Fast and Accurate Reconstruction of 3D Cardiac Displacement Fields from Sparse MRI-like Data via PBDW
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Personalized cardiac diagnostics require recovering myocardial displacement fields from limited imaging. This work presents an enhanced PBDW framework for reconstructing 3D cardiac displacement from sparse, MRI-like observations, focusing on two novelties: an H-size minibatch wOMP sensor-selection strategy that accelerates selection while preserving accuracy, and block-structured memory optimizations that improve computational efficiency. The method is validated on a high-fidelity 3D left-ventricular model with simulated scar tissue. Starting from noise-free data, Gaussian noise and spatial sparsity are progressively introduced to emulate realistic MRI acquisitions. The approach achieves a relative L2 error of about 1e−5 in noise-free cases, around 1e−2 under 10% Gaussian noise, and similar accuracy (~1e−2) with sparse and noisy measurements. The online stage yields a four-order-of-magnitude speed-up over full finite-element simulations, with reconstruction times below 0.1 seconds in sparse settings. These results suggest the method could serve as a practical and efficient tool for myocardial displacement reconstruction from low-resolution, sparse imaging, with further validation needed on clinical datasets and broader scenarios.
