to standard training. We evaluate our methods on the multi-coil fastMRI brain dataset with a novel denoising-specific architecture and find that it performs competitively with a benchmark trained on clean, fully sampled data.

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arXiv2022

A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noise

In recent years, there has been attention on leveraging the statistical modeling capabilities of neural networks for reconstructing sub-sampled Magnetic Resonance Imaging (MRI) data. Most proposed methods assume the existence of a representative fully-sampled dataset and use fully-supervised training. However, for many applications, fully sampled training data is not available, and may be highly impractical to acquire. The development and understanding of self-supervised methods, which use only sub-sampled data for training, are therefore highly desirable. This work extends the Noisier2Noise framework, which was originally constructed for self-supervised denoising tasks, to variable density sub-sampled MRI data. We use the Noisier2Noise framework to analytically explain the performance of Self-Supervised Learning via Data Undersampling (SSDU), a recently proposed method that performs well in practice but until now lacked theoretical justification. Further, we propose two modifications of SSDU that arise as a consequence of the theoretical developments. Firstly, we propose partitioning the sampling set so that the subsets have the same type of distribution as the original sampling mask. Secondly, we propose a loss weighting that compensates for the sampling and partitioning densities. On the fastMRI dataset we show that these changes significantly improve SSDU's image restoration quality and robustness to the partitioning parameters.

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arXiv2022

Tuning-free multi-coil compressed sensing MRI with Parallel Variable Density Approximate Message Passing (P-VDAMP)

Magnetic Resonance Imaging (MRI) has excellent soft tissue contrast but is hindered by an inherently slow data acquisition process. Compressed sensing, which reconstructs sparse signals from incoherently sampled data, has been widely applied to accelerate MRI acquisitions. Compressed sensing MRI requires one or more model parameters to be tuned, which is usually done by hand, giving sub-optimal tuning in general. To address this issue, we build on previous work by the authors on the single-coil Variable Density Approximate Message Passing (VDAMP) algorithm, extending the framework to multiple receiver coils to propose the Parallel VDAMP (P-VDAMP) algorithm. For Bernoulli random variable density sampling, P-VDAMP obeys a "state evolution", where the intermediate per-iteration image estimate is distributed according to the ground truth corrupted by a zero-mean Gaussian vector with approximately known covariance. To our knowledge, P-VDAMP is the first algorithm for multi-coil MRI data that obeys a state evolution with accurately tracked parameters. We leverage state evolution to automatically tune sparse parameters on-the-fly with Stein's Unbiased Risk Estimate (SURE). P-VDAMP is evaluated on brain, knee and angiogram datasets and compared with four variants of the Fast Iterative Shrinkage-Thresholding algorithm (FISTA), including two tuning-free variants from the literature. The proposed method is found to have a similar reconstruction quality and time to convergence as FISTA with an optimally tuned sparse weighting and offers substantial robustness and reconstruction quality improvements over competing tuning-free methods.

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arXiv2020

An Approximate Message Passing Algorithm for Rapid Parameter-Free Compressed Sensing MRI

For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance Imaging (MRI), where Fourier coefficients of a natural image are sampled with variable density, AMP encounters convergence problems. In response we present an algorithm based on Orthogonal AMP constructed specifically for variable density partial Fourier sensing matrices. For the first time in this setting a state evolution has been observed. A practical advantage of state evolution is that Stein's Unbiased Risk Estimate (SURE) can be effectively implemented, yielding an algorithm with no free parameters. We empirically evaluate the effectiveness of the parameter-free algorithm on simulated data and find that it converges over 5x faster and to a lower mean-squared error solution than Fast Iterative Shrinkage-Thresholding (FISTA).

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arXiv2020

Approximate Message Passing with a Colored Aliasing Model for Variable Density Fourier Sampled Images

The Approximate Message Passing (AMP) algorithm efficiently reconstructs signals which have been sampled with large i.i.d. sub-Gaussian sensing matrices. Central to AMP is its "state evolution", which guarantees that the difference between the current estimate and ground truth (the "aliasing") at every iteration obeys a Gaussian distribution that can be fully characterized by a scalar. However, when Fourier coefficients of a signal with non-uniform spectral density are sampled, such as in Magnetic Resonance Imaging (MRI), the aliasing is intrinsically colored, AMP's scalar state evolution is no longer accurate and the algorithm encounters convergence problems. In response, we propose the Variable Density Approximate Message Passing (VDAMP) algorithm, which uses the wavelet domain to model the colored aliasing. We present empirical evidence that VDAMP obeys a "colored state evolution", where the aliasing obeys a Gaussian distribution that can be fully characterized with one scalar per wavelet subband. A benefit of state evolution is that Stein's Unbiased Risk Estimate (SURE) can be effectively implemented, yielding an algorithm with subband-dependent thresholding that has no free parameters. We empirically evaluate the effectiveness of VDAMP on three variations of Fast Iterative Shrinkage-Thresholding (FISTA) and find that it converges in around 10 times fewer iterations on average than the next-fastest method, and to a comparable mean-squared-error.

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