This book covers recent advances in image processing and imaging sciences from an optimization viewpoint, especially convex optimization with the goal of designing tractable algorithms. Throughout the handbook, the authors introduce topics on the most key aspects of image acquisition and processing that are based on the formulation and solution of novel optimization problems. The first part includes a review of the mathematical methods and foundations required, and covers topics in image quality optimization and assessment. The second part of the book discusses concepts in image formation and capture from color imaging to radar and multispectral imaging. The third part focuses on sparsity constrained optimization in image processing and vision and includes inverse problems such as image restoration and de-noising, image classification and recognition and learning-based problems pertinent to image understanding. Throughout, convex optimization techniques are shown to be a critically important mathematical tool for imaging science problems and applied extensively.
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Introduction
Monga, Vishal
Optimizing Image Quality
Wang, Zhou et al.( Univ. Waterloo)
Computational Color Imaging
Bala, Raja et al.(PARC)
Optimization Methods for Synthetic Aperture Radar Imaging
Yazici, Birsen et al. (RPI)
Computational Spectral and Ultrafast Imaging via Convex Optimization
Kamalabadi, Farzad et al. (UIUC)
Discriminative Sparse Representations
Patel, Vishal et al.(Rutgers)
DICTOL -- The Dictionary Learning Toolbox
The toolbox implements many widely used generative and discriminative dictionary learning methods. Including but not limited to: Online Dictionary Learning, LC-KSVD, Dictionary Learning with structured incoherence (DLSI), Dictionary learning for separating particularity and commonality (COPAR), Fisher Discriminative Dictionary Learning (FDDL), and our aforementioned work (LRSDL). Many classical methods are sped up via new numerical optimization innovations, some of which are discussed in the LRSDL paper at the IEEE Explore link above.
Optimization of Regularized Deep Network
We strength the deep networks by domain knowledge. The regularized deep network takes advantages from robustness and efficiency brought by image processing knowledge. Projects like natural image Spuer-resolution, MRI Super-resolution use different regularized network and associated optimization procedures.
Non-convex Optimization For Image Alignment
Unlike most existing approaches that are feature-based, our algorithm works on pixels directly, and accounts for errors across the whole images globally. Technically, we formulate the alignment problem as rank-1 and sparse matrix decomposition over transformed images, and develop an efficient algorithm for solving this challenging non-convex optimization problem. The algorithm reduces to a sequence of subproblems, where we analytically establish exact recovery conditions, convergence and optimality, together with convergence rate and complexity.
Iterative Convex Refinement For Sparse Recovery
The Iterative Convex Refinement (ICR) aims to solve a hard non-convex optimization problem directly allowing for greater generality in the sparse structure. Essentially, ICR solves a sequence of convex optimization problems such that sequence of solutions converges to a sub-optimal solution of the original hard optimization problem. We propose two versions of our algorithm: a.) an unconstrained version, and b.) with a non-negativity constraint on sparse coefficients, which may be required in some real-world problems. Experimental validation is performed on both synthetic data and for a real-world image recovery problem, which illustrates merits of ICR over state of the art alternatives.
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