arXiv subjects

Mike E. Davies

Publications and source records attributed to Mike E. Davies.

At least 37 records · Page 2Linked to original sources

arXiv2020

Compressive MR Fingerprinting reconstruction with Neural Proximal Gradient iterations

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.

eess.IV↗

arXiv2020

Accelerated Search for Non-Negative Greedy Sparse Decomposition via Dimensionality Reduction

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. One fast implementation is the FNNOMP algorithm that updates the non-negative coefficients in an iterative manner. Even though FNNOMP is a good approach when working on libraries of small size, the operational time of the algorithm grows significantly when the size of the library is large. This is mainly due to the selection step of the algorithm that relies on matrix vector multiplications. We here introduce the Embedded Nearest Neighbor (E-NN) algorithm which accelerates the search over large datasets while it is guaranteed to find the most correlated atoms. We then replace the selection step of FNNOMP by E-NN. Furthermore we introduce the Update Nearest Neighbor (U-NN) at the look up table of FNNOMP in order to assure the non-negativity criteria of FNNOMP. The results indicate that the proposed methodology can accelerate FNNOMP with a factor 4 on a real dataset of Raman Spectra and with a factor of 22 on a synthetic dataset.

eess.SP↗

arXiv2020

Blur resolved OCT: full-range interferometric synthetic aperture microscopy through dispersion encoding

We present a computational method for full-range interferometric synthetic aperture microscopy (ISAM) under dispersion encoding. With this, one can effectively double the depth range of optical coherence tomography (OCT), whilst dramatically enhancing the spatial resolution away from the focal plane. To this end, we propose a model-based iterative reconstruction (MBIR) method, where ISAM is directly considered in an optimization approach, and we make the discovery that sparsity promoting regularization effectively recovers the full-range signal. Within this work, we adopt an optimal nonuniform discrete fast Fourier transform (NUFFT) implementation of ISAM, which is both fast and numerically stable throughout iterations. We validate our method with several complex samples, scanned with a commercial SD-OCT system with no hardware modification. With this, we both demonstrate full-range ISAM imaging, and significantly outperform combinations of existing methods.

eess.IV↗

arXiv2020

Quantitative cone-beam CT reconstruction with polyenergetic scatter model fusion

Scatter can account for large errors in cone-beam CT (CBCT) due to its wide field of view, and its complicated nature makes its compensation difficult. Iterative polyenergetic reconstruction algorithms offer the potential to provide quantitative imaging in CT, but they are usually incompatible with scatter contaminated measurements. In this work, we introduce a polyenergetic convolutional scatter model that is directly fused into the reconstruction process, and exploits information readily available at each iteration for a fraction of additional computational cost. We evaluate this method with numerical and real CBCT measurements, and show significantly enhanced electron density estimation and artifact mitigation over pre-calculated fast adaptive scatter kernel superposition (fASKS). We demonstrate our approach has two levels of benefit: reducing the bias introduced by estimating scatter prior to reconstruction; and adapting to the spectral and spatial properties of the specimen.

physics.med-ph↗

arXiv2019

(l1,l2)-RIP and Projected Back-Projection Reconstruction for Phase-Only Measurements

This letter analyzes the performances of a simple reconstruction method, namely the Projected Back-Projection (PBP), for estimating the direction of a sparse signal from its phase-only (or amplitude-less) complex Gaussian random measurements, i.e., an extension of one-bit compressive sensing to the complex field. To study the performances of this algorithm, we show that complex Gaussian random matrices respect, with high probability, a variant of the Restricted Isometry Property (RIP) relating to the l1 -norm of the sparse signal measurements to their l2 -norm. This property allows us to upper-bound the reconstruction error of PBP in the presence of phase noise. Monte Carlo simulations are performed to highlight the performance of our approach in this phase-only acquisition model when compared to error achieved by PBP in classical compressive sensing.

eess.SP↗

arXiv2019

A Fully Convolutional Network for MR Fingerprinting

Magnetic Resonance Fingerprinting (MRF) methods typically rely on dictionary matching to map the temporal MRF signals to quantitative tissue parameters. These methods suffer from heavy storage and computation requirements as the dictionary size grows. To address these issues, we proposed an end to end fully convolutional neural network for MRF reconstruction (MRF-FCNN), which firstly employ linear dimensionality reduction and then use neural network to project the data into the tissue parameters manifold space. Experiments on the MAGIC data demonstrate the effectiveness of the method.

eess.IV↗

arXiv2019

Compressive Learning for Semi-Parametric Models

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.

stat.ML↗

arXiv2019

Signed Laplacian Deep Learning with Adversarial Augmentation for Improved Mammography Diagnosis

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.

eess.IV↗

arXiv2019

Polyquant CT: direct electron and mass density reconstruction from a single polyenergetic source

Quantifying material mass and electron density from computed tomography (CT) reconstructions can be highly valuable in certain medical practices, such as radiation therapy planning. However, uniquely parameterising the X-ray attenuation in terms of mass or electron density is an ill-posed problem when a single polyenergetic source is used with a spectrally indiscriminate detector. Existing approaches to single source polyenergetic modelling often impose consistency with a physical model, such as water--bone or photoelectric--Compton decompositions, which will either require detailed prior segmentation or restrictive energy dependencies, and may require further calibration to the quantity of interest. In this work, we introduce a data centric approach to fitting the attenuation with piecewise-linear functions directly to mass or electron density, and present a segmentation-free statistical reconstruction algorithm for exploiting it, with the same order of complexity as other iterative methods. We show how this allows both higher accuracy in attenuation modelling, and demonstrate its superior quantitative imaging, with numerical chest and metal implant data, and validate it with real cone-beam CT measurements.

physics.med-ph↗

arXiv2019

A Deep DUAL-PATH Network for Improved Mammogram Image Processing

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.

cs.CV↗

arXiv2018

Analysis vs Synthesis - An Investigation of (Co)sparse Signal Models on Graphs

In this work, we present a theoretical study of signals with sparse representations in the vertex domain of a graph, which is primarily motivated by the discrepancy arising from respectively adopting a synthesis and analysis view of the graph Laplacian matrix. Sparsity on graphs and, in particular, the characterization of the subspaces of signals which are sparse with respect to the connectivity of the graph, as induced by analysis with a suitable graph operator, remains in general an opaque concept which we aim to elucidate. By leveraging the theory of cosparsity, we present a novel (co)sparse graph Laplacian-based signal model and characterize the underlying (structured) (co)sparsity, smoothness and localization of its solution subspaces on undirected graphs, while providing more refined statements for special cases such as circulant graphs. Ultimately, we substantiate fundamental discrepancies between the cosparse analysis and sparse synthesis models in this structured setting, by demonstrating that the former constitutes a special, constrained instance of the latter.

eess.SP↗

arXiv2018

Analysis vs Synthesis with Structure - An Investigation of Union of Subspace Models on Graphs

We consider the problem of characterizing the `duality gap' between sparse synthesis- and cosparse analysis-driven signal models through the lens of spectral graph theory, in an effort to comprehend their precise equivalencies and discrepancies. By detecting and exploiting the inherent connectivity structure, and hence, distinct set of properties, of rank-deficient graph difference matrices such as the graph Laplacian, we are able to substantiate discrepancies between the cosparse analysis and sparse synthesis models, according to which the former constitutes a constrained and translated instance of the latter. In view of a general union of subspaces model, we conduct a study of the associated subspaces and their composition, which further facilitates the refinement of specialized uniqueness and recovery guarantees, and discover an underlying structured sparsity model based on the graph incidence matrix. Furthermore, for circulant graphs, we provide an exact characterization of underlying subspaces by deriving closed-form expressions as well as demonstrating transitional properties between equivalence and non-equivalence for a parametric generalization of the graph Laplacian.

cs.DM↗

arXiv2018

Geometry of Deep Learning for Magnetic Resonance Fingerprinting

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.

cs.LG↗

arXiv2018

Cover Tree Compressed Sensing for Fast MR Fingerprint Recovery

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.

stat.ML↗

arXiv2018

CoverBLIP: scalable iterative matched filtering for MR Fingerprint recovery

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.

q-bio.QM↗

arXiv2018

Balanced multi-shot EPI for accelerated Cartesian MRF: An alternative to spiral MRF

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.

q-bio.QM↗

arXiv2018

Learning Discriminative Representation with Signed Laplacian Restricted Boltzmann Machine

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.

cs.CV↗

arXiv2018

Performance Analysis of Approximate Message Passing for Distributed Compressed Sensing

Bayesian approximate message passing (BAMP) is an efficient method in compressed sensing that is nearly optimal in the minimum mean squared error (MMSE) sense. Bayesian approximate message passing (BAMP) performs joint recovery of multiple vectors with identical support and accounts for correlations in the signal of interest and in the noise. In this paper, we show how to reduce the complexity of vector BAMP via a simple joint decorrelation diagonalization) transform of the signal and noise vectors, which also facilitates the subsequent performance analysis. We prove that BAMP and the corresponding state evolution (SE) are equivariant with respect to the joint decorrelation transform and preserve diagonality of the residual noise covariance for the Bernoulli-Gauss (BG) prior. We use these results to analyze the dynamics and the mean squared error (MSE) performance of BAMP via the replica method, and thereby understand the impact of signal correlation and number of jointly sparse signals.

cs.IT↗