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Register a new userOptimal control gradient precision trade-offs: application to fast generation of DeepControl libraries for MRI
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We have recently demonstrated supervised deep learning methods for rapid generation of radiofrequency pulses in magnetic resonance imaging (https://doi.org/10.1002/mrm.27740, https://doi.org/10.1002/mrm.28667). Unlike the previous iterative optimization approaches, deep learning methods generate a pulse using a fixed number of floating-point operations - this is important in MRI, where patient-specific pulses preferably must be produced in real time. However, deep learning requires vast training libraries, which must be generated using the traditional methods, e.g. iterative quantum optimal control methods. Those methods are usually variations of gradient descent, and the calculation of the fidelity gradient of the performance metric with respect to the pulse waveform can be the most numerically intensive step. In this communication, we explore various ways in which the calculation of fidelity gradients in quantum optimal control theory may be accelerated. Four optimization avenues are explored: truncated commutator series expansions at zeroth and first order, a novel midpoint truncation scheme at first order, and the exact complex-step method. For the spin systems relevant to MRI, the first-order truncation is found to be sufficiently accurate, but also up to five times faster than the machine precision gradient. This makes the generation of training databases for the machine learning methods considerably more realistic.
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In in-utero MRI, motion correction for fetal body and placenta poses a particular challenge due to the presence of local non-rigid transformations of organs caused by bending and stretching. The existing slice-to-volume registration (SVR) reconstruction methods are widely employed for motion correction of fetal brain that undergoes only rigid transformation. However, for reconstruction of fetal body and placenta, rigid registration cannot resolve the issue of misregistrations due to deformable motion, resulting in degradation of features in the reconstructed volume. We propose a Deformable SVR (DSVR), a novel approach for non-rigid motion correction of fetal MRI based on a hierarchical deformable SVR scheme to allow high resolution reconstruction of the fetal body and placenta. Additionally, a robust scheme for structure-based rejection of outliers minimises the impact of registration errors. The improved performance of DSVR in comparison to SVR and patch-to-volume registration (PVR) methods is quantitatively demonstrated in simulated experiments and 20 fetal MRI datasets from 28-31 weeks gestational age (GA) range with varying degree of motion corruption. In addition, we present qualitative evaluation of 100 fetal body cases from 20-34 weeks GA range.
This paper studies the optimal output-feedback control of a linear time-invariant system where a stochastic event-based scheduler triggers the communication between the sensor and the controller. The primary goal of the use of this type of scheduling strategy is to provide significant reductions in the usage of the sensor-to-controller communication and, in turn, improve energy expenditure in the network. In this paper, we aim to design an admissible control policy, which is a function of the observed output, to minimize a quadratic cost function while employing a stochastic event-triggered scheduler that preserves the Gaussian property of the plant state and the estimation error. For the infinite horizon case, we present analytical expressions that quantify the trade-off between the communication cost and control performance of such event-triggered control systems. This trade-off is confirmed quantitatively via numerical examples.
This study presents a comparison of quantitative MRI methods based on an efficiency metric that quantifies their intrinsic ability to extract information about tissue parameters. Under a regime of unbiased parameter estimates, an intrinsic efficiency metric $eta$ was derived for fully-sampled experiments which can be used to both optimize and compare sequences. Here we optimize and compare several steady-state and transient gradient-echo based qMRI methods, such as magnetic resonance fingerprinting (MRF), for joint T1 and T2 mapping. The impact of undersampling was also evaluated, assuming incoherent aliasing that is treated as noise by parameter estimation. In-vivo validation of the efficiency metric was also performed. Transient methods such as MRF can be up to 3.5 times more efficient than steady-state methods, when spatial undersampling is ignored. If incoherent aliasing is treated as noise during least-squares parameter estimation, the efficiency is reduced in proportion to the SNR of the data, with reduction factors of 5 often seen for practical SNR levels. In-vivo validation showed a very good agreement between the theoretical and experimentally predicted efficiency. This work presents and validates an efficiency metric to optimize and compare the performance of qMRI methods. Transient methods were found to be intrinsically more efficient than steady-state methods, however the effect of spatial undersampling can significantly erode this advantage.
Purpose: This study demonstrated an MR signal multitask learning method for 3D simultaneous segmentation and relaxometry of human brain tissues. Materials and Methods: A 3D inversion-prepared balanced steady-state free precession sequence was used for acquiring in vivo multi-contrast brain images. The deep neural network contained 3 residual blocks, and each block had 8 fully connected layers with sigmoid activation, layer norm, and 256 neurons in each layer. Online synthesized MR signal evolutions and labels were used to train the neural network batch-by-batch. Empirically defined ranges of T1 and T2 values for the normal gray matter, white matter and cerebrospinal fluid (CSF) were used as the prior knowledge. MRI brain experiments were performed on 3 healthy volunteers as well as animal (N=6) and prostate patient (N=1) experiments. Results: In animal validation experiment, the differences/errors (mean difference $pm$ standard deviation of difference) between the T1 and T2 values estimated from the proposed method and the ground truth were 113 $pm$ 486 and 154 $pm$ 512 ms for T1, and 5 $pm$ 33 and 7 $pm$ 41 ms for T2, respectively. In healthy volunteer experiments (N=3), whole brain segmentation and relaxometry were finished within ~5 seconds. The estimated apparent T1 and T2 maps were in accordance with known brain anatomy, and not affected by coil sensitivity variation. Gray matter, white matter, and CSF were successfully segmented. The deep neural network can also generate synthetic T1 and T2 weighted images. Conclusion: The proposed multitask learning method can directly generate brain apparent T1 and T2 maps, as well as synthetic T1 and T2 weighted images, in conjunction with segmentation of gray matter, white matter and CSF.
Extreme multi-label classification (XMC) aims to learn a model that can tag data points with a subset of relevant labels from an extremely large label set. Real world e-commerce applications like personalized recommendations and product advertising can be formulated as XMC problems, where the objective is to predict for a user a small subset of items from a catalog of several million products. For such applications, a common approach is to organize these labels into a tree, enabling training and inference times that are logarithmic in the number of labels. While training a model once a label tree is available is well studied, designing the structure of the tree is a difficult task that is not yet well understood, and can dramatically impact both model latency and statistical performance. Existing approaches to tree construction fall at an extreme point, either optimizing exclusively for statistical performance, or for latency. We propose an efficient information theory inspired algorithm to construct intermediary operating points that trade off between the benefits of both. Our algorithm enables interpolation between these objectives, which was not previously possible. We corroborate our theoretical analysis with numerical results, showing that on the Wiki-500K benchmark dataset our method can reduce a proxy for expected latency by up to 28% while maintaining the same accuracy as Parabel. On several datasets derived from e-commerce customer logs, our modified label tree is able to improve this expected latency metric by up to 20% while maintaining the same accuracy. Finally, we discuss challenges in realizing these latency improvements in deployed models.
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