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 strong device for successfully processing information in non-traditional methods. during this ebook, we spotlight a few 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 strong 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 snapshot 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 photo 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 mild delivery Sensing

Chapter four Compressive Sensing for Vision

4.1 Compressive goal 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 velocity 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 strong 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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This experiment shows that it is indeed possible to reconstruct SAR images from the k-space undersampled data. The advantages of using such undersampling in slow-time axis in SAR is discussed in [103]. In particular, it was shown that such undersampling leads to not only reduction in data but also provides resistance to strong countermeasures, allows for imaging in wider swaths and possible reduction in antenna size. 4 Compressive Passive Millimeter Wave Imaging Interest in millimeter wave (mmW) and terahertz imaging has increased in the past several years[4, 85, 162].

While this methodology yields a significant reduction in the number of Fourier samples required to recover a sparse-gradient image, it does not take advantage of additional sparsity that can be exploited by utilizing the two horizontal and vertical directional derivatives of the image. An example of a sparse-gradient image along with an image of its edges is shown in Fig. 3. An interesting approach to the problem of recovering a sparse gradient image from a small set of Fourier measurements was proposed in [108].

Where (k1 , k2 ) = argmin ω12 + ω22 . (ω1 ,ω2 )∈ /Ω As can be seen, the performance of this method depends on the selection of Ω . If Ω contains all the low frequencies within some radius r = k12 + k22 , then the final reconstruction error will be O(N/r) times worse than the maximum edge reconstruction error. In general, if Ω contains mostly low frequencies, then this method will generate better results than if Ω contained mostly high frequencies. As a result, this “integration” is very appropriate in applications such as CT where Ω will consist of radial lines that congregate near the DC frequency.

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