arXiv subjects

Jong Chul Ye

Publications and source records attributed to Jong Chul Ye.

At least 253 records · Page 14Linked to original sources

arXiv2018

A Mathematical Framework for Deep Learning in Elastic Source Imaging

An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms thereby enhancing their performance with sparse datasets. It is rigorously established that the proposed framework is equivalent to the so-called \emph{deep convolutional framelet expansion} in machine learning literature for inverse problems. Apposite numerical examples are furnished to substantiate the efficacy of the proposed framework.

math.OC↗

arXiv2018

Deep Residual Learning for Accelerated MRI using Magnitude and Phase Networks

Accelerated magnetic resonance (MR) scan acquisition with compressed sensing (CS) and parallel imaging is a powerful method to reduce MR imaging scan time. However, many reconstruction algorithms have high computational costs. To address this, we investigate deep residual learning networks to remove aliasing artifacts from artifact corrupted images. The proposed deep residual learning networks are composed of magnitude and phase networks that are separately trained. If both phase and magnitude information are available, the proposed algorithm can work as an iterative k-space interpolation algorithm using framelet representation. When only magnitude data is available, the proposed approach works as an image domain post-processing algorithm. Even with strong coherent aliasing artifacts, the proposed network successfully learned and removed the aliasing artifacts, whereas current parallel and CS reconstruction methods were unable to remove these artifacts. Comparisons using single and multiple coil show that the proposed residual network provides good reconstruction results with orders of magnitude faster computational time than existing compressed sensing methods. The proposed deep learning framework may have a great potential for accelerated MR reconstruction by generating accurate results immediately.

cs.CV↗

arXiv2018

Deep Convolutional Framelet Denosing for Low-Dose CT via Wavelet Residual Network

Model based iterative reconstruction (MBIR) algorithms for low-dose X-ray CT are computationally expensive. To address this problem, we recently proposed a deep convolutional neural network (CNN) for low-dose X-ray CT and won the second place in 2016 AAPM Low-Dose CT Grand Challenge. However, some of the texture were not fully recovered. To address this problem, here we propose a novel framelet-based denoising algorithm using wavelet residual network which synergistically combines the expressive power of deep learning and the performance guarantee from the framelet-based denoising algorithms. The new algorithms were inspired by the recent interpretation of the deep convolutional neural network (CNN) as a cascaded convolution framelet signal representation. Extensive experimental results confirm that the proposed networks have significantly improved performance and preserves the detail texture of the original images.

stat.ML↗

arXiv2018

Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT

X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using large receptive field neural networks such as U-Net have demonstrated impressive performance for sparse- view CT reconstruction. However, theoretical justification is still lacking. Inspired by the recent theory of deep convolutional framelets, the main goal of this paper is, therefore, to reveal the limitation of U-Net and propose new multi-resolution deep learning schemes. In particular, we show that the alternative U- Net variants such as dual frame and the tight frame U-Nets satisfy the so-called frame condition which make them better for effective recovery of high frequency edges in sparse view- CT. Using extensive experiments with real patient data set, we demonstrate that the new network architectures provide better reconstruction performance.

cs.CV↗

arXiv2018

Deep Convolutional Framelets: A General Deep Learning Framework for Inverse Problems

Recently, deep learning approaches with various network architectures have achieved significant performance improvement over existing iterative reconstruction methods in various imaging problems. However, it is still unclear why these deep learning architectures work for specific inverse problems. To address these issues, here we show that the long-searched-for missing link is the convolution framelets for representing a signal by convolving local and non-local bases. The convolution framelets was originally developed to generalize the theory of low-rank Hankel matrix approaches for inverse problems, and this paper further extends the idea so that we can obtain a deep neural network using multilayer convolution framelets with perfect reconstruction (PR) under rectilinear linear unit nonlinearity (ReLU). Our analysis also shows that the popular deep network components such as residual block, redundant filter channels, and concatenated ReLU (CReLU) do indeed help to achieve the PR, while the pooling and unpooling layers should be augmented with high-pass branches to meet the PR condition. Moreover, by changing the number of filter channels and bias, we can control the shrinkage behaviors of the neural network. This discovery leads us to propose a novel theory for deep convolutional framelets neural network. Using numerical experiments with various inverse problems, we demonstrated that our deep convolution framelets network shows consistent improvement over existing deep architectures.This discovery suggests that the success of deep learning is not from a magical power of a black-box, but rather comes from the power of a novel signal representation using non-local basis combined with data-driven local basis, which is indeed a natural extension of classical signal processing theory.

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arXiv2018

Deep Learning with Domain Adaptation for Accelerated Projection-Reconstruction MR

Purpose: The radial k-space trajectory is a well-established sampling trajectory used in conjunction with magnetic resonance imaging. However, the radial k-space trajectory requires a large number of radial lines for high-resolution reconstruction. Increasing the number of radial lines causes longer acquisition time, making it more difficult for routine clinical use. On the other hand, if we reduce the number of radial lines, streaking artifact patterns are unavoidable. To solve this problem, we propose a novel deep learning approach with domain adaptation to restore high-resolution MR images from under-sampled k-space data. Methods: The proposed deep network removes the streaking artifacts from the artifact corrupted images. To address the situation given the limited available data, we propose a domain adaptation scheme that employs a pre-trained network using a large number of x-ray computed tomography (CT) or synthesized radial MR datasets, which is then fine-tuned with only a few radial MR datasets. Results: The proposed method outperforms existing compressed sensing algorithms, such as the total variation and PR-FOCUSS methods. In addition, the calculation time is several orders of magnitude faster than the total variation and PR-FOCUSS methods.Moreover, we found that pre-training using CT or MR data from similar organ data is more important than pre-training using data from the same modality for different organ. Conclusion: We demonstrate the possibility of a domain-adaptation when only a limited amount of MR data is available. The proposed method surpasses the existing compressed sensing algorithms in terms of the image quality and computation time.

cs.CV↗

arXiv2018

Deep Learning Reconstruction for 9-View Dual Energy CT Baggage Scanner

For homeland and transportation security applications, 2D X-ray explosive detection system (EDS) have been widely used, but they have limitations in recognizing 3D shape of the hidden objects. Among various types of 3D computed tomography (CT) systems to address this issue, this paper is interested in a stationary CT using fixed X-ray sources and detectors. However, due to the limited number of projection views, analytic reconstruction algorithms produce severe streaking artifacts. Inspired by recent success of deep learning approach for sparse view CT reconstruction, here we propose a novel image and sinogram domain deep learning architecture for 3D reconstruction from very sparse view measurement. The algorithm has been tested with the real data from a prototype 9-view dual energy stationary CT EDS carry-on baggage scanner developed by GEMSS Medical Systems, Korea, which confirms the superior reconstruction performance over the existing approaches.

cs.CV↗

arXiv2018

Deep Learning Interior Tomography for Region-of-Interest Reconstruction

Interior tomography for the region-of-interest (ROI) imaging has advantages of using a small detector and reducing X-ray radiation dose. However, standard analytic reconstruction suffers from severe cupping artifacts due to existence of null space in the truncated Radon transform. Existing penalized reconstruction methods may address this problem but they require extensive computations due to the iterative reconstruction. Inspired by the recent deep learning approaches to low-dose and sparse view CT, here we propose a deep learning architecture that removes null space signals from the FBP reconstruction. Experimental results have shown that the proposed method provides near-perfect reconstruction with about 7-10 dB improvement in PSNR over existing methods in spite of significantly reduced run-time complexity.

cs.CV↗

arXiv2017

Topological Sensitivity Based Far-Field Detection of Elastic Inclusions

The aim of this article is to present and rigorously analyze topological sensitivity based algorithms for detection of diametrically small inclusions in an isotropic homogeneous elastic formation using single and multiple measurements of the far-field scattering amplitudes. A $L^2-$cost functional is considered and a location indicator is constructed from its topological derivative. The performance of the indicator is analyzed in terms of the topological sensitivity for location detection and stability with respect to measurement and medium noises. It is established that the location indicator does not guarantee inclusion detection and achieves only a low resolution when there is mode-conversion in an elastic formation. Accordingly, a weighted location indicator is designed to tackle the mode-conversion phenomenon. It is substantiated that the weighted function renders the location of an inclusion stably with resolution as per Rayleigh criterion.

math.NA↗

arXiv2017

Deep Learning for Accelerated Ultrasound Imaging

In portable, 3-D, or ultra-fast ultrasound (US) imaging systems, there is an increasing demand to reconstruct high quality images from limited number of data. However, the existing solutions require either hardware changes or computationally expansive algorithms. To overcome these limitations, here we propose a novel deep learning approach that interpolates the missing RF data by utilizing the sparsity of the RF data in the Fourier domain. Extensive experimental results from sub-sampled RF data from a real US system confirmed that the proposed method can effectively reduce the data rate without sacrificing the image quality.

cs.CV↗

arXiv2017

A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstruction

Due to the potential risk of inducing cancers, radiation dose of X-ray CT should be reduced for routine patient scanning. However, in low-dose X-ray CT, severe artifacts usually occur due to photon starvation, beamhardening, etc, which decrease the reliability of diagnosis. Thus, high quality reconstruction from low-dose X-ray CT data has become one of the important research topics in CT community. Conventional model-based denoising approaches are, however, computationally very expensive, and image domain denoising approaches hardly deal with CT specific noise patterns. To address these issues, we propose an algorithm using a deep convolutional neural network (CNN), which is applied to wavelet transform coefficients of low-dose CT images. Specifically, by using a directional wavelet transform for extracting directional component of artifacts and exploiting the intra- and inter-band correlations, our deep network can effectively suppress CT specific noises. Moreover, our CNN is designed to have various types of residual learning architecture for faster network training and better denoising. Experimental results confirm that the proposed algorithm effectively removes complex noise patterns of CT images, originated from the reduced X-ray dose. In addition, we show that wavelet domain CNN is efficient in removing the noises from low-dose CT compared to an image domain CNN. Our results were rigorously evaluated by several radiologists and won the second place award in 2016 AAPM Low-Dose CT Grand Challenge. To the best of our knowledge, this work is the first deep learning architecture for low-dose CT reconstruction that has been rigorously evaluated and proven for its efficacy.

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arXiv2017

Unified Theory for Recovery of Sparse Signals in a General Transform Domain

Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many real-world applications, a signal of interest is typically sparse not in the canonical basis but in a certain transform domain, such as wavelets or the finite difference. The theory of compressed sensing was extended to the analysis sparsity model but known extensions are limited to specific choices of sensing matrix and sparsifying transform. In this paper, we propose a unified theory for robust recovery of sparse signals in a general transform domain by convex programming. In particular, our results apply to general acquisition and sparsity models and show how the number of measurements for recovery depends on properties of measurement and sparsifying transforms. Moreover, we also provide extensions of our results to the scenarios where the atoms in the transform has varying incoherence parameters and the unknown signal exhibits a structured sparsity pattern. In particular, for the partial Fourier recovery of sparse signals over a circulant transform, our main results suggest a uniformly random sampling. Numerical results demonstrate that the variable density random sampling by our main results provides superior recovery performance over known sampling strategies.

cs.IT↗

arXiv2017

Beyond Deep Residual Learning for Image Restoration: Persistent Homology-Guided Manifold Simplification

The latest deep learning approaches perform better than the state-of-the-art signal processing approaches in various image restoration tasks. However, if an image contains many patterns and structures, the performance of these CNNs is still inferior. To address this issue, here we propose a novel feature space deep residual learning algorithm that outperforms the existing residual learning. The main idea is originated from the observation that the performance of a learning algorithm can be improved if the input and/or label manifolds can be made topologically simpler by an analytic mapping to a feature space. Our extensive numerical studies using denoising experiments and NTIRE single-image super-resolution (SISR) competition demonstrate that the proposed feature space residual learning outperforms the existing state-of-the-art approaches. Moreover, our algorithm was ranked third in NTIRE competition with 5-10 times faster computational time compared to the top ranked teams. The source code is available on page : https://github.com/iorism/CNN.git

cs.CV↗

arXiv2017

Geometric GAN

Generative Adversarial Nets (GANs) represent an important milestone for effective generative models, which has inspired numerous variants seemingly different from each other. One of the main contributions of this paper is to reveal a unified geometric structure in GAN and its variants. Specifically, we show that the adversarial generative model training can be decomposed into three geometric steps: separating hyperplane search, discriminator parameter update away from the separating hyperplane, and the generator update along the normal vector direction of the separating hyperplane. This geometric intuition reveals the limitations of the existing approaches and leads us to propose a new formulation called geometric GAN using SVM separating hyperplane that maximizes the margin. Our theoretical analysis shows that the geometric GAN converges to a Nash equilibrium between the discriminator and generator. In addition, extensive numerical results show that the superior performance of geometric GAN.

stat.ML↗

arXiv2017

Multi-Scale Wavelet Domain Residual Learning for Limited-Angle CT Reconstruction

Limited-angle computed tomography (CT) is often used in clinical applications such as C-arm CT for interventional imaging. However, CT images from limited angles suffers from heavy artifacts due to incomplete projection data. Existing iterative methods require extensive calculations but can not deliver satisfactory results. Based on the observation that the artifacts from limited angles have some directional property and are globally distributed, we propose a novel multi-scale wavelet domain residual learning architecture, which compensates for the artifacts. Experiments have shown that the proposed method effectively eliminates artifacts, thereby preserving edge and global structures of the image.

cs.CV↗

arXiv2017

Wavelet Domain Residual Network (WavResNet) for Low-Dose X-ray CT Reconstruction

Model based iterative reconstruction (MBIR) algorithms for low-dose X-ray CT are computationally complex because of the repeated use of the forward and backward projection. Inspired by this success of deep learning in computer vision applications, we recently proposed a deep convolutional neural network (CNN) for low-dose X-ray CT and won the second place in 2016 AAPM Low-Dose CT Grand Challenge. However, some of the texture are not fully recovered, which was unfamiliar to some radiologists. To cope with this problem, here we propose a direct residual learning approach on directional wavelet domain to solve this problem and to improve the performance against previous work. In particular, the new network estimates the noise of each input wavelet transform, and then the de-noised wavelet coefficients are obtained by subtracting the noise from the input wavelet transform bands. The experimental results confirm that the proposed network has significantly improved performance, preserving the detail texture of the original images.

cs.CV↗

arXiv2017

Deep artifact learning for compressed sensing and parallel MRI

Purpose: Compressed sensing MRI (CS-MRI) from single and parallel coils is one of the powerful ways to reduce the scan time of MR imaging with performance guarantee. However, the computational costs are usually expensive. This paper aims to propose a computationally fast and accurate deep learning algorithm for the reconstruction of MR images from highly down-sampled k-space data. Theory: Based on the topological analysis, we show that the data manifold of the aliasing artifact is easier to learn from a uniform subsampling pattern with additional low-frequency k-space data. Thus, we develop deep aliasing artifact learning networks for the magnitude and phase images to estimate and remove the aliasing artifacts from highly accelerated MR acquisition. Methods: The aliasing artifacts are directly estimated from the distorted magnitude and phase images reconstructed from subsampled k-space data so that we can get an aliasing-free images by subtracting the estimated aliasing artifact from corrupted inputs. Moreover, to deal with the globally distributed aliasing artifact, we develop a multi-scale deep neural network with a large receptive field. Results: The experimental results confirm that the proposed deep artifact learning network effectively estimates and removes the aliasing artifacts. Compared to existing CS methods from single and multi-coli data, the proposed network shows minimal errors by removing the coherent aliasing artifacts. Furthermore, the computational time is by order of magnitude faster. Conclusion: As the proposed deep artifact learning network immediately generates accurate reconstruction, it has great potential for clinical applications.

cs.CV↗

arXiv2017

A Joint Sparse Recovery Framework for Accurate Reconstruction of Inclusions in Elastic Media

A robust algorithm is proposed to reconstruct the spatial support and the Lamé parameters of multiple inclusions in a homogeneous background elastic material using a few measurements of the displacement field over a finite collection of boundary points. The algorithm does not require any linearization or iterative update of Green's function but still allows very accurate reconstruction. The breakthrough comes from a novel interpretation of Lippmann-Schwinger type integral representation of the displacement field in terms of unknown densities having common sparse support on the location of inclusions. Accordingly, the proposed algorithm consists of a two-step approach. First, the localization problem is recast as a joint sparse recovery problem that renders the densities and the inclusion support simultaneously. Then, a noise robust constrained optimization problem is formulated for the reconstruction of elastic parameters. An efficient algorithm is designed for numerical implementation using the Multiple Sparse Bayesian Learning (M-SBL) for joint sparse recovery problem and the Constrained Split Augmented Lagrangian Shrinkage Algorithm (C-SALSA) for the constrained optimization problem. The efficacy of the proposed framework is manifested through extensive numerical simulations. To the best of our knowledge, this is the first algorithm tailored for parameter reconstruction problems in elastic media using highly under-sampled data in the sense of Nyquist rate.

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