arXiv subjects

Mohammad Golbabaee

Publications and source records attributed to Mohammad Golbabaee.

At least 37 records · Page 2Linked to original sources

arXiv2020

Rapid three-dimensional multiparametric MRI with quantitative transient-state imaging

Novel methods for quantitative, transient-state multiparametric imaging are increasingly being demonstrated for assessment of disease and treatment efficacy. Here, we build on these by assessing the most common Non-Cartesian readout trajectories (2D/3D radials and spirals), demonstrating efficient anti-aliasing with a k-space view-sharing technique, and proposing novel methods for parameter inference with neural networks that incorporate the estimation of proton density. Our results show good agreement with gold standard and phantom references for all readout trajectories at 1.5T and 3T. Parameters inferred with the neural network were within 6.58% difference from the parameters inferred with a high-resolution dictionary. Concordance correlation coefficients were above 0.92 and the normalized root mean squared error ranged between 4.2% - 12.7% with respect to gold-standard phantom references for T1 and T2. In vivo acquisitions demonstrate sub-millimetric isotropic resolution in under five minutes with reconstruction and inference times < 7 minutes. Our 3D quantitative transient-state imaging approach could enable high-resolution multiparametric tissue quantification within clinically acceptable acquisition and reconstruction times.

physics.med-ph↗

arXiv2020

Compressive MRI quantification using convex spatiotemporal priors and deep auto-encoders

We propose a dictionary-matching-free pipeline for multi-parametric quantitative MRI image computing. Our approach has two stages based on compressed sensing reconstruction and deep learned quantitative inference. The reconstruction phase is convex and incorporates efficient spatiotemporal regularisations within an accelerated iterative shrinkage algorithm. This minimises the under-sampling (aliasing) artefacts from aggressively short scan times. The learned quantitative inference phase is purely trained on physical simulations (Bloch equations) that are flexible for producing rich training samples. We propose a deep and compact auto-encoder network with residual blocks in order to embed Bloch manifold projections through multiscale piecewise affine approximations, and to replace the nonscalable dictionary-matching baseline. Tested on a number of datasets we demonstrate effectiveness of the proposed scheme for recovering accurate and consistent quantitative information from novel and aggressively subsampled 2D/3D quantitative MRI acquisition protocols.

cs.CV↗

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

The Practicality of Stochastic Optimization in Imaging Inverse Problems

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature to have optimal complexities in theory, and provide great improvement empirically over the deterministic gradient methods. Surprisingly, in some tasks such as image deblurring, many of such methods fail to converge faster than the accelerated deterministic gradient methods, even in terms of epoch counts. We investigate this phenomenon and propose a theory-inspired mechanism for the practitioners to efficiently characterize whether it is beneficial for an inverse problem to be solved by stochastic optimization techniques or not. Using standard tools in numerical linear algebra, we derive conditions on the spectral structure of the inverse problem for being a suitable application of stochastic gradient methods. Particularly, we show that, for an imaging inverse problem, if and only if its Hessain matrix has a fast-decaying eigenspectrum, then the stochastic gradient methods can be more advantageous than deterministic methods for solving such a problem. Our results also provide guidance on choosing appropriately the partition minibatch schemes, showing that a good minibatch scheme typically has relatively low correlation within each of the minibatches. Finally, we propose an accelerated primal-dual SGD algorithm in order to tackle another key bottleneck of stochastic optimization which is the heavy computation of proximal operators. The proposed method has fast convergence rate in practice, and is able to efficiently handle non-smooth regularization terms which are coupled with linear operators.

math.OC↗

arXiv2019

Multi-shot Echo Planar Imaging for accelerated Cartesian MR Fingerprinting: an alternative to conventional spiral MR Fingerprinting

Purpose: To develop an accelerated Cartesian MRF implementation using a multi-shot EPI sequence for rapid simultaneous quantification of T1 and T2 parameters. Methods: The proposed Cartesian MRF method involved the acquisition of highly subsampled MR images using a 16-shot EPI readout. A linearly varying flip angle train was used for rapid, simultaneous T1 and T2 quantification. The accuracy of parametric map estimations were improved by using an iterative projection algorithm. The results were compared to a conventional spiral MRF implementation. The acquisition time per slice was 8s and this method was validated on a phantom and a healthy volunteer brain in vivo. Results: Joint T1 and T2 estimations using the 16-shot EPI readout are in good agreement with the spiral implementation using the same acquisition parameters (deviation less than 3% for T1 and less than 4% for T2) for the healthy volunteer brain. The T1 and T2 values also agree with the conventional values previously reported in the literature. The visual quality of the multi-parametric maps generated by the multi-shot EPI-MRF and spiral-MRF implementations were comparable. Conclusion: The multi-shot EPI-MRF method generated accurate quantitative multi-parametric maps similar to conventional Spiral - MRF. This multi-shot approach achieved provides an alternative for performing MRF using an accelerated Cartesian readout, thereby increasing the potential usability of MRF.

physics.med-ph↗

arXiv2019

Deep MR Fingerprinting with total-variation and low-rank subspace priors

Deep learning (DL) has recently emerged to address the heavy storage and computation requirements of the baseline dictionary-matching (DM) for Magnetic Resonance Fingerprinting (MRF) reconstruction. Fed with non-iterated back-projected images, the network is unable to fully resolve spatially-correlated corruptions caused from the undersampling artefacts. We propose an accelerated iterative reconstruction to minimize these artefacts before feeding into the network. This is done through a convex regularization that jointly promotes spatio-temporal regularities of the MRF time-series. Except for training, the rest of the parameter estimation pipeline is dictionary-free. We validate the proposed approach on synthetic and in-vivo datasets.

cs.CV↗

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

CoverBLIP: accelerated and scalable iterative matched-filtering for Magnetic Resonance Fingerprint reconstruction

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy computations of a matched-filtering step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. We address this shortcoming by arranging dictionary atoms in the form of cover tree structures and adopt the corresponding fast approximate nearest neighbour searches to accelerate matched-filtering. For datasets belonging to smooth low-dimensional manifolds cover trees offer search complexities logarithmic in terms of data population. With this motivation we propose an iterative reconstruction algorithm, named CoverBLIP, to address large-size MRF problems where the fingerprint dictionary i.e. discrete manifold of Bloch responses, encodes several intrinsic NMR parameters. We study different forms of convergence for this algorithm and we show that provided with a notion of embedding, the inexact and non-convex iterations of CoverBLIP linearly convergence toward a near-global solution with the same order of accuracy as using exact brute-force searches. Our further examinations on both synthetic and real-world datasets and using different sampling strategies, indicates between 2 to 3 orders of magnitude reduction in total search computations. Cover trees are robust against the curse-of-dimensionality and therefore CoverBLIP provides a notion of scalability -- a consistent gain in time-accuracy performance-- for searching high-dimensional atoms which may not be easily preprocessed (i.e. for dimensionality reduction) due to the increasing degrees of non-linearities appearing in the emerging multi-parametric MRF dictionaries.

cs.CV↗

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

Rest-Katyusha: Exploiting the Solution's Structure via Scheduled Restart Schemes

We propose a structure-adaptive variant of the state-of-the-art stochastic variance-reduced gradient algorithm Katyusha for regularized empirical risk minimization. The proposed method is able to exploit the intrinsic low-dimensional structure of the solution, such as sparsity or low rank which is enforced by a non-smooth regularization, to achieve even faster convergence rate. This provable algorithmic improvement is done by restarting the Katyusha algorithm according to restricted strong-convexity constants. We demonstrate the effectiveness of our approach via numerical experiments.

math.OC↗

arXiv2017

Structure-Adaptive, Variance-Reduced, and Accelerated Stochastic Optimization

In this work we explore the fundamental structure-adaptiveness of state of the art randomized first order algorithms on regularized empirical risk minimization tasks, where the solution has intrinsic low-dimensional structure (such as sparsity and low-rank). Such structure is often enforced by non-smooth regularization or constraints. We start by establishing the fast linear convergence rate of the SAGA algorithm on non-strongly-convex objectives with convex constraints, via an argument of cone-restricted strong convexity. Then for the composite minimization task with a coordinate-wise separable convex regularization term, we propose and analyse a two stage accelerated coordinate descend algorithm (Two-Stage APCG). We provide the convergence analysis showing that the proposed method has a global convergence in general and enjoys a local accelerated linear convergence rate with respect to the low-dimensional structure of the solution. Then based on this convergence result, we proposed an adaptive variant of the two-stage APCG method which does not need to foreknow the restricted strong convexity beforehand, but estimate it on the fly. In numerical experiments we compare the adaptive two-stage APCG with various state of the art variance-reduced stochastic gradient methods on sparse regression tasks, and demonstrate the effectiveness of our approach.

math.OC↗

arXiv2017

Gradient Projection Iterative Sketch for Large-Scale Constrained Least-Squares

We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide theoretical convergence analysis for both proposed algorithms and demonstrate our methods' computational efficiency compared to classical accelerated gradient method, and the state of the art variance-reduced stochastic gradient methods through numerical experiments in various large synthetic/real data sets.

math.OC↗

arXiv2017

Exploiting the Structure via Sketched Gradient Algorithms

Sketched gradient algorithms have been recently introduced for efficiently solving the large-scale constrained Least-squares regressions. In this paper we provide novel convergence analysis for the basic method {\it Gradient Projection Classical Sketch} (GPCS) to reveal the fast linear convergence rate of GPCS towards a vicinity of the solution thanks to the intrinsic low-dimensional geometric structure of the solution prompted by constraint set. Similar to our analysis we observe computational and sketch size trade-offs in numerical experiments. Hence we justify that the combination of gradient methods and the sketching technique is a way of designing efficient algorithms which can actively exploit the low-dimensional structure to accelerate computation in large scale data regression and signal processing applications.

math.OC↗

arXiv2017

Inexact Gradient Projection and Fast Data Driven Compressed Sensing

We study convergence of the iterative projected gradient (IPG) algorithm for arbitrary (possibly nonconvex) sets and when both the gradient and projection oracles are computed approximately. We consider different notions of approximation of which we show that the Progressive Fixed Precision (PFP) and the $(1+ε)$-optimal oracles can achieve the same accuracy as for the exact IPG algorithm. We show that the former scheme is also able to maintain the (linear) rate of convergence of the exact algorithm, under the same embedding assumption. In contrast, the $(1+ε)$-approximate oracle requires a stronger embedding condition, moderate compression ratios and it typically slows down the convergence. We apply our results to accelerate solving a class of data driven compressed sensing problems, where we replace iterative exhaustive searches over large datasets by fast approximate nearest neighbour search strategies based on the cover tree data structure. For datasets with low intrinsic dimensions our proposed algorithm achieves a complexity logarithmic in terms of the dataset population as opposed to the linear complexity of a brute force search. By running several numerical experiments we conclude similar observations as predicted by our theoretical analysis.

cs.IT↗

arXiv2017

Insense: Incoherent Sensor Selection for Sparse Signals

Sensor selection refers to the problem of intelligently selecting a small subset of a collection of available sensors to reduce the sensing cost while preserving signal acquisition performance. The majority of sensor selection algorithms find the subset of sensors that best recovers an arbitrary signal from a number of linear measurements that is larger than the dimension of the signal. In this paper, we develop a new sensor selection algorithm for sparse (or near sparse) signals that finds a subset of sensors that best recovers such signals from a number of measurements that is much smaller than the dimension of the signal. Existing sensor selection algorithms cannot be applied in such situations. Our proposed Incoherent Sensor Selection (Insense) algorithm minimizes a coherence-based cost function that is adapted from recent results in sparse recovery theory. Using six datasets, including two real-world datasets on microbial diagnostics and structural health monitoring, we demonstrate the superior performance of Insense for sparse-signal sensor selection.

cs.OH↗

arXiv2014

Model Selection with Low Complexity Priors

Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated. A line of recent work has studied regularization models with various types of low-dimensional structures. In such settings, the general approach is to solve a regularized optimization problem, which combines a data fidelity term and some regularization penalty that promotes the assumed low-dimensional/simple structure. This paper provides a general framework to capture this low-dimensional structure through what we coin partly smooth functions relative to a linear manifold. These are convex, non-negative, closed and finite-valued functions that will promote objects living on low-dimensional subspaces. This class of regularizers encompasses many popular examples such as the L1 norm, L1-L2 norm (group sparsity), as well as several others including the Linfty norm. We also show that the set of partly smooth functions relative to a linear manifold is closed under addition and pre-composition by a linear operator, which allows to cover mixed regularization, and the so-called analysis-type priors (e.g. total variation, fused Lasso, finite-valued polyhedral gauges). Our main result presents a unified sharp analysis of exact and robust recovery of the low-dimensional subspace model associated to the object to recover from partial measurements. This analysis is illustrated on a number of special and previously studied cases, and on an analysis of the performance of Linfty regularization in a compressed sensing scenario.

math.OC↗