Rizwan Ahmad

Jeffrey Wen, Rizwan Ahmad, Philip Schniter

Accelerated magnetic resonance (MR) imaging attempts to reduce acquisition time by collecting data below the Nyquist rate. As an ill-posed inverse problem, many plausible solutions exist, yet the majority of deep learning approaches generate only a single solution. We instead focus on sampling from the posterior distribution, which provides more comprehensive information for downstream inference tasks. To do this, we design a novel conditional normalizing flow (CNF) that infers the signal component in the measurement operator's nullspace, which is later combined with measured data to form complete images. Using fastMRI brain and knee data, we demonstrate fast inference and accuracy that surpasses recent posterior sampling techniques for MRI. Code is available at https://github.com/jwen307/mri_cnf/

Hassan Iftikhar, Rizwan Ahmad, Arunark Kolipaka

The Multimodal Direct Inversion (MMDI) algorithm is widely used in Magnetic Resonance Elastography (MRE) to estimate tissue shear stiffness. However, MMDI relies on the Helmholtz equation, which assumes wave propagation in a uniform, homogeneous, and infinite medium. Furthermore, the use of the Laplacian operator makes MMDI highly sensitive to noise, which compromises the accuracy and reliability of stiffness estimates. In this study, we propose the Deep-Learning driven Inversion Framework for Shear Modulus Estimation in MRE (DIME), aimed at enhancing the robustness of inversion. DIME is trained on the displacement fields-stiffness maps pair generated through Finite Element Modelling (FEM) simulations. To capture local wave behavior and improve robustness to global image variations, DIME is trained on small image patches. We first validated DIME using homogeneous and heterogeneous datasets simulated with FEM, where DIME produced stiffness maps with low inter-pixel variability, accurate boundary delineation, and higher correlation with ground truth (GT) compared to MMDI. Next, DIME was evaluated in a realistic anatomy-informed simulated liver dataset with known GT and compared directly to MMDI. DIME reproduced ground-truth stiffness patterns with high fidelity (r = 0.99, R^2 = 0.98), while MMDI showed greater underestimation. After validating DIME on synthetic data, we tested the model in in vivo liver MRE data from eight healthy and seven fibrotic subjects. DIME preserved physiologically consistent stiffness patterns and closely matched MMDI, which showed directional bias. Overall, DIME showed higher correlation with ground truth and visually similar stiffness patterns, whereas MMDI displayed a larger bias that can potentially be attributed to directional filtering. These preliminary results highlight the feasibility of DIME for clinical applications in MRE.

Jeffrey Wen, Rizwan Ahmad, Philip Schniter

In imaging inverse problems, we would like to know how close the recovered image is to the true image in terms of full-reference image quality (FRIQ) metrics like PSNR, SSIM, LPIPS, etc. This is especially important in safety-critical applications like medical imaging, where knowing that, say, the SSIM was poor could potentially avoid a costly misdiagnosis. But since we don't know the true image, computing FRIQ is non-trivial. In this work, we combine conformal prediction with approximate posterior sampling to construct bounds on FRIQ that are guaranteed to hold up to a user-specified error probability. We demonstrate our approach on image denoising and accelerated magnetic resonance imaging (MRI) problems. Code is available at https://github.com/jwen307/quality_uq.

Matt C. Bendel, Saurav K. Shastri, Rizwan Ahmad et al.

Imaging inverse problems can be solved in an unsupervised manner using pre-trained diffusion models, but doing so requires approximating the gradient of the measurement-conditional score function in the diffusion reverse process. We show that the approximations produced by existing methods are relatively poor, especially early in the reverse process, and so we propose a new approach that iteratively reestimates and "renoises" the estimate several times per diffusion step. This iterative approach, which we call Fast Iterative REnoising (FIRE), injects colored noise that is shaped to ensure that the pre-trained diffusion model always sees white noise, in accordance with how it was trained. We then embed FIRE into the DDIM reverse process and show that the resulting "DDfire" offers state-of-the-art accuracy and runtime on several linear inverse problems, as well as phase retrieval. Our implementation is at https://github.com/matt-bendel/DDfire

Marc Vornehm, Chong Chen, Muhammad Ahmad Sultan et al.

Cardiovascular magnetic resonance imaging is a powerful diagnostic tool for assessing cardiac structure and function. However, traditional breath-held imaging protocols pose challenges for patients with arrhythmias or limited breath-holding capacity. This work aims to overcome these limitations by developing a reconstruction framework that enables high-quality imaging in free-breathing conditions for various dynamic cardiac MRI protocols. Multi-Dynamic Deep Image Prior (M-DIP), a novel unsupervised reconstruction framework for accelerated real-time cardiac MRI, is introduced. To capture contrast or content variation, M-DIP first employs a spatial dictionary to synthesize a time-dependent intermediate image. Then, this intermediate image is further refined using time-dependent deformation fields that model cardiac and respiratory motion. Unlike prior DIP-based methods, M-DIP simultaneously captures physiological motion and frame-to-frame content variations, making it applicable to a wide range of dynamic applications. We validate M-DIP using simulated MRXCAT cine phantom data as well as free-breathing real-time cine, single-shot late gadolinium enhancement (LGE), and first-pass perfusion data from clinical patients. Comparative analyses against state-of-the-art supervised and unsupervised approaches demonstrate M-DIP's performance and versatility. M-DIP achieved better image quality metrics on phantom data, higher reader scores on in-vivo cine and LGE data, and comparable scores on in-vivo perfusion data relative to another DIP-based approach. M-DIP enables high-quality reconstructions of real-time free-breathing cardiac MRI without requiring external training data. Its ability to model physiological motion and content variations makes it a promising approach for various dynamic imaging applications.

Jeffrey Wen, Rizwan Ahmad, Philip Schniter

In ill-posed imaging inverse problems, uncertainty quantification remains a fundamental challenge, especially in safety-critical applications. Recently, conformal prediction has been used to quantify the uncertainty that the inverse problem contributes to downstream tasks like image classification, image quality assessment, fat mass quantification, etc. While existing works handle only a scalar estimation target, practical applications often involve multiple targets. In response, we propose an asymptotically minimax approach to multi-target conformal prediction that provides tight prediction intervals while ensuring joint marginal coverage. We then outline how our minimax approach can be applied to multi-metric blind image quality assessment, multi-task uncertainty quantification, and multi-round measurement acquisition. Finally, we numerically demonstrate the benefits of our minimax method, relative to existing multi-target conformal prediction methods, using both synthetic and magnetic resonance imaging (MRI) data.

Rizwan Ahmad, Charles A. Bouman, Gregery T. Buzzard et al.

Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool that provides excellent soft-tissue contrast without the use of ionizing radiation. Compared to other clinical imaging modalities (e.g., CT or ultrasound), however, the data acquisition process for MRI is inherently slow, which motivates undersampling and thus drives the need for accurate, efficient reconstruction methods from undersampled datasets. In this article, we describe the use of "plug-and-play" (PnP) algorithms for MRI image recovery. We first describe the linearly approximated inverse problem encountered in MRI. Then we review several PnP methods, where the unifying commonality is to iteratively call a denoising subroutine as one step of a larger optimization-inspired algorithm. Next, we describe how the result of the PnP method can be interpreted as a solution to an equilibrium equation, allowing convergence analysis from the equilibrium perspective. Finally, we present illustrative examples of PnP methods applied to MRI image recovery.