Covariant Wavelet Scattering for Robust MRI Reconstruction

Unrolled variational networks are the dominant framework for accelerated MRI reconstruction, but their learned regularizers can overfit the sampling pattern seen in training. We replace the learned spatial operator of the regularizer with a fixed covariant wavelet scattering transform: a low-pass filter and oriented Morlet wavelets followed by a modulus, without the averaging that makes standard scattering invariant. The resulting operator tiles the full frequency plane with explicit frame bounds, and we prove it is translation-equivariant, retains every frequency band through a lower frame bound, and is non-expansive and stable to small deformations. The filterbank itself has no trainable parameters. On fastMRI knee and brain data, AnalyticVarNet improves over a neural-operator baseline in-distribution and is substantially more robust to unseen incoherent sampling masks, with $2.47\times$ fewer parameters.