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The work seeks to develop an algorithm for image reconstruction by directly inverting the non-linear data model in spectral CT. Using the non-linear data model, we formulate the image-reconstruction problem as a non-convex optimization…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies…
The primal-dual algorithm recently proposed by Chambolle & Pock (abbreviated as CPA) for structured convex optimization is very efficient and popular. It was shown by Chambolle & Pock in \cite{CP11} and also by Shefi & Teboulle in…
One of the challenges of supervised learning training is the need to procure an substantial amount of tagged data. A well-known method of solving this problem is to use synthetic data in a copy-paste fashion, so that we cut objects and…
Dimensionality reduction (DR) is frequently used for analyzing and visualizing high-dimensional data as it provides a good first glance of the data. However, to interpret the DR result for gaining useful insights from the data, it would…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…
In this paper we review several algorithms for image inpainting based on the hypoelliptic diffusion naturally associated with a mathematical model of the primary visual cortex. In particular, we present one algorithm that does not exploit…
Pooling is a ubiquitous operation in image processing algorithms that allows for higher-level processes to collect relevant low-level features from a region of interest. Currently, max-pooling is one of the most commonly used operators in…
Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
With the widespread accumulation of observational data, researchers obtain a new direction to learn counterfactual effects in many domains (e.g., health care and computational advertising) without Randomized Controlled Trials(RCTs).…
We propose an automatic video inpainting algorithm which relies on the optimisation of a global, patch-based functional. Our algorithm is able to deal with a variety of challenging situations which naturally arise in video inpainting, such…
Recent image inpainting methods show promising results due to the power of deep learning, which can explore external information available from a large training dataset. However, many state-of-the-art inpainting networks are still limited…
It is an ill-posed problem to recover the true scene colors from a color biased image by discounting the effects of scene illuminant and camera spectral sensitivity (CSS) at the same time. Most color constancy (CC) models have been designed…
In the literature, there are a few researches to design some parameters in the Proximal Point Algorithm (PPA), especially for the multi-objective convex optimizations. Introducing some parameters to PPA can make it more flexible and…
Modern optical flow methods are often composed of a cascade of many independent steps or formulated as a black box neural network that is hard to interpret and analyze. In this work we seek for a plain, interpretable, but learnable…
PCA can be used for rotation invariant features, describing a shape with its $p_{ab}=E[(x_i-E[x_a])(x_b-E[x_b])]$ covariance matrix approximating shape by ellipsoid, allowing for rotation invariants like its traces of powers. However, real…
The second order optical response of centrosymmetric materials manifests itself mostly at their surface, being strongly suppressed in their bulk. However, the overall surface response is also suppressed in nanoparticles with a…
We develop a control algorithm that ensures the safety, in terms of confinement in a set, of a system with unknown, 2nd-order nonlinear dynamics. The algorithm establishes novel connections between data-driven and robust, nonlinear control.…
In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…