Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training expenses, and may not always achieve the desired accuracy required in many scientific and engineering disciplines. In this paper, we propose a new learning framework to address these issues. A new spatiotemporal adaptation is proposed to generalize any Fourier Neural Operator (FNO) variant to learn maps between Bochner spaces, which can perform an arbitrary-length temporal super-resolution for the first time. To better exploit this capacity, a new paradigm is proposed to refine the commonly adopted end-to-end neural operator training and evaluations with the help from the wisdom from traditional numerical PDE theory and techniques. Specifically, in the learning problems for the turbulent flow modeled by the Navier-Stokes Equations (NSE), the proposed paradigm trains an FNO only for a few epochs. Then, only the newly proposed spatiotemporal spectral convolution layer is fine-tuned without the frequency truncation. The spectral fine-tuning loss function uses a negative Sobolev norm for the first time in operator learning, defined through a reliable functional-type a posteriori error estimator whose evaluation is exact thanks to the Parseval identity. Moreover, unlike the difficult nonconvex optimization problems in the end-to-end training, this fine-tuning loss is convex. Numerical experiments on commonly used NSE benchmarks demonstrate significant improvements in both computational efficiency and accuracy, compared to end-to-end evaluation and traditional numerical PDE solvers under certain conditions. The source code is publicly available at https://github.com/scaomath/torch-cfd.
Despite recent advancements in semantic segmentation, where and what pixels are hard to segment remains largely unexplored. Existing research only separates an image into easy and hard regions and empirically observes the latter are associated with object boundaries. In this paper, we conduct a comprehensive analysis of hard pixel errors, categorizing them into three types: false responses, merging mistakes, and displacements. Our findings reveal a quantitative association between hard pixels and aliasing, which is distortion caused by the overlapping of frequency components in the Fourier domain during downsampling. To identify the frequencies responsible for aliasing, we propose using the equivalent sampling rate to calculate the Nyquist frequency, which marks the threshold for aliasing. Then, we introduce the aliasing score as a metric to quantify the extent of aliasing. While positively correlated with the proposed aliasing score, three types of hard pixels exhibit different patterns. Here, we propose two novel de-aliasing filter (DAF) and frequency mixing (FreqMix) modules to alleviate aliasing degradation by accurately removing or adjusting frequencies higher than the Nyquist frequency. The DAF precisely removes the frequencies responsible for aliasing before downsampling, while the FreqMix dynamically selects high-frequency components within the encoder block. Experimental results demonstrate consistent improvements in semantic segmentation and low-light instance segmentation tasks. The code is available at: https://github.com/Linwei-Chen/Seg-Aliasing.
Deep MRI reconstruction is commonly performed with conditional models that de-alias undersampled acquisitions to recover images consistent with fully-sampled data. Since conditional models are trained with knowledge of the imaging operator, they can show poor generalization across variable operators. Unconditional models instead learn generative image priors decoupled from the operator to improve reliability against domain shifts related to the imaging operator. Recent diffusion models are particularly promising given their high sample fidelity. Nevertheless, inference with a static image prior can perform suboptimally. Here we propose the first adaptive diffusion prior for MRI reconstruction, AdaDiff, to improve performance and reliability against domain shifts. AdaDiff leverages an efficient diffusion prior trained via adversarial mapping over large reverse diffusion steps. A two-phase reconstruction is executed following training: a rapid-diffusion phase that produces an initial reconstruction with the trained prior, and an adaptation phase that further refines the result by updating the prior to minimize data-consistency loss. Demonstrations on multi-contrast brain MRI clearly indicate that AdaDiff outperforms competing conditional and unconditional methods under domain shifts, and achieves superior or on par within-domain performance.
Current spatiotemporal deep learning approaches to Magnetic Resonance Fingerprinting (MRF) build artefact-removal models customised to a particular k-space subsampling pattern which is used for fast (compressed) acquisition. This may not be useful when the acquisition process is unknown during training of the deep learning model and/or changes during testing time. This paper proposes an iterative deep learning plug-and-play reconstruction approach to MRF which is adaptive to the forward acquisition process. Spatiotemporal image priors are learned by an image denoiser i.e. a Convolutional Neural Network (CNN), trained to remove generic white gaussian noise (not a particular subsampling artefact) from data. This CNN denoiser is then used as a data-driven shrinkage operator within the iterative reconstruction algorithm. This algorithm with the same denoiser model is then tested on two simulated acquisition processes with distinct subsampling patterns. The results show consistent de-aliasing performance against both acquisition schemes and accurate mapping of tissues' quantitative bio-properties. Software available: https://github.com/ketanfatania/QMRI-PnP-Recon-POC
Purpose: To introduce a novel deep learning based approach for fast and high-quality dynamic multi-coil MR reconstruction by learning a complementary time-frequency domain network that exploits spatio-temporal correlations simultaneously from complementary domains. Theory and Methods: Dynamic parallel MR image reconstruction is formulated as a multi-variable minimisation problem, where the data is regularised in combined temporal Fourier and spatial (x-f) domain as well as in spatio-temporal image (x-t) domain. An iterative algorithm based on variable splitting technique is derived, which alternates among signal de-aliasing steps in x-f and x-t spaces, a closed-form point-wise data consistency step and a weighted coupling step. The iterative model is embedded into a deep recurrent neural network which learns to recover the image via exploiting spatio-temporal redundancies in complementary domains. Results: Experiments were performed on two datasets of highly undersampled multi-coil short-axis cardiac cine MRI scans. Results demonstrate that our proposed method outperforms the current state-of-the-art approaches both quantitatively and qualitatively. The proposed model can also generalise well to data acquired from a different scanner and data with pathologies that were not seen in the training set. Conclusion: The work shows the benefit of reconstructing dynamic parallel MRI in complementary time-frequency domains with deep neural networks. The method can effectively and robustly reconstruct high-quality images from highly undersampled dynamic multi-coil data ($16 \times$ and $24 \times$ yielding 15s and 10s scan times respectively) with fast reconstruction speed (2.8s). This could potentially facilitate achieving fast single-breath-hold clinical 2D cardiac cine imaging.
Consistency of the predictions with respect to the physical forward model is pivotal for reliably solving inverse problems. This consistency is mostly un-controlled in the current end-to-end deep learning methodologies proposed for the Magnetic Resonance Fingerprinting (MRF) problem. To address this, we propose ProxNet, a learned proximal gradient descent framework that directly incorporates the forward acquisition and Bloch dynamic models within a recurrent learning mechanism. The ProxNet adopts a compact neural proximal model for de-aliasing and quantitative inference, that can be flexibly trained on scarce MRF training datasets. Our numerical experiments show that the ProxNet can achieve a superior quantitative inference accuracy, much smaller storage requirement, and a comparable runtime to the recent deep learning MRF baselines, while being much faster than the dictionary matching schemes. Code has been released at https://github.com/edongdongchen/PGD-Net.
Generative deep learning has sparked a new wave of Super-Resolution (SR) algorithms that enhance single images with impressive aesthetic results, albeit with imaginary details. Multi-frame Super-Resolution (MFSR) offers a more grounded approach to the ill-posed problem, by conditioning on multiple low-resolution views. This is important for satellite monitoring of human impact on the planet -- from deforestation, to human rights violations -- that depend on reliable imagery. To this end, we present HighRes-net, the first deep learning approach to MFSR that learns its sub-tasks in an end-to-end fashion: (i) co-registration, (ii) fusion, (iii) up-sampling, and (iv) registration-at-the-loss. Co-registration of low-resolution views is learned implicitly through a reference-frame channel, with no explicit registration mechanism. We learn a global fusion operator that is applied recursively on an arbitrary number of low-resolution pairs. We introduce a registered loss, by learning to align the SR output to a ground-truth through ShiftNet. We show that by learning deep representations of multiple views, we can super-resolve low-resolution signals and enhance Earth Observation data at scale. Our approach recently topped the European Space Agency's MFSR competition on real-world satellite imagery.