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The alternating direction method of multipliers (ADMM) is a popular method for solving convex separable minimization problems with linear equality constraints. The generalization of the two-block ADMM to the three-block ADMM is not trivial…
We consider an image decomposition model involving a variational (minimization) problem and an evolutionary partial differential equation (PDE). We utilize a linear inhomogenuous diffusion constrained and weighted total variation (TV)…
Face analysis is a core part of computer vision, in which remarkable progress has been observed in the past decades. Current methods achieve recognition and tracking with invariance to fundamental modes of variation such as illumination, 3D…
We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…
We consider the computation of the entanglement-assisted quantum rate-distortion function, which plays a central role in quantum information theory. We propose an efficient alternating minimization algorithm based on the Lagrangian…
Fourier ptychography microscopy (FPM), sharing its roots with synthetic aperture technique and phase retrieval method, is a recently developed computational microscopic super-resolution technique. By turning on the light-emitting diode…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
Image compression is one of the essential methods of image processing. Its most prominent advantage is the significant reduction of image size allowing for more efficient storage and transfer. However, lossy compression is associated with…
In this thesis, we offer a thorough investigation of different regularisation terms used in variational imaging problems, together with detailed optimisation processes of these problems. We begin by studying smooth problems and partially…
In this paper, we present a Fast Motion Deblurring-Conditional Generative Adversarial Network (FMD-cGAN) that helps in blind motion deblurring of a single image. FMD-cGAN delivers impressive structural similarity and visual appearance after…
We propose a new incremental aggregation algorithm for multi-image deblurring with automatic image selection. The primary motivation is that current bursts deblurring methods do not handle well situations in which misalignment or…
Blind Super-Resolution (SR) usually involves two sub-problems: 1) estimating the degradation of the given low-resolution (LR) image; 2) super-resolving the LR image to its high-resolution (HR) counterpart. Both problems are ill-posed due to…
Thresholding iterative methods are recently successfully applied to image deblurring problems. In this paper, we investigate the modified linearized Bregman algorithm (MLBA) used in image deblurring problems, with a proper treatment of the…
Low-rank Deconvolution (LRD) has appeared as a new multi-dimensional representation model that enjoys important efficiency and flexibility properties. In this work we ask ourselves if this analytical model can compete against Deep Learning…
The alternating direction method of multipliers (ADMM) algorithm is a powerful and flexible tool for complex optimization problems of the form $\min\{f(x)+g(y) : Ax+By=c\}$. ADMM exhibits robust empirical performance across a range of…
2D Total Variation Denoising (TVD) is a widely used technique for image denoising. It is also an important nonparametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to…
We consider the estimation of the regularization parameter for the simultaneous deblurring of multiple noisy images via Tikhonov regularization. We approach the problem in three ways. We first reduce the problem to a single-image deblurring…
Image restoration requires a careful balance between noise suppression and structure preservation. While first-order total variation (TV) regularization effectively preserves edges, it often introduces staircase artifacts, whereas…
This paper presents a new algorithm, Accelerated Wirtinger Flow (AWF), for ptychographic image reconstruction from phaseless diffraction pattern measurements. AWF is based on combining Nesterov's acceleration approach with Wirtinger…
For the success of video deblurring, it is essential to utilize information from neighboring frames. Most state-of-the-art video deblurring methods adopt motion compensation between video frames to aggregate information from multiple frames…