Application Fields and Fundamental Merits of Complex‐Valued Neural Networks

Hirose, Akira

doi:10.1002/9781118590072.ch1

Cited by 10 publications

(7 citation statements)

References 53 publications

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“…We use Wirtinger calculus 55 – 57 during backpropagation to update the complex-valued weights of each layer with respect to the real-valued loss function. In the backward pass due to linearity of all involved operations the gradient simplifies to …”

Section: Methodsmentioning

confidence: 99%

CINENet: deep learning-based 3D cardiac CINE MRI reconstruction with multi-coil complex-valued 4D spatio-temporal convolutions

Küstner

Fuin

Hammernik

et al. 2020

Sci Rep

178

135

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cardiac cine magnetic resonance imaging is the gold-standard for the assessment of cardiac function. Imaging accelerations have shown to enable 3D CINE with left ventricular (LV) coverage in a single breath-hold. However, 3D imaging remains limited to anisotropic resolution and long reconstruction times. Recently deep learning has shown promising results for computationally efficient reconstructions of highly accelerated 2D CINE imaging. In this work, we propose a novel 4D (3D + time) deep learning-based reconstruction network, termed 4D CINENet, for prospectively undersampled 3D Cartesian CINE imaging. CINENet is based on (3 + 1)D complex-valued spatio-temporal convolutions and multi-coil data processing. We trained and evaluated the proposed cinenet on in-house acquired 3D CINE data of 20 healthy subjects and 15 patients with suspected cardiovascular disease. The proposed cinenet network outperforms iterative reconstructions in visual image quality and contrast (+ 67% improvement). We found good agreement in LV function (bias ± 95% confidence) in terms of end-systolic volume (0 ± 3.3 ml), end-diastolic volume (− 0.4 ± 2.0 ml) and ejection fraction (0.1 ± 3.2%) compared to clinical gold-standard 2D CINE, enabling single breath-hold isotropic 3D CINE in less than 10 s scan and ~ 5 s reconstruction time. Cardiac CINE magnetic resonance imaging (MRI) is the gold standard for the assessment of cardiac morphology and function. Conventionally, multi-slice 2D CINE imaging is performed under multiple breath-holds to achieve left ventricular (LV) coverage. For fast LV coverage only a few (~ 12) short-axis 2D slices with anisotropic resolution in the slice direction are acquired throughout multiple breath-holds of < 15 s duration each. Imperfect (e.g. drifts) or varying breath-hold positions and the anisotropic image resolution can cause slice misalignments which may lead to staircasing artifacts and erroneous assessment of the ventricular volume. The LV function assessment is assessed by epicardial and endocardial segmentation of the images in short-axis orientation. Indeed, the anisotropic resolution of the short-axis 2D CINE does not allow for reformats to arbitrary orientations. Further images in other long axis orientations are required for a comprehensive assessment of cardiac morphology and function which in turn requires multiple acquisitions to be performed in several geometric views and thereby increasing overall planning and scan time. To overcome these limitations, 2D 1,2 and 3D 3-5 free-breathing cardiac CINE imaging with retrospective motion correction have been proposed to minimize slice misalignment and improve patient comfort. Data are acquired under free-breathing and respiratory and cardiac motion is resolved retrospectively which comes however at the expense of a prolonged scan time in the order of several minutes. Moreover, these approaches usually require long reconstruction times associated with the high-dimensional (spatial, respiratory temporal and cardiac temporal) data processing or with the nat...

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Section: Methodsmentioning

confidence: 99%

CINENet: deep learning-based 3D cardiac CINE MRI reconstruction with multi-coil complex-valued 4D spatio-temporal convolutions

Küstner

Fuin

Hammernik

et al. 2020

Sci Rep

178

135

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“…Popular applications of this type of networks include antenna design, estimation of direction of arrival and beamforming, radar imaging, communications signal processing, image processing, and many others (for an extensive presentation, see [11]). …”

Section: Introductionmentioning

confidence: 99%

Scaled Conjugate Gradient Learning for Complex-Valued Neural Networks

Popa

2015

Advances in Intelligent Systems and Computing

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In this paper, we present the full deduction of the scaled conjugate gradient method for training complex-valued feedforward neural networks. Because this algorithm had better training results for the real-valued case, an extension to the complex-valued case is a natural way to enhance the performance of the complex backpropagation algorithm. The proposed method is exemplified on well-known synthetic and real-world applications, and experimental results show an improvement over the complex gradient descent algorithm.

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“…However, the representation and operation of CNN in real values limit their applications in the field of complex-valued datasets. Complex-valued CNN (CV-CNN) has been developed and applied to various fields ( Hirose, 2013 ; Tygert et al, 2016 ). Some studies have demonstrated that CV-CNN outperforms real-valued CNN after making full use of phase information in complex-valued data, such as magnetic resonance imaging (MRI) ( Cole et al, 2021 ), steady-state visually evoked potentials (SSVEP) ( Ravi et al, 2020 ).…”

Section: Introductionmentioning

confidence: 99%

Classifying epileptic phase-amplitude coupling in SEEG using complex-valued convolutional neural network

Liu²,

Wang³

et al. 2023

Front. Physiol.

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EEG phase-amplitude coupling (PAC), the amplitude of high-frequency oscillations modulated by the phase of low-frequency oscillations (LFOs), is a useful biomarker to localize epileptogenic tissue. It is commonly represented in a comodulogram of coupling strength but without coupled phase information. The phase-amplitude coupling is also found in the normal brain, and it is difficult to discriminate pathological phase-amplitude couplings from normal ones. This study proposes a novel approach based on complex-valued phase-amplitude coupling (CV-PAC) for classifying epileptic phase-amplitude coupling. The CV-PAC combines both the coupling strengths and the coupled phases of low-frequency oscillations. The complex-valued convolutional neural network (CV-CNN) is then used to classify epileptic CV-PAC. Stereo-electroencephalography (SEEG) recordings from nine intractable epilepsy patients were analyzed. The leave-one-out cross-validation is performed, and the area-under-curve (AUC) value is used as the indicator of the performance of different measures. Our result shows that the area-under-curve value is .92 for classifying epileptic CV-PAC using CV-CNN. The area-under-curve value decreases to .89, .80, and .88 while using traditional convolutional neural networks, support vector machine, and random forest, respectively. The phases of delta (1–4 Hz) and alpha (8–10 Hz) bands are different between epileptic and normal CV-PAC. The phase information of CV-PAC is important for improving classification performance. The proposed approach of CV-PAC/CV-CNN promises to identify more accurate epileptic brain activities for potential surgical intervention.

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Application Fields and Fundamental Merits of Complex‐Valued Neural Networks

Cited by 10 publications

References 53 publications

CINENet: deep learning-based 3D cardiac CINE MRI reconstruction with multi-coil complex-valued 4D spatio-temporal convolutions

CINENet: deep learning-based 3D cardiac CINE MRI reconstruction with multi-coil complex-valued 4D spatio-temporal convolutions

Scaled Conjugate Gradient Learning for Complex-Valued Neural Networks

Classifying epileptic phase-amplitude coupling in SEEG using complex-valued convolutional neural network

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