Sparse Representations and Compressive Sensing for Imaging and Vision

Compressed sensing or compressive sensing is a new concept in signal processing where one measures a small number of non-adaptive linear combinations of the signal. These measurements are usually much smaller than the number of samples that define the signal. From these small numbers of measurements, the signal is then reconstructed by non-linear procedure. Compressed sensing has recently emerged as a powerful tool for efficiently processing data in non-traditional ways. In this book, we highlight some of the key mathematical insights underlying sparse representation and compressed sensing and illustrate the role of these theories in classical vision, imaging and biometrics problems. Table of Contents Cover Sparse Representations and Compressive Sensing for Imaging and Vision ISBN 9781461463801 ISBN 9781461463818 Acknowledgements Contents Chapter 1 Introduction 1.1 Outline Chapter 2 Compressive Sensing 2.1 Sparsity 2.2 Incoherent Sampling 2.3 Recovery 2.3.1 Robust CS o 2.3.1.1 The Dantzig selector 2.3.2 CS Recovery Algorithms o 2.3.2.1 Iterative Thresholding Algorithms o 2.3.2.2 Greedy Pursuits o 2.3.2.3 Other Algorithms 2.4 Sensing Matrices 2.5 Phase Transition Diagrams 2.6 Numerical Examples Chapter 3 Compressive Acquisition 3.1 Single Pixel Camera 3.2 Compressive Magnetic Resonance Imaging 3.2.1 Image Gradient Estimation 3.2.2 Image Reconstruction from Gradients 3.2.3 Numerical Examples 3.3 Compressive Synthetic Aperture Radar Imaging 3.3.1 Slow-time Undersampling 3.3.2 Image Reconstruction 3.3.3 Numerical Examples 3.4 Compressive Passive Millimeter Wave Imaging 3.4.1 Millimeter Wave Imaging System 3.4.2 Accelerated Imaging with Extended Depth-of-Field 3.4.3 Experimental Results 3.5 Compressive Light Transport Sensing Chapter 4 Compressive Sensing for Vision 4.1 Compressive Target Tracking 4.1.1 Compressive Sensing for Background Subtraction 4.1.2 Kalman Filtered Compressive Sensing 4.1.3 Joint Compressive Video Coding and Analysis 4.1.4 Compressive Sensing for Multi-View Tracking 4.1.5 Compressive Particle Filtering 4.2 Compressive Video Processing 4.2.1 Compressive Sensing for High-Speed Periodic Videos 4.2.2 Programmable Pixel Compressive Camerafor High Speed Imaging 4.2.3 Compressive Acquisition of Dynamic Textures o 4.2.3.1 Dynamic Textures and Linear Dynamical Systems o 4.2.3.2 Compressive Acquisition of LDS o 4.2.3.3 Experimental Results 4.3 Shape from Gradients 4.3.1 Sparse Gradient Integration 4.3.2 Numerical Examples Chapter 5 Sparse Representation-based Object Recognition 5.1 Sparse Representation 5.2 Sparse Representation-based Classification 5.2.1 Robust Biometrics Recognitionusing Sparse Representation 5.3 Non-linear Kernel Sparse Representation 5.3.1 Kernel Sparse Coding 5.3.2 Kernel Orthogonal Matching Pursuit 5.3.3 Kernel Simultaneous Orthogonal Matching Pursuit 5.3.4 Experimental Results 5.4 Multimodal Multivariate Sparse Representation 5.4.1 Multimodal Multivariate Sparse Representation 5.4.2 Robust Multimodal Multivariate Sparse Representation 5.4.3 Experimental Results o 5.4.3.1 Preprocessing o 5.4.3.2 Feature Extraction o 5.4.3.3 Experimental Set-up 5.5 Kernel Space Multimodal Recognition 5.5.1 Multivariate Kernel Sparse Representation 5.5.2 Composite Kernel Sparse Representation 5.5.3 Experimental Results Chapter 6 Dictionary Learning 6.1 Dictionary Learning Algorithms 6.2 Discriminative Dictionary Learning 6.3 Non-Linear Kernel Dictionary Learning Chapter 7 Concluding Remarks References