  Deep learning has been extensively applied in medical image reconstruction,
where Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs)
represent the predominant paradigms, each possessing distinct advantages and
inherent limitations: CNNs exhibit linear complexity with local sensitivity,
whereas ViTs demonstrate quadratic complexity with global sensitivity. The
emerging Mamba has shown superiority in learning visual representation, which
combines the advantages of linear scalability and global sensitivity. In this
study, we introduce MambaMIR, an Arbitrary-Masked Mamba-based model with
wavelet decomposition for joint medical image reconstruction and uncertainty
estimation. A novel Arbitrary Scan Masking (ASM) mechanism "masks out"
redundant information to introduce randomness for further uncertainty
estimation. Compared to the commonly used Monte Carlo (MC) dropout, our
proposed MC-ASM provides an uncertainty map without the need for hyperparameter
tuning and mitigates the performance drop typically observed when applying
dropout to low-level tasks. For further texture preservation and better
perceptual quality, we employ the wavelet transformation into MambaMIR and
explore its variant based on the Generative Adversarial Network, namely
MambaMIR-GAN. Comprehensive experiments have been conducted for multiple
representative medical image reconstruction tasks, demonstrating that the
proposed MambaMIR and MambaMIR-GAN outperform other baseline and
state-of-the-art methods in different reconstruction tasks, where MambaMIR
achieves the best reconstruction fidelity and MambaMIR-GAN has the best
perceptual quality. In addition, our MC-ASM provides uncertainty maps as an
additional tool for clinicians, while mitigating the typical performance drop
caused by the commonly used dropout.
