Spatial aliasing affects spaced microphone arrays, causing directional ambiguity above certain frequencies, degrading spatial and spectral accuracy of beamformers. Given the limitations of conventional signal processing and the scarcity of deep learning approaches to spatial aliasing mitigation, we propose a novel approach using a U-Net architecture to predict a signal-dependent de-aliasing filter, which reduces aliasing in conventional beamforming for spatial capture. Two types of multichannel filters are considered, one which treats the channels independently and a second one that models cross-channel dependencies. The proposed approach is evaluated in two common spatial capture scenarios: stereo and first-order Ambisonics. The results indicate a very significant improvement, both objective and perceptual, with respect to conventional beamforming. This work shows the potential of deep learning to reduce aliasing in beamforming, leading to improvements in multi-microphone setups.
Deep learning technologies have significantly improved performance in the field of synthetic aperture radar (SAR) image target recognition compared to traditional methods. However, the inherent ``black box" property of deep learning models leads to a lack of transparency in decision-making processes, making them difficult to be widespread applied in practice. To tackle this issue, this study proposes a physically explainable framework for complex-valued SAR image recognition, designed based on the physical process of microwave propagation. This framework utilizes complex-valued SAR data to explore the amplitude and phase information and its intrinsic physical properties. The network architecture is fully parameterized, with all learnable parameters endowed with clear physical meanings. Experiments on both the complex-valued MSTAR dataset and a self-built Qilu-1 complex-valued dataset were conducted to validate the effectiveness of framework. The de-overlapping capability of EMWaveNet enables accurate recognition of overlapping target categories, whereas other models are nearly incapable of performing such recognition. Against 0dB forest background noise, it boasts a 20\% accuracy improvement over traditional neural networks. When targets are 60\% masked by noise, it still outperforms other models by 9\%. An end-to-end complex-valued synthetic aperture radar automatic target recognition (SAR-ATR) algorithm is constructed to perform recognition tasks in interference SAR scenarios. The results demonstrate that the proposed method possesses a strong physical decision logic, high physical explainability and robustness, as well as excellent de-aliasing capabilities. Finally, a perspective on future applications is provided.
A central problem in data science is to use potentially noisy samples of an unknown function to predict values for unseen inputs. In classical statistics, predictive error is understood as a trade-off between the bias and the variance that balances model simplicity with its ability to fit complex functions. However, over-parameterized models exhibit counterintuitive behaviors, such as "double descent" in which models of increasing complexity exhibit decreasing generalization error. Others may exhibit more complicated patterns of predictive error with multiple peaks and valleys. Neither double descent nor multiple descent phenomena are well explained by the bias-variance decomposition. We introduce a novel decomposition that we call the generalized aliasing decomposition (GAD) to explain the relationship between predictive performance and model complexity. The GAD decomposes the predictive error into three parts: 1) model insufficiency, which dominates when the number of parameters is much smaller than the number of data points, 2) data insufficiency, which dominates when the number of parameters is much greater than the number of data points, and 3) generalized aliasing, which dominates between these two extremes. We demonstrate the applicability of the GAD to diverse applications, including random feature models from machine learning, Fourier transforms from signal processing, solution methods for differential equations, and predictive formation enthalpy in materials discovery. Because key components of the GAD can be explicitly calculated from the relationship between model class and samples without seeing any data labels, it can answer questions related to experimental design and model selection before collecting data or performing experiments. We further demonstrate this approach on several examples and discuss implications for predictive modeling and data science.
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.
Three-dimensional coronary magnetic resonance angiography (CMRA) demands reconstruction algorithms that can significantly suppress the artifacts from a heavily undersampled acquisition. While unrolling-based deep reconstruction methods have achieved state-of-the-art performance on 2D image reconstruction, their application to 3D reconstruction is hindered by the large amount of memory needed to train an unrolled network. In this study, we propose a memory-efficient deep compressed sensing method by employing a sparsifying transform based on a pre-trained artifact estimation network. The motivation is that the artifact image estimated by a well-trained network is sparse when the input image is artifact-free, and less sparse when the input image is artifact-affected. Thus, the artifact-estimation network can be used as an inherent sparsifying transform. The proposed method, named De-Aliasing Regularization based Compressed Sensing (DARCS), was compared with a traditional compressed sensing method, de-aliasing generative adversarial network (DAGAN), model-based deep learning (MoDL), and plug-and-play for accelerations of 3D CMRA. The results demonstrate that the proposed method improved the reconstruction quality relative to the compared methods by a large margin. Furthermore, the proposed method well generalized for different undersampling rates and noise levels. The memory usage of the proposed method was only 63% of that needed by MoDL. In conclusion, the proposed method achieves improved reconstruction quality for 3D CMRA with reduced memory burden.
Magnetic resonance imaging (MRI) plays an important role in modern medical diagnostic but suffers from prolonged scan time. Current deep learning methods for undersampled MRI reconstruction exhibit good performance in image de-aliasing which can be tailored to the specific k-space undersampling scenario. But it is very troublesome to configure different deep networks when the sampling setting changes. In this work, we propose a deep plug-and-play method for undersampled MRI reconstruction, which effectively adapts to different sampling settings. Specifically, the image de-aliasing prior is first learned by a deep denoiser trained to remove general white Gaussian noise from synthetic data. Then the learned deep denoiser is plugged into an iterative algorithm for image reconstruction. Results on in vivo data demonstrate that the proposed method provides nice and robust accelerated image reconstruction performance under different undersampling patterns and sampling rates, both visually and quantitatively.
Parallel imaging accelerates MRI data acquisition by acquiring additional sensitivity information with an array of receiver coils, resulting in fewer phase encoding steps. Because of fewer data requirements than parallel imaging, compressed sensing magnetic resonance imaging (CS-MRI) has gained popularity in the field of medical imaging. Parallel imaging and compressed sensing (CS) both reduce the amount of data captured in the k-space, which speeds up traditional MRI acquisition. As acquisition time is inversely proportional to sample count, forming an image from reduced k-space samples results in faster acquisition but with aliasing artifacts. For de-aliasing the reconstructed image, this paper proposes a novel Generative Adversarial Network (GAN) called RECGAN-GR that is supervised with multi-modal losses. In comparison to existing GAN networks, our proposed method introduces a novel generator network, RemU-Net, which is integrated with dual-domain loss functions such as weighted magnitude and phase loss functions, as well as parallel imaging-based loss, GRAPPA consistency loss. As refinement learning, a k-space correction block is proposed to make the GAN network self-resistant to generating unnecessary data, which speeds up the reconstruction process. Comprehensive results show that the proposed RECGAN-GR not only improves the PSNR by 4 dB over GAN-based methods but also by 2 dB over conventional state-of-the-art CNN methods available in the literature for single-coil data. The proposed work significantly improves image quality for low-retained data, resulting in five to ten times faster acquisition.
Global correlations are widely seen in human anatomical structures due to similarity across tissues and bones. These correlations are reflected in magnetic resonance imaging (MRI) scans as a result of close-range proton density and T1/T2 parameters. Furthermore, to achieve accelerated MRI, k-space data are undersampled which causes global aliasing artifacts. Convolutional neural network (CNN) models are widely utilized for accelerated MRI reconstruction, but those models are limited in capturing global correlations due to the intrinsic locality of the convolution operation. The self-attention-based transformer models are capable of capturing global correlations among image features, however, the current contributions of transformer models for MRI reconstruction are minute. The existing contributions mostly provide CNN-transformer hybrid solutions and rarely leverage the physics of MRI. In this paper, we propose a physics-based stand-alone (convolution free) transformer model titled, the Multi-head Cascaded Swin Transformers (McSTRA) for accelerated MRI reconstruction. McSTRA combines several interconnected MRI physics-related concepts with the transformer networks: it exploits global MR features via the shifted window self-attention mechanism; it extracts MR features belonging to different spectral components separately using a multi-head setup; it iterates between intermediate de-aliasing and k-space correction via a cascaded network with data consistency in k-space and intermediate loss computations; furthermore, we propose a novel positional embedding generation mechanism to guide self-attention utilizing the point spread function corresponding to the undersampling mask. Our model significantly outperforms state-of-the-art MRI reconstruction methods both visually and quantitatively while depicting improved resolution and removal of aliasing artifacts.
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.
Recently, deep neural networks have greatly advanced undersampled Magnetic Resonance Image (MRI) reconstruction, wherein most studies follow the one-anatomy-one-network fashion, i.e., each expert network is trained and evaluated for a specific anatomy. Apart from inefficiency in training multiple independent models, such convention ignores the shared de-aliasing knowledge across various anatomies which can benefit each other. To explore the shared knowledge, one naive way is to combine all the data from various anatomies to train an all-round network. Unfortunately, despite the existence of the shared de-aliasing knowledge, we reveal that the exclusive knowledge across different anatomies can deteriorate specific reconstruction targets, yielding overall performance degradation. Observing this, in this study, we present a novel deep MRI reconstruction framework with both anatomy-shared and anatomy-specific parameterized learners, aiming to "seek common ground while reserving differences" across different anatomies.Particularly, the primary anatomy-shared learners are exposed to different anatomies to model flourishing shared knowledge, while the efficient anatomy-specific learners are trained with their target anatomy for exclusive knowledge. Four different implementations of anatomy-specific learners are presented and explored on the top of our framework in two MRI reconstruction networks. Comprehensive experiments on brain, knee and cardiac MRI datasets demonstrate that three of these learners are able to enhance reconstruction performance via multiple anatomy collaborative learning.
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.
We present two deep learning approaches to narrative text understanding for character relationship modelling. The temporal evolution of these relations is described by dynamic word embeddings, that are designed to learn semantic changes over time. An empirical analysis of the corresponding character trajectories shows that such approaches are effective in depicting dynamic evolution. A supervised learning approach based on the state-of-the-art transformer model BERT is used instead to detect static relations between characters. The empirical validation shows that such events (e.g., two characters belonging to the same family) might be spotted with good accuracy, even when using automatically annotated data. This provides a deeper understanding of narrative plots based on the identification of key facts. Standard clustering techniques are finally used for character de-aliasing, a necessary pre-processing step for both approaches. Overall, deep learning models appear to be suitable for narrative text understanding, while also providing a challenging and unexploited benchmark for general natural language understanding.
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.
In this work we address the problem of real-time dynamic medical MRI and X Ray CT image reconstruction from parsimonious samples Fourier frequency space for MRI and sinogram tomographic projections for CT. Today the de facto standard for such reconstruction is compressed sensing. CS produces high quality images (with minimal perceptual loss, but such reconstructions are time consuming, requiring solving a complex optimization problem. In this work we propose to learn the reconstruction from training samples using an autoencoder. Our work is based on the universal function approximation capacity of neural networks. The training time for the autoencoder is large, but is offline and hence does not affect performance during operation. During testing or operation, our method requires only a few matrix vector products and hence is significantly faster than CS based methods. In fact, it is fast enough for real-time reconstruction the images are reconstructed as fast as they are acquired with only slight degradation of image quality. However, in order to make the autoencoder suitable for our problem, we depart from the standard Euclidean norm cost function of autoencoders and use a robust l1-norm instead. The ensuing problem is solved using the Split Bregman method.
Parallel imaging has been an essential technique to accelerate MR imaging. Nevertheless, the acceleration rate is still limited due to the ill-condition and challenges associated with the undersampled reconstruction. In this paper, we propose a model-based convolutional de-aliasing network with adaptive parameter learning to achieve accurate reconstruction from multi-coil undersampled k-space data. Three main contributions have been made: a de-aliasing reconstruction model was proposed to accelerate parallel MR imaging with deep learning exploring both spatial redundancy and multi-coil correlations; a split Bregman iteration algorithm was developed to solve the model efficiently; and unlike most existing parallel imaging methods which rely on the accuracy of the estimated multi-coil sensitivity, the proposed method can perform parallel reconstruction from undersampled data without explicit sensitivity calculation. Evaluations were conducted on \emph{in vivo} brain dataset with a variety of undersampling patterns and different acceleration factors. Our results demonstrated that this method could achieve superior performance in both quantitative and qualitative analysis, compared to three state-of-the-art methods.
We propose a convolutional neural network (CNN) denoising based method for seismic data interpolation. It provides a simple and efficient way to break though the lack problem of geophysical training labels that are often required by deep learning methods. The new method consists of two steps: (1) Train a set of CNN denoisers from natural image clean-noisy pairs to learn denoising; (2) Integrate the trained CNN denoisers into project onto convex set (POCS) framework to perform seismic data interpolation. The method alleviates the demanding of seismic big data with similar features as applications of end-to-end deep learning on seismic data interpolation. Additionally, the proposed method is flexible for many cases of traces missing because missing cases are not involved in the training step, and thus it is of plug-and-play nature. These indicate the high generalizability of our approach and the reduction of the need of the problem-specific training. Primary results on synthetic and field data show promising interpolation performances of the presented CNN-POCS method in terms of signal-to-noise ratio, de-aliasing and weak-feature reconstruction, in comparison with traditional $f$-$x$ prediction filtering and curvelet transform based POCS methods.
Fast Magnetic Resonance Imaging (MRI) is highly in demand for many clinical applications in order to reduce the scanning cost and improve the patient experience. This can also potentially increase the image quality by reducing the motion artefacts and contrast washout. However, once an image field of view and the desired resolution are chosen, the minimum scanning time is normally determined by the requirement of acquiring sufficient raw data to meet the Nyquist-Shannon sampling criteria. Compressive Sensing (CS) theory has been perfectly matched to the MRI scanning sequence design with much less required raw data for the image reconstruction. Inspired by recent advances in deep learning for solving various inverse problems, we propose a conditional Generative Adversarial Networks-based deep learning framework for de-aliasing and reconstructing MRI images from highly undersampled data with great promise to accelerate the data acquisition process. By coupling an innovative content loss with the adversarial loss our de-aliasing results are more realistic. Furthermore, we propose a refinement learning procedure for training the generator network, which can stabilise the training with fast convergence and less parameter tuning. We demonstrate that the proposed framework outperforms state-of-the-art CS-MRI methods, in terms of reconstruction error and perceptual image quality. In addition, our method can reconstruct each image in 0.22ms--0.37ms, which is promising for real-time applications.