Mike E. Davies

Sangnam Nam, Mike E. Davies, Michael Elad et al.

After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative, is markedly different. Surprisingly, the analysis model did not get a similar attention, and its understanding today is shallow and partial. In this paper we take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one. This work proposes effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior, accompanied by a preliminary theoretical study of their performance. We demonstrate the effectiveness of the analysis model in several experiments.

Julián Tachella, Michael P. Sheehan, Mike E. Davies

Single-photon light detection and ranging (lidar) captures depth and intensity information of a 3D scene. Reconstructing a scene from observed photons is a challenging task due to spurious detections associated with background illumination sources. To tackle this problem, there is a plethora of 3D reconstruction algorithms which exploit spatial regularity of natural scenes to provide stable reconstructions. However, most existing algorithms have computational and memory complexity proportional to the number of recorded photons. This complexity hinders their real-time deployment on modern lidar arrays which acquire billions of photons per second. Leveraging a recent lidar sketching framework, we show that it is possible to modify existing reconstruction algorithms such that they only require a small sketch of the photon information. In particular, we propose a sketched version of a recent state-of-the-art algorithm which uses point cloud denoisers to provide spatially regularized reconstructions. A series of experiments performed on real lidar datasets demonstrates a significant reduction of execution time and memory requirements, while achieving the same reconstruction performance than in the full data case.

Dongdong Chen, Julián Tachella, Mike E. Davies

Deep networks provide state-of-the-art performance in multiple imaging inverse problems ranging from medical imaging to computational photography. However, most existing networks are trained with clean signals which are often hard or impossible to obtain. Equivariant imaging (EI) is a recent self-supervised learning framework that exploits the group invariance present in signal distributions to learn a reconstruction function from partial measurement data alone. While EI results are impressive, its performance degrades with increasing noise. In this paper, we propose a Robust Equivariant Imaging (REI) framework which can learn to image from noisy partial measurements alone. The proposed method uses Stein's Unbiased Risk Estimator (SURE) to obtain a fully unsupervised training loss that is robust to noise. We show that REI leads to considerable performance gains on linear and nonlinear inverse problems, thereby paving the way for robust unsupervised imaging with deep networks. Code is available at: https://github.com/edongdongchen/REI.

Dongdong Chen, Julián Tachella, Mike E. Davies

In various imaging problems, we only have access to compressed measurements of the underlying signals, hindering most learning-based strategies which usually require pairs of signals and associated measurements for training. Learning only from compressed measurements is impossible in general, as the compressed observations do not contain information outside the range of the forward sensing operator. We propose a new end-to-end self-supervised framework that overcomes this limitation by exploiting the equivariances present in natural signals. Our proposed learning strategy performs as well as fully supervised methods. Experiments demonstrate the potential of this framework on inverse problems including sparse-view X-ray computed tomography on real clinical data and image inpainting on natural images. Code has been made available at: https://github.com/edongdongchen/EI.

Dongdong Chen, Mike E. Davies, Mohammad Golbabaee

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.

Dongdong Chen, Mike E. Davies

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in neural network training and deploying. The appropriate supervision and explicit calibration by the information of the physic model can enhance the neural network learning and its practical performance. In this paper, inspired by the geometry that data can be decomposed by two components from the null-space of the forward operator and the range space of its pseudo-inverse, we train neural networks to learn the two components and therefore learn the decomposition, i.e. we explicitly reformulate the neural network layers as learning range-nullspace decomposition functions with reference to the layer inputs, instead of learning unreferenced functions. We empirically show that the proposed framework demonstrates superior performance over recent deep residual learning, unrolled learning and nullspace learning on tasks including compressive sensing medical imaging and natural image super-resolution. Our code is available at https://github.com/edongdongchen/DDN.

Michael P. Sheehan, Mike E. Davies

Compressive learning forms the exciting intersection between compressed sensing and statistical learning where one exploits forms of sparsity and structure to reduce the memory and/or computational complexity of the learning task. In this paper, we look at the independent component analysis (ICA) model through the compressive learning lens. In particular, we show that solutions to the cumulant based ICA model have particular structure that induces a low dimensional model set that resides in the cumulant tensor space. By showing a restricted isometry property holds for random cumulants e.g. Gaussian ensembles, we prove the existence of a compressive ICA scheme. Thereafter, we propose two algorithms of the form of an iterative projection gradient (IPG) and an alternating steepest descent (ASD) algorithm for compressive ICA, where the order of compression asserted from the restricted isometry property is realised through empirical results. We provide analysis of the CICA algorithms including the effects of finite samples. The effects of compression are characterised by a trade-off between the sketch size and the statistical efficiency of the ICA estimates. By considering synthetic and real datasets, we show the substantial memory gains achieved over well-known ICA algorithms by using one of the proposed CICA algorithms. Finally, we conclude the paper with open problems including interesting challenges from the emerging field of compressive learning.

Heyi Li, Dongdong Chen, William H. Nailon et al.

Computer-aided breast cancer diagnosis in mammography is a challenging problem, stemming from mammographical data scarcity and data entanglement. In particular, data scarcity is attributed to the privacy and expensive annotation. And data entanglement is due to the high similarity between benign and malignant masses, of which manifolds reside in lower dimensional space with very small margin. To address these two challenges, we propose a deep learning framework, named Contrastive Identifier Network (\textsc{COIN}), which integrates adversarial augmentation and manifold-based contrastive learning. Firstly, we employ adversarial learning to create both on- and off-distribution mass contained ROIs. After that, we propose a novel contrastive loss with a built Signed graph. Finally, the neural network is optimized in a contrastive learning manner, with the purpose of improving the deep model's discriminativity on the extended dataset. In particular, by employing COIN, data samples from the same category are pulled close whereas those with different labels are pushed further in the deep latent space. Moreover, COIN outperforms the state-of-the-art related algorithms for solving breast cancer diagnosis problem by a considerable margin, achieving 93.4\% accuracy and 95.0\% AUC score. The code will release on ***.

Heyi Li, Dongdong Chen, William H. Nailon et al.

Deep convolutional neural networks (CNNs) have emerged as a new paradigm for Mammogram diagnosis. Contemporary CNN-based computer-aided-diagnosis (CAD) for breast cancer directly extract latent features from input mammogram image and ignore the importance of morphological features. In this paper, we introduce a novel deep learning framework for mammogram image processing, which computes mass segmentation and simultaneously predict diagnosis results. Specifically, our method is constructed in a dual-path architecture that solves the mapping in a dual-problem manner, with an additional consideration of important shape and boundary knowledge. One path called the Locality Preserving Learner (LPL), is devoted to hierarchically extracting and exploiting intrinsic features of the input. Whereas the other path, called the Conditional Graph Learner (CGL) focuses on generating geometrical features via modeling pixel-wise image to mask correlations. By integrating the two learners, both the semantics and structure are well preserved and the component learning paths in return complement each other, contributing an improvement to the mass segmentation and cancer classification problem at the same time. We evaluated our method on two most used public mammography datasets, DDSM and INbreast. Experimental results show that DualCoreNet achieves the best mammography segmentation and classification simultaneously, outperforming recent state-of-the-art models.

Konstantinos A. Voulgaris, Mike E. Davies, Mehrdad Yaghoobi

Non-negative signals form an important class of sparse signals. Many algorithms have already beenproposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. The greedy techniques are low computational cost algorithms, which have also been modified to incorporate the non-negativity of the representations. One such modification has been proposed for Matching Pursuit (MP) based algorithms, which first chooses positive coefficients and uses a non-negative optimisation technique that guarantees the non-negativity of the coefficients. The performance of greedy algorithms, like all non-exhaustive search methods, suffer from high coherence with the linear generative model, called the dictionary. We here first reformulate the non-negative matching pursuit algorithm in the form of a deep neural network. We then show that the proposed model after training yields a significant improvement in terms of exact recovery performance, compared to other non-trained greedy algorithms, while keeping the complexity low.

Michael P. Sheehan, Antoine Gonon, Mike E. Davies

In the compressive learning theory, instead of solving a statistical learning problem from the input data, a so-called sketch is computed from the data prior to learning. The sketch has to capture enough information to solve the problem directly from it, allowing to discard the dataset from the memory. This is useful when dealing with large datasets as the size of the sketch does not scale with the size of the database. In this paper, we reformulate the original compressive learning framework to explicitly cater for the class of semi-parametric models. The reformulation takes account of the inherent topology and structure of semi-parametric models, creating an intuitive pathway to the development of compressive learning algorithms. We apply our developed framework to both the semi-parametric models of independent component analysis and subspace clustering, demonstrating the robustness of the framework to explicitly show when a compression in complexity can be achieved.

Heyi Li, Dongdong Chen, William H. Nailon et al.

Computer-aided breast cancer diagnosis in mammography is limited by inadequate data and the similarity between benign and cancerous masses. To address this, we propose a signed graph regularized deep neural network with adversarial augmentation, named \textsc{DiagNet}. Firstly, we use adversarial learning to generate positive and negative mass-contained mammograms for each mass class. After that, a signed similarity graph is built upon the expanded data to further highlight the discrimination. Finally, a deep convolutional neural network is trained by jointly optimizing the signed graph regularization and classification loss. Experiments show that the \textsc{DiagNet} framework outperforms the state-of-the-art in breast mass diagnosis in mammography.

Heyi Li, Dongdong Chen, William H. Nailon et al.

We present, for the first time, a novel deep neural network architecture called \dcn with a dual-path connection between the input image and output class label for mammogram image processing. This architecture is built upon U-Net, which non-linearly maps the input data into a deep latent space. One path of the \dcnn, the locality preserving learner, is devoted to hierarchically extracting and exploiting intrinsic features of the input, while the other path, called the conditional graph learner, focuses on modeling the input-mask correlations. The learned mask is further used to improve classification results, and the two learning paths complement each other. By integrating the two learners our new architecture provides a simple but effective way to jointly learn the segmentation and predict the class label. Benefiting from the powerful expressive capacity of deep neural networks a more discriminative representation can be learned, in which both the semantics and structure are well preserved. Experimental results show that \dcn achieves the best mammography segmentation and classification simultaneously, outperforming recent state-of-the-art models.

Arnold Julian Vinoj Benjamin, Pedro A. Gómez, Mohammad Golbabaee et al.

The main purpose of this study is to show that a highly accelerated Cartesian MRF scheme using a multi-shot EPI readout (i.e. multi-shot EPI-MRF) can produce good quality multi-parametric maps such as T1, T2 and proton density (PD) in a sufficiently short scan duration that is similar to conventional MRF. This multi-shot approach allows considerable subsampling while traversing the entire k-space trajectory, can yield better SNR, reduced blurring, less distortion and can also be used to collect higher resolution data compared to existing single-shot EPI-MRF implementations. The generated parametric maps are compared to an accelerated spiral MRF implementation with the same acquisition parameters to evaluate the performance of this method. Additionally, an iterative reconstruction algorithm is applied to improve the accuracy of parametric map estimations and the fast convergence of EPI-MRF is also demonstrated.

Mohammad Golbabaee, Zhouye Chen, Yves Wiaux et al.

Current proposed solutions for the high dimensionality of the MRF reconstruction problem rely on a linear compression step to reduce the matching computations and boost the efficiency of fast but non-scalable searching schemes such as the KD-trees. However such methodologies often introduce an unfavourable compromise in the estimation accuracy when applied to nonlinear data structures such as the manifold of Bloch responses with possible increased dynamic complexity and growth in data population. To address this shortcoming we propose an inexact iterative reconstruction method, dubbed as the Cover BLoch response Iterative Projection (CoverBLIP). Iterative methods improve the accuracy of their non-iterative counterparts and are additionally robust against certain accelerated approximate updates, without compromising their final accuracy. Leveraging on these results, we accelerate matched-filtering using an ANNS algorithm based on Cover trees with a robustness feature against the curse of dimensionality.

Mohammad Golbabaee, Dongdong Chen, Pedro A. Gómez et al.

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy storage and computation requirements of a dictionary-matching (DM) step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. In this paper we study a deep learning approach to address these shortcomings. Coupled with a dimensionality reduction first layer, the proposed MRF-Net is able to reconstruct quantitative maps by saving more than 60 times in memory and computations required for a DM baseline. Fine-grid manifold enumeration i.e. the MRF dictionary is only used for training the network and not during image reconstruction. We show that the MRF-Net provides a piece-wise affine approximation to the Bloch response manifold projection and that rather than memorizing the dictionary, the network efficiently clusters this manifold and learns a set of hierarchical matched-filters for affine regression of the NMR characteristics in each segment.

Dongdong Chen, Jiancheng Lv, Mike E. Davies

We investigate the potential of a restricted Boltzmann Machine (RBM) for discriminative representation learning. By imposing the class information preservation constraints on the hidden layer of the RBM, we propose a Signed Laplacian Restricted Boltzmann Machine (SLRBM) for supervised discriminative representation learning. The model utilizes the label information and preserves the global data locality of data points simultaneously. Experimental results on the benchmark data set show the effectiveness of our method.

Cagdas Ulas, Giles Tetteh, Michael J. Thrippleton et al.

Dynamic contrast-enhanced (DCE) MRI is an evolving imaging technique that provides a quantitative measure of pharmacokinetic (PK) parameters in body tissues, in which series of T1-weighted images are collected following the administration of a paramagnetic contrast agent. Unfortunately, in many applications, conventional clinical DCE-MRI suffers from low spatiotemporal resolution and insufficient volume coverage. In this paper, we propose a novel deep learning based approach to directly estimate the PK parameters from undersampled DCE-MRI data. Specifically, we design a custom loss function where we incorporate a forward physical model that relates the PK parameters to corrupted image-time series obtained due to subsampling in k-space. This allows the network to directly exploit the knowledge of true contrast agent kinetics in the training phase, and hence provide more accurate restoration of PK parameters. Experiments on clinical brain DCE datasets demonstrate the efficacy of our approach in terms of fidelity of PK parameter reconstruction and significantly faster parameter inference compared to a model-based iterative reconstruction method.

Mohammad Golbabaee, Zhouye Chen, Yves Wiaux et al.

We adopt data structure in the form of cover trees and iteratively apply approximate nearest neighbour (ANN) searches for fast compressed sensing reconstruction of signals living on discrete smooth manifolds. Levering on the recent stability results for the inexact Iterative Projected Gradient (IPG) algorithm and by using the cover tree's ANN searches, we decrease the projection cost of the IPG algorithm to be logarithmically growing with data population for low dimensional smooth manifolds. We apply our results to quantitative MRI compressed sensing and in particular within the Magnetic Resonance Fingerprinting (MRF) framework. For a similar (or sometimes better) reconstruction accuracy, we report 2-3 orders of magnitude reduction in computations compared to the standard iterative method which uses brute-force searches.

Chunli Guo, Mike E. Davies

We propose the notion of a sample distortion (SD) function for independent and identically distributed (i.i.d) compressive distributions to fundamentally quantify the achievable reconstruction performance of compressed sensing for certain encoder-decoder pairs at a given sampling ratio. Two lower bounds on the achievable performance and the intrinsic convexity property is derived. A zeroing procedure is then introduced to improve non convex SD functions. The SD framework is then applied to analyse compressed imaging with a multi-resolution statistical image model using both the generalized Gaussian distribution and the two-state Gaussian mixture distribution. We subsequently focus on the Gaussian encoder-Bayesian optimal approximate message passing (AMP) decoder pair, whose theoretical SD function is provided by the rigorous analysis of the AMP algorithm. Given the image statistics, analytic bandwise sample allocation for bandwise independent model is derived as a reverse water-filling scheme. Som and Schniter's turbo message passing approach is further deployed to integrate the bandwise sampling with the exploitation of the hidden Markov tree structure of wavelet coefficients. Natural image simulations confirm that with oracle image statistics, the SD function associated with the optimized sample allocation can accurately predict the possible compressed sensing gains. Finally, a general sample allocation profile based on average image statistics not only illustrates preferable performance but also makes the scheme practical.

Mehrdad Yaghoobi, Sangnam Nam, Remi Gribonval et al.

We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using sparse synthesis coefficients. This famous sparse model has a less well known counterpart, in analysis form, called the cosparse analysis model. In this new model, signals are characterised by their parsimony in a transformed domain using an overcomplete (linear) analysis operator. We propose to learn an analysis operator from a training corpus using a constrained optimisation framework based on L1 optimisation. The reason for introducing a constraint in the optimisation framework is to exclude trivial solutions. Although there is no final answer here for which constraint is the most relevant constraint, we investigate some conventional constraints in the model adaptation field and use the uniformly normalised tight frame (UNTF) for this purpose. We then derive a practical learning algorithm, based on projected subgradients and Douglas-Rachford splitting technique, and demonstrate its ability to robustly recover a ground truth analysis operator, when provided with a clean training set, of sufficient size. We also find an analysis operator for images, using some noisy cosparse signals, which is indeed a more realistic experiment. As the derived optimisation problem is not a convex program, we often find a local minimum using such variational methods. Some local optimality conditions are derived for two different settings, providing preliminary theoretical support for the well-posedness of the learning problem under appropriate conditions.