Sparse Representations and Compressive Sensing for Imaging by Vishal M. Patel

By Vishal M. Patel

Compressed sensing or compressive sensing is a brand new notion in sign processing the place one measures a small variety of non-adaptive linear combos of the sign. those measurements tend to be a lot smaller than the variety of samples that outline the sign. From those small numbers of measurements, the sign is then reconstructed by way of non-linear method. Compressed sensing has lately emerged as a robust software for successfully processing information in non-traditional methods. during this publication, we spotlight a number of the key mathematical insights underlying sparse illustration and compressed sensing and illustrate the position of those theories in classical imaginative and prescient, imaging and biometrics problems.

Table of Contents


Sparse Representations and Compressive Sensing for Imaging and imaginative and prescient

ISBN 9781461463801 ISBN 9781461463818



Chapter 1 Introduction

1.1 Outline

Chapter 2 Compressive Sensing

2.1 Sparsity
2.2 Incoherent Sampling
2.3 Recovery
2.3.1 powerful CS
o The Dantzig selector
2.3.2 CS restoration Algorithms
o Iterative Thresholding Algorithms
o grasping Pursuits
o different Algorithms
2.4 Sensing Matrices
2.5 section Transition Diagrams
2.6 Numerical Examples

Chapter three Compressive Acquisition

3.1 unmarried Pixel Camera
3.2 Compressive Magnetic Resonance Imaging
3.2.1 picture Gradient Estimation
3.2.2 picture Reconstruction from Gradients
3.2.3 Numerical Examples
3.3 Compressive man made Aperture Radar Imaging
3.3.1 Slow-time Undersampling
3.3.2 picture Reconstruction
3.3.3 Numerical Examples
3.4 Compressive Passive Millimeter Wave Imaging
3.4.1 Millimeter Wave Imaging System
3.4.2 speeded up Imaging with prolonged Depth-of-Field
3.4.3 Experimental Results
3.5 Compressive gentle delivery Sensing

Chapter four Compressive Sensing for Vision

4.1 Compressive objective Tracking
4.1.1 Compressive Sensing for historical past 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 excessive pace Imaging
4.2.3 Compressive Acquisition of Dynamic Textures
o Dynamic Textures and Linear Dynamical Systems
o Compressive Acquisition of LDS
o Experimental Results
4.3 form from Gradients
4.3.1 Sparse Gradient Integration
4.3.2 Numerical Examples

Chapter five Sparse Representation-based item Recognition

5.1 Sparse Representation
5.2 Sparse Representation-based Classification
5.2.1 powerful 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 powerful Multimodal Multivariate Sparse Representation
5.4.3 Experimental Results
o Preprocessing
o function Extraction
o Experimental Set-up
5.5 Kernel house 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 studying Algorithms
6.2 Discriminative Dictionary Learning
6.3 Non-Linear Kernel Dictionary Learning

Chapter 7 Concluding Remarks


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Extra resources for Sparse Representations and Compressive Sensing for Imaging and Vision

Example text

Thus, CS has provided a means by which to reduce the up-front data costs associated with the system while retaining the information necessary to track. 2 Kalman Filtered Compressive Sensing A more general problem regarding signal tracking using compressive observations ∞ , is assumed to be both is considered in [146]. The signal being tracked, {xt }t=0 sparse and have a slowly-changing sparsity pattern. Given these assumptions, if the support set of xt , Tt , is known, the relationship between xt and yt can be written as: yt = Φ Tt (x)Tt + wt .

FΩ Y − b 2 ≤ ε. 5) Several other methods have also been proposed that make use of the TV norm for recovering images from compressive measurements [35], [151], [143], [79], [158], [91], [70], [141], [159]. It was shown in [108] that instead of reconstructing an image by TV minimization, one can reconstruct the image by separately reconstructing the gradients and then solving for the image. This allows one to reconstruct the image with a far fewer number of measurements than required by the TV minimization method.

2 Compressive Video Processing As we saw in the previous sections, recent advances in CS have led to the development of many imaging devices that sense static signals such as images at measurement rates lower than the Nyquist rate. Tremendous progress has also been made in compressively sensing temporal sequences or videos. In this chapter, we highlight some of these techniques for compressively sensing videos. In particular, we present an overview of compressive sensing of high-speed periodic videos [147], programable pixel camera for compressively sensing high speed videos [117] and compressive acquisition of dynamic scenes [127].

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