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Discovering dominant patterns and exploring dynamic behaviors especially critical state transitions and tipping points in high-dimensional time-series data are challenging tasks in study of real-world complex systems, which demand…

It is well-known that in inverse problems, end-to-end trained networks overfit the degradation model seen in the training set, i.e., they do not generalize to other types of degradations well. Recently, an approach to first map images…

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

Recent advances in deep learning have shown exciting promise in filling large holes in natural images with semantically plausible and context aware details, impacting fundamental image manipulation tasks such as object removal. While these…

Cyclic spectral analysis is a signal processing technique designed to deal with stochastic signals whose statistics vary periodically with time. Pulsar radio emission is a textbook example of this signal class, known as cyclostationary…

This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the…

Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage adaptive estimate. In the first stage, the number and location of the change…

The detection of clinically significant prostate cancer lesions (csPCa) from biparametric magnetic resonance imaging (bp-MRI) has emerged as a noninvasive imaging technique for improving accurate diagnosis. Nevertheless, the analysis of…

Bregman proximal point algorithm (BPPA) has witnessed emerging machine learning applications, yet its theoretical understanding has been largely unexplored. We study the computational properties of BPPA through learning linear classifiers…

In Convolutional Neural Networks (CNNs) information flows across a small neighbourhood of each pixel of an image, preventing long-range integration of features before reaching deep layers in the network. We propose a novel architecture that…

Detecting regime shifts in chaotic time series is hard because observation-space signals are entangled with intrinsic variability. We propose Parameter--Space Changepoint Detection (Param--CPD), a two--stage framework that first amortizes…

A general conversion strategy by involving a shifted parameter $\theta$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such…

Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…

Conventional rendering techniques are primarily designed and optimized for single-frame rendering. In practical applications, such as scene editing and animation rendering, users frequently encounter scenes where only a small portion is…

The latest deep learning-based approaches have shown promising results for the challenging task of inpainting missing regions of an image. However, the existing methods often generate contents with blurry textures and distorted structures…

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…

Autonomous driving algorithms usually employ sRGB images as model input due to their compatibility with the human visual system. However, visually pleasing sRGB images are possibly sub-optimal for downstream tasks when compared to RAW…

The problem of inpainting involves reconstructing the missing areas of an image. Inpainting has many applications, such as reconstructing old damaged photographs or removing obfuscations from images. In this paper we present the directional…

Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often…

Principal component analysis (PCA) has been widely used in analyzing high-dimensional data. It converts a set of observed data points of possibly correlated variables into a set of linearly uncorrelated variables via an orthogonal…