9,643 research outputs found

    On two subgroups of U(n), useful for quantum computing

    Get PDF
    As two basic building blocks for any quantum circuit, we consider the 1-qubit PHASOR circuit Phi(theta) and the 1-qubit NEGATOR circuit N(theta). Both are roots of the IDENTITY circuit. Indeed: both (NO) and N(0) equal the 2 x 2 unit matrix. Additionally, the NEGATOR is a root of the classical NOT gate. Quantum circuits (acting on w qubits) consisting of controlled PHASORs are represented by matrices from ZU(2(w)); quantum circuits consisting of controlled NEGATORs are represented by matrices from XU(2(w)). Here, ZU(n) and XU(n) are subgroups of the unitary group U(n): the group XU(n) consists of all n x n unitary matrices with all 2n line sums (i.e. all n row sums and all n column sums) equal to 1 and the group ZU(n) consists of all n x n unitary diagonal matrices with first entry equal to 1. Any U(n) matrix can be decomposed into four parts: U = exp(i alpha) Z(1)XZ(2), where both Z(1) and Z(2) are ZU(n) matrices and X is an XU(n) matrix. We give an algorithm to find the decomposition. For n = 2(w) it leads to a four-block synthesis of an arbitrary quantum computer

    A Deep Learning Framework for Unsupervised Affine and Deformable Image Registration

    Full text link
    Image registration, the process of aligning two or more images, is the core technique of many (semi-)automatic medical image analysis tasks. Recent studies have shown that deep learning methods, notably convolutional neural networks (ConvNets), can be used for image registration. Thus far training of ConvNets for registration was supervised using predefined example registrations. However, obtaining example registrations is not trivial. To circumvent the need for predefined examples, and thereby to increase convenience of training ConvNets for image registration, we propose the Deep Learning Image Registration (DLIR) framework for \textit{unsupervised} affine and deformable image registration. In the DLIR framework ConvNets are trained for image registration by exploiting image similarity analogous to conventional intensity-based image registration. After a ConvNet has been trained with the DLIR framework, it can be used to register pairs of unseen images in one shot. We propose flexible ConvNets designs for affine image registration and for deformable image registration. By stacking multiple of these ConvNets into a larger architecture, we are able to perform coarse-to-fine image registration. We show for registration of cardiac cine MRI and registration of chest CT that performance of the DLIR framework is comparable to conventional image registration while being several orders of magnitude faster.Comment: Accepted: Medical Image Analysis - Elsevie

    Automatic calcium scoring in low-dose chest CT using deep neural networks with dilated convolutions

    Full text link
    Heavy smokers undergoing screening with low-dose chest CT are affected by cardiovascular disease as much as by lung cancer. Low-dose chest CT scans acquired in screening enable quantification of atherosclerotic calcifications and thus enable identification of subjects at increased cardiovascular risk. This paper presents a method for automatic detection of coronary artery, thoracic aorta and cardiac valve calcifications in low-dose chest CT using two consecutive convolutional neural networks. The first network identifies and labels potential calcifications according to their anatomical location and the second network identifies true calcifications among the detected candidates. This method was trained and evaluated on a set of 1744 CT scans from the National Lung Screening Trial. To determine whether any reconstruction or only images reconstructed with soft tissue filters can be used for calcification detection, we evaluated the method on soft and medium/sharp filter reconstructions separately. On soft filter reconstructions, the method achieved F1 scores of 0.89, 0.89, 0.67, and 0.55 for coronary artery, thoracic aorta, aortic valve and mitral valve calcifications, respectively. On sharp filter reconstructions, the F1 scores were 0.84, 0.81, 0.64, and 0.66, respectively. Linearly weighted kappa coefficients for risk category assignment based on per subject coronary artery calcium were 0.91 and 0.90 for soft and sharp filter reconstructions, respectively. These results demonstrate that the presented method enables reliable automatic cardiovascular risk assessment in all low-dose chest CT scans acquired for lung cancer screening
    corecore