Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In this work, we present a new approach to solving the inverse problem for elliptic PDEs, using only boundary data. Our method leverages the Dirichlet-to-Neumann (DtN) map, which captures the relationship between boundary inputs and flux responses. This enables the reconstruction of the unknown physical properties within the domain from boundary measurements alone. Our framework employs a self-supervised machine learning algorithm that integrates a Finite Element Method (FEM) in the inner loop for the forward problem, ensuring high accuracy. Moreover, our approach illustrates its effectiveness in challenging scenarios with only partial boundary observations, which is often the case in real-world scenarios. In addition, the proposed algorithm effectively handles discontinuities by incorporating carefully designed loss functions. This combined FEM and machine learning approach offers a robust, accurate solution strategy for a broad range of inverse problems, enabling improved estimation of critical parameters in applications from medical diagnostics to subsurface exploration.

Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In this work, we present a new approach to solving the inverse problem for elliptic PDEs, using only boundary data. Our method leverages the Dirichlet-to-Neumann (DtN) map, which captures the relationship between boundary inputs and flux responses. This enables the reconstruction of the unknown physical properties within the domain from boundary measurements alone. Our framework employs a self-supervised machine learning algorithm that integrates a Finite Element Method (FEM) in the inner loop for the forward problem, ensuring high accuracy. Moreover, our approach illustrates its effectiveness in challenging scenarios with only partial boundary observations, which is often the case in real-world scenarios. In addition, the proposed algorithm effectively handles discontinuities by incorporating carefully designed loss functions. This combined FEM and machine learning approach offers a robust, accurate solution strategy for a broad range of inverse problems, enabling improved estimation of critical parameters in applications from medical diagnostics to subsurface exploration.

This paper proposes a data clustering algorithm that is inspired by the prominent convergence property of the Projection onto Convex Sets (POCS) method, termed the POCS-based clustering algorithm. For disjoint convex sets, the form of simultaneous projections of the POCS method can result in a minimum mean square error solution. Relying on this important property, the proposed POCS-based clustering algorithm treats each data point as a convex set and simultaneously projects the cluster prototypes onto respective member data points, the projections are convexly combined via adaptive weight values in order to minimize a predefined objective function for data clustering purposes. The performance of the proposed POCS-based clustering algorithm has been verified through a large scale of experiments and data sets. The experimental results have shown that the proposed POCS-based algorithm is competitive in terms of both effectiveness and efficiency against some of the prevailing clustering approaches such as the K-Means/K-Means+⁣+ and Fuzzy C-Means (FCM) algorithms. Based on extensive comparisons and analyses, we can confirm the validity of the proposed POCS-based clustering algorithm for practical purposes.

A two-stage knowledge transfer framework for distilling efficient dehazing networks is proposed in this paper. Recently, lightweight dehazing studies based on knowledge distillation have shown great promise and potential. However, existing approaches have only focused on exploiting knowledge extracted from clean images (hard knowledge) while neglecting the concise knowledge encoded from hazy images (soft knowledge). Additionally, recent methods have solely emphasized process-oriented learning rather than response-oriented learning. Motivated by these observations, the proposed framework is targeted toward aptly exploiting soft knowledge and response-oriented learning to produce improved dehazing models. A general encoder-decoder dehazing structure is utilized as the teacher network as well as a basis for constructing the student model with drastic complexity reduction using a channel multiplier. A transmissionaware loss is adopted that leverages the transmission information to enhance the network's generalization ability across different haze densities. The derived network, called Soft knowledgebased Distilled Dehazing Network (SDDN), achieves a significant reduction in complexity while maintaining satisfactory performance or even showing better generalization capability in certain cases. Experiments on various benchmark datasets have demonstrated that SDDN can be compared competitively with prevailing dehazing approaches. Moreover, SDDN shows a promising applicability to intelligent driving systems. When combined with YOLOv4, SDDN can improve the detection performance under hazy weather by 9.1% with only a negligible increase in the number of parameters (0.87%). The code of this work is publicly available at https://github.com/tranleanh/sddn.

This paper proposes an image dehazing prior, called Regional Saturation-Value Translation (RSVT), in order to address the color distortion issues produced by prevailing prior-based dehazing methods when processing hazy images with large sky regions. The proposed RSVT prior is derived from statistical analyses of the correlation between hazy points and respective haze-free points in the HSV color space. The prior is based upon two key observations in the sky areas. First, the difference in terms of hue for a pair of hazy and haze-free points is very small, raising an assumption that the variability of pixel values caused by haze mostly occurs in the saturation and value spaces. This leads to the second observation that, in the 2D saturation-value coordinate system, almost all the lines passing through corresponding pairs of hazy-clean points, termed S-V lines, are likely to intersect around the airlight coordinates. A hybrid refined dark channel is introduced in order to decompose the input hazy image into sky and non-sky regions and to estimate the global atmospheric light. Combining the prior with the hybrid refined dark channel, a novel single image dehazing framework is proposed. Haze removal is performed separately for the sky and non-sky regions by adopting the proposed RSVT prior and Koschmieder's law, respectively. The experimental results have shown that the proposed dehazing method can restore visually compelling sky color and effectively handle the color distortion issues associated with large sky regions.

This paper proposes a data augmentation method for improving the robustness of driving object detectors against domain shift. Domain shift problem arises when there is a significant change between the distribution of the source data domain used in the training phase and that of the target data domain in the deployment phase. Domain shift is known as one of the most popular reasons resulting in the considerable drop in the performance of deep neural network models. In order to address this problem, one effective approach is to increase the diversity of training data. To this end, we propose a data synthesis module that can be utilized to train more robust and effective object detectors. By adopting YOLOv4 as a base object detector, we have witnessed a remarkable improvement in performance on both the source and target domain data.

Projection onto Convex Set (POCS) is a powerful signal processing tool for various convex optimization problems. For non-intersecting convex sets, the simultaneous POCS method can result in a minimum mean square error solution. This property of POCS has been applied to clustering analysis and the POCS-based clustering algorithm was proposed earlier. In the POCS-based clustering algorithm, each data point is treated as a convex set, and a parallel projection operation from every cluster prototype to its corresponding data members is carried out in order to minimize the objective function and to update the memberships and prototypes. The algorithm works competitively against conventional clustering methods in terms of execution speed and clustering error on general clustering tasks. In this paper, the performance of the POCS-based clustering algorithm on a more complex task, embedding clustering, is investigated in order to further demonstrate its potential in benefiting other high-level tasks. To this end, an off-the-shelf FaceNet model and an autoencoder network are adopted to synthesize two sets of feature embeddings from the Five Celebrity Faces and MNIST datasets, respectively, for experiments and analyses. The empirical evaluations show that the POCS-based clustering algorithm can yield favorable results when compared with other prevailing clustering schemes such as the K-Means and Fuzzy C-Means algorithms in embedding clustering problems.

전쟁과 분쟁지역에 매설된 지뢰와 폭발물 테러 공격을 사전에 감지할 수 있는 폭발물 감지 시스템의 개발이 필요하다. 고분자 형광 소광 현상을 이용하여 폭발물의 증기가 형광 폴리머 물질과 결합하여 형광의 세기의 감소하는 현상을 광학 시스템으로 선별하고 증폭기 회로와 ADC를 통하여 디지털화한다. 음의 기울기를 갖는 구간의 상대적인 차이를 적분하고 적분된 값이 임계값을 넘어가면 폭발물질이 탐지된 것으로 판단하는 알고리즘을 적용하였다. 본 연구의 공기 흡기식 폭발물 탐지 시스템은 TNT 9.15ppb 농도까지 탐지 가능하고 응답시간은 5초 이내로 신속한 탐지가 가능하다.