Il Yong Chun (chun.ilyong at gmail)

From Convolutional Operator Learning to Neural Network: Theory and Application

"Learning" convolutional operators from large datasets and applying the learned operators is a growing trend in a wide range of applications in signal/image processing and computer vision. Patch-based approach—referred to the local approach—is a well-known kernel learning framework for offering straightforward mathematical formulation and optimization. However, this approach is not well-suited to learning kernels from "big data" and/or applying the learned operators to solve large-dimensional inverse problems, because it needs to store many overlapping patches extracted from the training or testing images. This becomes even more problematic in forming (deep) hierarchical representations, e.g., (de)convolutional neural network ((de)CNN). The recent global approach resolves the issues by learning kernels and obtaining (sparse) representations directly in the image domain without storing many overlapping patches. I am a pioneer in developing fast and convergence-guaranteed convolutional operator learning frameworks within the global approach, e.g., convolutional analysis operator learning (CAOL [1]) and convolutional dictionary learning (CDL [2]), via the so-called Block Proximal Gradient method using Majorizer (BPG-M [1, 2]) that sheds new light on tight majorization in solving block multi-(non)convex problems. The learned convolutional operators improved image recovery performance for some extreme imaging applications, e.g., sparse-view CT [1, 4], extremely undersampled MRI [3], and denoising low SNR images [2].

From 2015, researchers have been studying algorithmic properties of training (deep) CNNs by reformulating their objective function. More recently, there have been some attempts to moderate some problems of stochastic gradient methods in which gradients are computed by back-propagation—the most widely used optimization technique in training CNN. However, there exist no solid algorithmic frameworks—particularly based on accelerated proximal gradient methods—to maximally accelerate the training convergence of CNN. On the application sides, researchers have begun to apply (deep) NNs to iterative signal/image recovery models. However, they lack "complete" mathematical models in iterative signal recovery; it limits comprehensively understand/analyze them in terms of both signal recovery and algorithmic properties, e.g., acceleration and convergence. I am the first researcher in mathematically formulating CNNs (e.g., LeNet-5) particularly suitable for iterative signal/image recovery, while overcoming the aforementioned limitations via the CAOL and BPG-M frameworks [1].

References
[1] Il Yong Chun and Jeffrey A. Fessler, "Convolutional analysis operator learning: Acceleration, convergence, application, and neural networks," submitted to IEEE Trans. Image Process., Jan. 2018. [Online] Available: http://arxiv.org/abs/1802.05584
[2] Il Yong Chun and Jeffrey A. Fessler, "Convolutional dictionary learning: Acceleration and convergence," IEEE Trans. Image Process., vol. 27, no. 4, Apr. 2018.
[3] Il Yong Chun and Jeffrey A. Fessler, "Deep BCD-Net using identical encoding-decoding CNN structures for iterative image recovery," in Proc. IEEE IVMSP Workshop, Apr. 2018.
[Online] Available: http://arxiv.org/abs/1802.07129
[4] Il Yong Chun, Xuehang Zheng, Zhipeng Li, Yong Long, and Jeffrey A. Fessler, "Sparse-view X-ray CT reconstruction using ℓ₁ prior with learned transform," submitted to IEEE Trans. Rad. Plasma Med. Sci., Oct. 2017. [Online] Available: http://arxiv.org/abs/1711.00905

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Compressed Sensing and Parallel Acquisition: Theory and Application

Parallel acquisition systems are employed successfully in a variety of different sensing/imaging applications (e.g., parallel MRI, multi-view imaging, wireless sensor networks, light-field imaging with multiple focal stacks, synthetic aperture radar imaging, derivative sampling in seismic imaging, etc.) when a single sensor cannot provide enough measurements for a high-quality signal recovery. Compressed sensing (CS), random sub-sampling theory dependent on the sparsity of signal, has been used to establish the theoretical improvements of such systems by providing recovery guarantees for which, subject to appropriate conditions, the number of measurements required per sensor decreases linearly with the total number of sensors [4, 5]. I am a pioneer in establishing theoretical improvements of CS parallel acquisition architecture [4, 5, 6], developing CS-based imaging fundamentals, and applying these theories in practical applications, e.g., parallel MRI (MRI using multiple receive coils [6]) and light-field photography with multiple focal stacks.

References
[4] Il Yong Chun and Ben Adcock, "Compressed sensing and parallel acquisition," IEEE Trans. Inf. Theory, vol. 63, no. 8, pp. 4860--4882, May 2017.
[5] Il Yong Chun and Ben Adcock, "Uniform recovery from subgaussian multi-sensor measurements," under review for Appl. Comput. Harmon. Anal., Feb. 2018. [Online] Available: http://arxiv.org/abs/1610.05758
[6] Il Yong Chun, Ben Adcock, and Thomas M. Talavage, "Efficient compressed sensing SENSE pMRI reconstruction with joint sparsity promotion," IEEE Trans. Med. Imag., vol. 5, no. 1, pp. 354--368, Jan. 2016.

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Adaptive Computational Imaging: Theory and Application

Most imaging devices have complicated imaging physics and suffer from various types of noise. This is the main reason that underlying mathematical analyses are largely absent in their image recovery performance. If undersampling schemes are involved, the performance analysis becomes a tricky math problem. By exploiting signal processing estimation techniques (e.g., mean square error, MSE, and SNR) and stochastic modeling, my third research interest is to adaptively control imaging techniques to improve the quality of reconstructed images. For example, I initially established the imaging fundamentals of (high-field) MRI using multiple transmit/receive coils and its relation to MSE, and proposed a new excitation pattern design which further reduces MSE and manages the specific absorption rate [7]. In particular, adaptively considering the spatial information of transmit and receive coils and expected aliasing patterns, the proposed excitation pattern not only successfully reduces the error variances but also suppresses the aliasing artifacts caused by extremely accelerating (i.e., 8-fold) scanning.

References
[7] Il Yong Chun, Song Noh, David J. Love, Thomas M. Talavage, Stephen Beckley, and Sherman J. Kisner, "Mean squared error (MSE)-based excitation pattern design for parallel transmit and receive SENSE MRI image reconstruction," IEEE Trans. Comput. Imag., vol. 2, no. 4, pp. 424--439, Dec. 2016.

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Neuroimaging and Neuroscience

Recently, rapid interest has grown in the neuroscience community in evaluating the impact of brain changes caused by repetitive sub-concussive hits to the head. Using diffusion tensor MRI, I evaluated longitudinal white matter changes in high-school football players and examined how these changes may be linked to an athlete’s history of accumulated head collision events during practices and games [8, 9].

On the other hand, an appropriate statistical image analysis framework (e.g., hypothesis testing) to reliably detect subtle changes in athletes who experienced repetitive sub-concussive head blows is largely absent. I initially proposed a stronger randomized hypothesis testing method that exploits both completely and incompletely paired data [9]. The method successfully detects more significantly deviated regions in the sub-concussed brains, thereby providing a stronger evidence to suggest that head impacts commonly occur during contact sports have the potential for neurological injury although those impacts do not result in visible symptoms of neurological dysfunction.

References
[8] Il Yong Chun, Xianglun Mao, Eric L. Breedlove, Larry J. Leverenz, Eric A. Nauman, and Thomas M. Talavage, "DTI detection of longitudinal WM abnormalities due to accumulated head impacts," Dev. Neuropsychol., vol. 40, no. 2, pp. 92--97, May 2015.
[9] Sumra Bari, Il Yong Chun, Larry J. Leverenz, Eric A. Nauman, and Thomas M. Talavage, "DTI detection of WM abnormalities using randomization test with complete and incomplete pairs," in Proc. Org. for Hum. Brain Mapp. (OHBM), Honolulu, HI, Jun. 2015.

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