Jakeoung Koo

Kyungmin Choi, JaKeoung Koo, Stephen McLaughlin et al.

Single-photon Lidar imaging offers a significant advantage in 3D imaging due to its high resolution and long-range capabilities, however it is challenging to apply in noisy environments with multiple targets per pixel. To tackle these challenges, several methods have been proposed. Statistical methods demonstrate interpretability on the inferred parameters, but they are often limited in their ability to handle complex scenes. Deep learning-based methods have shown superior performance in terms of accuracy and robustness, but they lack interpretability or they are limited to a single-peak per pixel. In this paper, we propose a deep unrolling algorithm for dual-peak single-photon Lidar imaging. We introduce a hierarchical Bayesian model for multiple targets and propose a neural network that unrolls the underlying statistical method. To support multiple targets, we adopt a dual depth maps representation and exploit geometric deep learning to extract features from the point cloud. The proposed method takes advantages of statistical methods and learning-based methods in terms of accuracy and quantifying uncertainty. The experimental results on synthetic and real data demonstrate the competitive performance when compared to existing methods, while also providing uncertainty information.

Jakeoung Koo, Anders B. Dahl, J. Andreas Bærentzen et al.

In computed tomography, the reconstruction is typically obtained on a voxel grid. In this work, however, we propose a mesh-based reconstruction method. For tomographic problems, 3D meshes have mostly been studied to simulate data acquisition, but not for reconstruction, for which a 3D mesh means the inverse process of estimating shapes from projections. In this paper, we propose a differentiable forward model for 3D meshes that bridge the gap between the forward model for 3D surfaces and optimization. We view the forward projection as a rendering process, and make it differentiable by extending recent work in differentiable rendering. We use the proposed forward model to reconstruct 3D shapes directly from projections. Experimental results for single-object problems show that the proposed method outperforms traditional voxel-based methods on noisy simulated data. We also apply the proposed method on electron tomography images of nanoparticles to demonstrate the applicability of the method on real data.

Byung-Woo Hong, Ja-Keoung Koo, Martin Burger et al.

We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the iterative optimization, so that regularization is strongest initially, and wanes as data fidelity improves, with the weight of the regularizer being minimized at convergence. We also introduce the use of a Huber loss function in both data fidelity and regularization terms, and present an efficient convex optimization algorithm based on the alternating direction method of multipliers (ADMM) using the equivalent relation between the Huber function and the proximal operator of the one-norm. We illustrate and validate our adaptive Huber-Huber model on synthetic and real images in segmentation, motion estimation, and denoising problems.

Byung-Woo Hong, Ja-Keoung Koo, Stefano Soatto

We present a variational multi-label segmentation algorithm based on a robust Huber loss for both the data and the regularizer, minimized within a convex optimization framework. We introduce a novel constraint on the common areas, to bias the solution towards mutually exclusive regions. We also propose a regularization scheme that is adapted to the spatial statistics of the residual at each iteration, resulting in a varying degree of regularization being applied as the algorithm proceeds: the effect of the regularizer is strongest at initialization, and wanes as the solution increasingly fits the data. This minimizes the bias induced by the regularizer at convergence. We design an efficient convex optimization algorithm based on the alternating direction method of multipliers using the equivalent relation between the Huber function and the proximal operator of the one-norm. We empirically validate our proposed algorithm on synthetic and real images and offer an information-theoretic derivation of the cost-function that highlights the modeling choices made.

Byung-Woo Hong, Ja-Keoung Koo, Hendrik Dirks et al.

We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are considered as optimal solutions of the energy functionals that mainly consist of data fidelity, regularization and a control parameter for their trade-off. We presents an algorithm to determine the relative weight between data fidelity and regularization based on the residual that measures how well the observation fits the model. Our adaptive regularization scheme is designed to locally control the regularization at each pixel based on the assumption that the diversity of the residual of a given imaging model spatially varies. The energy optimization is presented in the alternating direction method of multipliers (ADMM) framework where the adaptive regularization is iteratively applied along with mathematical analysis of the proposed algorithm. We demonstrate the robustness and effectiveness of our adaptive regularization through experimental results presenting that the qualitative and quantitative evaluation results of each imaging task are superior to the results with a constant regularization scheme. The desired properties, robustness and effectiveness, of the regularization parameter selection in a variational framework for imaging problems are achieved by merely replacing the static regularization parameter with our adaptive one.