Research
My research interests include signal processing, optimization, and machine learning. My work focuses on using structural information in data representation and network topology to reduce complexity and improve the recovery performance. My research can be grouped into three categories: (1) signal processing with structural information, (2) machine learning algorithms to process Big Data in a distributed manner, and (3) optimization with structural information.
1. Signal processing with structural information
Signal recovery with structural information: super-resolution
Fig. 1.1. Optical microscopy
My research on super-resolution for spectrally (resp. spatially) sparse signals has the goal of improving the recovery performance in obtaining precise spectral information from as few time (resp. frequency) samples as possible. Since the frequency of a signal of interest (resp. the spike of a signal in space domain) can take any value, we need to consider the continuous dictionary for possible frequency regions (resp. spatial regions); namely, the number of possible choices for frequencies (resp. spikes in space) is infinite. Therefore, recovery of frequency (resp. time/space) information in the continuous dictionary from coarsely chosen time samples (resp. frequency samples) is a challenging problem. Moreover, when the frequencies of a signal of interest (spikes in spatial domain) are located closely to each other, estimating frequency (resp. time/space) information from few time samples (resp. frequency samples) becomes even harder. To deal with this problem, the total variation minimization and atomic norm minimization were introduced in others’ previous research. It is then natural to ask whether there are efficient frequency (resp. signal in the spatial domain) recovery algorithms that can further improve the performance or relax the frequency (resp. time/space) separation conditions when compared with the total variation minimization or atomic norm minimization. In addition, for applications such as microscopy, MRI, and X-ray crystallography, fast algorithms to handle large scale super-resolution problem are demanding.
• Super-resolution with prior information
In this research, my colleagues and I improved the performance of the atomic norm minimization by using prior knowledge about the range of frequency locations. The result of the research is that if we know the frequency block that true frequencies are located in a priori, then we can have better recovery performance than the standard atomic norm minimization. To derive the Semidefinite Programming (SDP) formulation of atomic norm minimization with prior information, we used the positive trigonometric polynomial theorem [1]. Also, we considered the case when we have no prior information and proposed block iterative reweighted algorithms to improve the recovery performance of spectral super-resolution [2].
• Fast algorithm for super-resolution
This research aims to develop fast algorithms for super-resolution. For this purpose, my colleagues and I proposed the projected alternating gradient descent algorithm using the Wirtinger derivative. In the algorithm, we use the low rank structure of Hankel matrix as well as Toeplitz matrix. [3].
• Phaseless super-resolution
Due to the physical limitation in measurement tools such as microscopy, X-ray crystallography, and MRI, we are sometimes able to measure only a part of the signal such as low frequency information, a low resolution image, and the magnitude of a signal. An optical microscopy is a good example having such physical limitations including low-frequency measurements and phaseless measurements. I proposed an SDP-based signal recovery method to achieve phaseless super-resolution in the continuous domain [5, 6].
• Super-resolution for multidimensional signals
For applications including images, super-resolution for multidimensional signals is highly required. We propose the exact SDP formulation for multidimensional super-resolution [6, 7]
• Mitigating resolution limit in super-resolution
The atomic norm minimization has resolution limit in the distance between any two spikes to have perfect recovery. This research is to mitigate the resolution limit of the atomic norm minimization. The result of this research is that the Hankel matrix completion, which is interpreted as the orthogonal atomic norm minimization, can achieve the perfect recovery without suffering from the resolution limit unlike the atomic norm minimization. We provided the reason for this in [8,9].
References
[1] K. V. Mishra, M. Cho, A. Kruger, and W. Xu, “Spectral super-resolution with prior knowledge,” IEEE Transactions on Signal Processing, vol. 63, no. 20, pp. 5342-5357, 2015.
[2] M. Cho, K. V. Mishra, J.-F. Cai, and W. Xu, “Block iterative reweighted algorithms for super-resolution of spectrally sparse signals,” IEEE Signal Processing Letters, vol. 22, no. 12, pp. 2319-2323, 2015.
[3] M. Cho, J.-F. Cai, S. Liu, Y. C. Eldar and W. Xu, “Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2016, pp. 4638-4642.
[4] M. Cho, J. Yi, J.-F. Cai, S. Liu, Y. C. Eldar and W. Xu, “Non-convex algorithms for recovery of spectrally sparse signals via rank minimization of structured matrix,” in preparation.
[5] M. Cho, C. Thrampoulidis, W. Xu, and B. Hassibi, “Phaseless super-resolution in the continuous domain,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2017, pp. 3814-3818.
[6] M. Cho, C. Thrampoulidis, W. Xu, and B. Hassibi, “2D Phaseless super-resolution in the continuous domain,” in Proceedings of SPIE Optical Engineering and Applications, Wavelets and Sparsity XVII, 2017, vol. 10394, pp. 103941H.
[7] W. Xu, J.-F. Cai, K. V. Mishra, M. Cho, and A. Kruger, “Precise semidefinite programming formulation of atomic norm minimization for recovering d-dimensional (d ≥ 2) off-the-grid frequencies,” in Proceedings of Information Theory and Applications (ITA) Workshop, 2014, pp. 1-4.
[8] W. Xu, J. Yi, S. Dasgupta, J.-F. Cai, M. Jacob, M. Cho, "Separation-Free Super-Resolution from Compressed Measurements is Possible: an Orthonormal Atomic Norm Minimization Approach", in Proceedings of IEEE International Symposium on Information Theory (ISIT), 2018.
[9] W. Xu, J. Yi, S. Dasgupta, J.-F. Cai, M. Jacob, M. Cho, "Separation-Free Super-Resolution from Compressed Measurements is Possible: an Orthonormal Atomic Norm Minimization Approach", submitted to IEEE Transaction on Information Theory, 2018.
Direction of Arrival and moving target tracking
Fig.1.2. Direction of Arrival (DoA) Problem with unknown sensor parameters
Direction-of-Arrival (DoA) aims at finding the direction of signal sources from samples of signals arrived at a point with an array of sensors. However, sensors typically need to be calibrated since their performance or sensitivity may deviate from prescription during deployment. Thus, it is required to calibrate the sensor parameters as well as recover the signal of interest from the collected measurements at the same time to achieve high system performance. Blind sensor calibration for spectrum estimation is the problem of estimating the unknown sensor calibration parameters as well as the parameters-of-interest of the impinging signals simultaneously from snapshots of measurements obtained from an array of sensors. Additionally, related to DoA, moving target tracking aims to localize the signal sources in a streaming of measurements. It finds applications in radar and sonar, wireless communications, and video surveillance. In recent years, it is recognized that a low-dimensional subspace can be estimated and tracked reliably even when the data vectors are partially observed with many missing entries, which is greatly desirable when processing high- dimensional and high-rate data to reduce the sampling requirement.
• Blind deconvolution (simultaneous sensor calibration and signal recovery)
We consider blind phase and gain calibration (BPGC) problem for DoA estimation with multiple snapshots of measurements obtained from an uniform array of sensors, where each sensor is perturbed by an unknown gain and phase parameter. Due to the unknown sensor and signal parameters, BPGC problem is a highly nonlinear problem. Assuming that the sources are uncorrelated, the covariance matrix of the measurements in a perfectly calibrated array is a Toeplitz matrix. In this research, we provide a way to solve the BPGC problem via non-convex optimization approach using the Toeplitz matrix structure [1].
• Moving target tracking with structural information
In a streaming setting, data vectors arrive sequentially over time, and the goal of subspace tracking is to estimate, and possibly track, a low-dimensional subspace that explains most of variability in the data without having to store all the history data in an online manner at a low complexity. This research investigates the problem of tracking DoA from subsampled observations in a unitary linear array, where the signals lie in a subspace spanned by columns of a Vandermonde matrix. We exploit the shift-invariance structure by mapping the data vector to a latent Hankel matrix, and then perform tracking over the Hankel matrices by exploiting their low-rank properties [2].
References
[1] M. Cho, W. Liao, and Y. Chi, “A non-convex approach to joint sensor calibration and spectrum estimation,” in Proceedings of IEEE Statistical Signal Processing (SSP) Workshop, 2018, pp. 398-402.
[2] M. Cho and Y. Chi, “Shift-Invariant Subspace Tracking with Missing Data,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2019, pp. 8222-8225.
[3] M. Cho, J. Klinefelter, H. Chiapa, and L. Ralston, "Moving Target Tracking with Missing Data in 2-D or Higher Dimension," In Proceedings of Asilomar Conference on Signals, Systems, and Computers, 2021, pp. 1098-1103.
Performance verification of a sensing matrix in compressed sensing
Fig.1.3. Compressed sensing
The research on verifying the Null Space Condition (NSC) is related to designing efficient algorithms to find a global optimal solution in non-convex optimization problems. NSC for L1 minimization in compressed sensing is a necessary and sufficient condition on the sensing matrices under which a sparse signal can be uniquely recovered from the observation data via L1 minimization. However, verifying NSC is known to be NP hard. Most of the existing methods can provide only upper and lower bounds on the proportion parameter that characterizes NSC, since the optimization problem for the proportion parameter is stated as a non-convex optimization problem. Our work enriches previous results on verifying NSC and is different from the Restricted Isometry Property (RIP) or the neighborly polytope framework for analyzing the sparse recovery capability of random sensing matrices. Our methods do not resort to a probabilistic analysis and are applicable for any given deterministic sensing matrix. Therefore, for any given sensing matrix A in compressed sensing, our methods can provide the recoverable sparsity of a signal x from given observation y satisfying y = Ax in L1 minimization. In [2], we also introduced finding defective paths in a network tomography problem, which is a possible application of this research.
References
[1] M. Cho, and W. Xu, “New algorithms for verifying the null space conditions in compressed sensing,” in Proceedings of Asilomar Conference on Signals, Systems, and Computers, 2013, pp. 1038-1042.
[2] M. Cho, K. V. Mishra, and W. Xu, “Computable performance guarantees for compressed sensing matrices,” EURASIP Journal on Advances in Signal Processing, 2018.
2. Machine learning with structural information in distributed systems
Computation of big data: efficient algorithms in distributed network systems
Fig.2.1. Tree Network
With explosion of data size and limited storage space at a single location, data are often distributed at different locations. We thus face the challenge of performing large- scale machine learning from these distributed data through communication networks. Also, there are various types of communication networks such as ring, star, and tree. In this research, it is studied that how the network communication constraints will impact the convergence speed of distributed machine learning optimization algorithms. Based on the research, we introduce how to optimize the convergence rate of a distributed algorithm depending on the network communication constraints.
References
[1] M. Cho, L. Lai, and W. Xu, “Generalized distributed dual coordinate ascent in a tree network for machine learning,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2019, pp. 3512-3516.
[2] M. Cho, L. Lai, and W. Xu, "Distributed dual coordinate ascent in general tree networks and communication network effect on synchronous machine learning," IEEE Journal on Selected Areas in Communication (JSAC), vol. 39, no. 7, pp. 2105-2119, 2021.
Reduction of communication burden in large-scale distributed control systems
Fig. 2.2. Distributed large-scale control system having multiple agents
In the control field, the optimal control design is important problem. Especially, in large-scale distributed control systems having multi-agents such as smart grid and multi-agent drone systems, communication among the multi-agents is required to make the whole systems stable. However, due to the network constraints such as limited communication bandwidth, limited communication power, or limited response time, the communication among the multi-agents can become a burden in the large-scale distributed control systems. In this research, we study the optimal control design with sparse network constraints in order to reduce communication burden in the large-scale distributed control systems.
References
[1] M. Cho and A. Chakrabortty, “Iterative Shrinkage-thresholding Algorithm and Model-based Neural Network for Sparse Optimal Control Design,” In Proceedings of European Control Conference (ECC), 2022, pp. 2311-2316.
[2] M. Cho and A. S. Abdallah, "Communication-efficient Optimal Control Design for Distributed Control Systems in Cooperative Vehicular Networks," In Proceedings of IEEE Vehicular Technology Society Conference (VTC2020-Spring), 2020, pp. 1-5
[3] M. Cho, "Deep Neural Networks Based on Iterative Thresholding and Projection Algorithms for Sparse LQR Control Design," Submitted to IEEE Transactions on Automatic Control, 2022.
Statistical analysis of big data: large-scale hypothesis testing
Fig. 2.3. Body Area Network
In many areas of science and engineering such as network tomography, cognitive radio, and radar, one needs to infer statistical information for signals of interest. Statistical information of interest can be the mean, variance, or even distributions of certain random variables. Obtaining such statistical information is essential in detecting anomalous behaviors of random signals. For example, inferring distributions of random variables has important applications in quick detection of potential hazards, in detecting changes in statistical behaviors of random variables, and also in detecting congested links with abnormal delay statistics in network tomography. We proposed algorithms to find abnormal random variables with mixed observations. Furthermore, we implemented the message passing method to detect abnormal random variables in a large scale optimization problem considering lots of random variables [1].
References
[1] M. Cho, W. Xu, and L. Lai, “Compressed hypothesis testing: to mix or not to mix?,” Submitted to IEEE Transaction on Information Theory, 2019.
3. Optimization with structural information
Large scale biomedical optimization problem: cancer treatment planning
Fig. 3.1. Illustration of multi-helix brachytherapy (H-RSBT)
The Rotating-Shield BrachyTherapy (RSBT) is a practical biomedical application for cancer treatment. For practical use in a clinic, calculating optimal treatment plans for RSBT is required. However, RSBT cancer treatment planning has a high degree of freedom due to lots of variables such as radiation exposure duration time in each radiation source carried by a needle, number of needles used in treatment, and needle locations, which makes the problem difficult. The goal of my research on this practical application is providing a fast optimization solution for optimal cancer treatment in RSBT. For this purpose, we consider the Alternating Direction Method of Multipliers (ADMM) and Douglas-Rachford splitting method. In addition, in order to find optimal needle locations for optimal cancer treatment planning, we deal with the block sparsity in ADMM. In this project, I have been interacting and co-working with a number of colleagues including medical doctors, biomedical professors, and physicists.
References
[1] M. Cho, X. Wu, H. Dadkhah, Jirong Yi, R. T. Flynn, Y. Kim, and W. Xu, “Fast dose optimization for rotating shield brachytherapy," Medical Physics, doi:10.1002/mp.12486, 2017.
[2] M. Cho, X. Wu, H. Dadkhah, R. T. Flynn, Y. Kim, and W. Xu, “Fast computational optimization method for rotating-shield brachytherapy treatment planning,” in Proceedings of American Association of Physicists in Medicine (AAPM)-John R. Cameron Young Investigator Symposium (Oral presentation), 2017.
[3] K. A. Patwardhan, H. Dadkhah, M. Cho, Y. Kim, W. Xu, X. Wu, and R. T. Flynn, “Multi-Catheter Rotating Shield Brachytherapy Control System,” in Proceedings of American Association of Physicists in Medicine (AAPM) (Oral presentation), 2017.
[4] R. Flynn, H. Dadkhah, K. A. Patwardhan, M. Cho, "A rotating shield brachytherapy system," U.S. Patent Application No. 16/092,851, and PCT International Publication No. WO 2017/184728A1.
[5] A. Le, W. Xu, R. Flynn, Y. Kim, J. Yi, M. Cho, and X. Wu. "Keyway Selection Optimization for Multi-helix Rotating Shield Brachytherapy" in review, 2019
4. Working experience: circuit design in flash memories
I have working experience at a semiconductor company for 4.5 years as a staff engineer designing analog and digital circuits in flash memories. Through this working experience, I learned about circuit design and obtained 13 US patents in the field of flash memory circuit design. Hence, I am also interested in hardware implementation, especially, embedded systems targeting healthcare devices and systems. The patents and the related conference paper are listed below.
References
[1] Ji-Hwan Kim, Myung Cho, “Nonvolatile memory device and operating method of the same,” US Patent Application No. 13/177,888.
[2] Myung Cho, "Programming method for nonvolatile memory apparatus," US Patent No. 8780644.
[3] Hwang Huh, Myung Cho, "Page buffer of nonvolatile memory device and method of performing program verification operation using the same," US Patent No. 8194464.
[4] Myung Cho, Seong-Je Park, Jung-Hwan Lee, Ji-Hwan Kim, Beom-Seok Hah, "Nonvolatile memory device and method of operating the same," US Patent No. 8767481.
[5] Myung Cho, Seong-Je Park, Jung-Hwan Lee, Ji-hwan Kim, Beom-Seok Hah, "Memory device and method for operating the same," US Patent No. 8750048.
[6] Myung Cho, Hwang Huh, Jung-Hwan Lee, Ji-Hwan Kim, "Semiconductor memory device and method of operating the same," US Patent No. 8582367.
[7] Myung Cho, "Nonvolatile memory and method for verifying the same," US Patent No. 8520444.
[8] Seong-Je Park, Jung-Hwan Lee, Ji-hwan Kim, Myung Cho, Beom-Seok Hah, "Non-volatile memory device and method for operating the same," US Patent No. 8451665.
[9] Beom-Seok Hah, Jung-Hwan Lee, Ji-Hwan Kim, Myung Cho, "Nonvolatile memory device and operating method thereof," US Patent No. 9036429.
[10] Myung Cho, Ji-hwan Kim, "Non-volatile memory device and programming method thereof," Application No.13/116,978.
[11] Ji-Hwan Kim, Seong-Je Park, Jung-Hwan Lee, Myung Cho, Beom-Seok Hah, "Semiconductor memory device and method of operating the same," US Patent No. 8456907.
[12] Jung-Hwan Lee, Seong-Je Park, Ji-Hwan Kim, Myung Cho, Beom-Seok Hah, "Semiconductor memory device and method of operating the same," US Patent No. 8576600.
[13] Myung Cho, Seong-Je Park, Jung-Hwan Lee, "Apparatus and methods of bit line setup," US Patent No. 8743623.
[14] Seung-Ho Chang, Sok-Kyu Lee, Seong-Je Park, Min-Joong Jung, Jung-Chul Han, In-Soo Wang, KyuHee Lim, Jung-Hwan Lee, Ji-Hwan Kim,Won-Kyung Kang, Tai-Kyu Kang, Hee-Su Byun, Yujong Noh, Lee-Hyun Kwon, Bon-Kwang Koo, Myung Cho, Joong-Seob Yang, Yo-Hwan Koh, "A 48nm 32Gb 8- level NAND flash memory with 5.5MB/s program throughput," In Proceedings of IEEE International Solid-State Circuit Conference (ISSCC), 2009, pp. 240-241,241a.