Abstract
In vivo hemodynamics can be measured by 4D flow MRI, but long acquisition times limit clinical use. Deep learning reconstruction of undersampled data offers large speed gains over compressed sensing. FlowVN, the CMRx4DFlow2026 challenge reference model, uses shared, real-valued convolution weights to real and imaginary parts of the image. The image phase, which encodes velocity, is then not directly controlled by the regularizer. We present three modifications to FlowVN. Complex FlowVN replaces convolution kernels of the regularizer with complex-valued ones; State-Augmented FlowVN propagates the accumulated update between unrolled stages; Ablated Complex FlowVN reduces the network to six unrolled stages with alternating data consistency application. Complex FlowVN improved in all Regular Task 1 metrics, compared to the challenge reference. It also improved on real-valued FlowVN with matched training protocol, reducing nRMSE from 0.058 to 0.054 and angular error from 41.0° to 37.8°. In the trained kernels, the imaginary-to-real kernel magnitude rose from 0.10 at initialization to 0.25–0.78 in all 40 cascade–filter-bank combinations, indicating active use of complex coupling. An ablated variant reduced inference time from 7.97 to 6.97 minutes without matching baseline complex difference error, and state augmentation did not improve accuracy. Complex-valued FlowVN improves reconstruction accuracy at negligible computational cost.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026-sat/paper/CMRxRecon2026_015.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: https://papers.miccai.org/miccai-2026-sat/supp/CMRxRecon2026_015_supp.pdf
Link to Open Review
Open Review Page: https://openreview.net/forum?id=KSGk6rM6RI
BibTex
@InProceedings{ApoCha_ComplexValued_MICCAISAT2026,
author = { Apostolidis, Charilaos AND Elbayumi, Mohamed AND Dong, William AND Berhane, Haben AND Johnson, Ethan},
title = { { Complex-Valued and State-Augmented Variational Networks for Accelerated 4D Flow MRI Reconstruction } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026 Workshops and Challenges},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 17267},
month = {pending},
page = {pending}
}