Compressive Sensing in Healthcare (Advances in ubiquitous sensing applications for healthcare)

Contents
List of contributors
1 Compressive sensing theoretical foundations in a nutshell
	1.1 Introduction
	1.2 Digital signal acquisition
	1.3 Vectorial representation of signal
		l1 norm
		l2 norm
		l∞ norm
		Spheres made by different lp norms as distance criterion
		Basis/dictionary
		Orthonormal basis/dictionary
		Frame/ over-complete dictionary
		Alternate/dual frame
	1.4 Sparsity
		k-sparse signal
		Non-linearity of sparsity
		Sparsity and compressibility
	1.5 Compressive sensing
		Compressive sensing model
	1.6 Essential properties of compressive sensing matrix
		1.6.1 Null space property (NSP)
			The essence of the concept of recovery
			Maximum compression in compressive sensing (lower bound of m)
		1.6.2 Restricted isometry property
		1.6.3 Coherence a simple way to check NSP
			Relation between coherence and spark of a matrix
			Coherence approach to RIP
	1.7 Summary
	1.A
		Null space property of order 2k
	References
2 Recovery in compressive sensing: a review
	2.1 Introduction
		2.1.1 Compressive sensing formulation
	2.2 Criteria required for a compressive sensing matrix
		2.2.1 Null space property
			Null space property of order k
			2.2.1.1 Uniqueness theorem [46]
			Maximum compression in compressive sensing
		2.2.2 Restricted isometry property
		2.2.3 Coherence property
			2.2.3.1 Coherence and spark of a matrix
			2.2.3.2 The upper bound of sparsity level
	2.3 Recovery
		2.3.1 Recovery via minimization of l1 norm
		2.3.2 Greedy algorithms
			2.3.2.1 Pursuits
			2.3.2.2 Matching pursuit
			2.3.2.3 Orthogonal matching pursuit
			2.3.2.4 Iterative hard thresholding
	2.4 Summary
	References
3 A descriptive review to sparsity measures
	3.1 Introduction
	3.2 Compressive sensing
	3.3 Sparsity
		k-sparse signal
	3.4 Review to sparsity measures
		Robin Hood: Dalton's first law
		Scaling: Dalton's second law
		Rising tide: Dalton's third law
		Cloning: Dalton's fourth law
		Bill Gates
		Babies
			Measure Sl0
			Measure Sl0,ε
			Measure Stanha,b
			Measure Slog
			Measure Sl1
			Measure Slp
			Measure Sl2/l1
				The ratio of l2 distance to l1 distance from the center
			Measure κ4
			Measure Suθ
			Measures HG, HS, H'S, and l-p
			Hoyer measure
			pq-mean measure
			Measure SGini
	3.5 Summary
	References
4 Compressive sensing in practice and potential advancements
	4.1 Introduction
	4.2 Compressive sensing theory
	4.3 Example compressive sensing implementations
		4.3.1 Compressive sensing in physiological signal monitoring
			In the field application results
		4.3.2 Compressive sensing in THEMIS imaging
			In-the-field application results
	4.4 Review of CS literature
		4.4.1 Practical manifestations of theoretical bounds
	4.5 Advancements in compressive sensing
		4.5.1 Personalized basis
			Challenges
		4.5.2 Non-linear model-based compressive sensing
			Challenges
		4.5.3 ROI aware compressive sensing
			Challenges
	4.6 Conclusion
	Acknowledgments
	References
5 A review of deterministic sensing matrices
	5.1 Introduction
	5.2 Compressive sensing
	5.3 Chirp codes compressive matrices
		5.3.1 Φ for sparse spectrum signals
	5.4 Second order Reed-Muller compressive sensing matrix
		5.4.1 Fast reconstruction algorithm
	5.5 Amini approach to RIP-satisfying matrices
	5.6 Amini-Marvasti binary matrix
		5.6.1 BCH-code
		5.6.2 Extremal Set Theory
		5.6.3 Unbalanced expander graphs
	5.7 Sensing matrices with statistical restricted isometry property
	5.8 Deterministic compressive matrix by algebraic curves over finite fields
	5.9 Summary
	References
6 Deterministic compressive sensing by chirp codes: a descriptive tutorial
	6.1 Introduction
	6.2 The standard formulation compressive sensing
	6.3 Compressive sensing by chirp codes
		6.3.1 Building the compressive sensing matrix by chirp codes
		6.3.2 Restricted isometry property for the chirp code compressive sensing
	6.4 Recovery of chirp code compressively sensed signal
		6.4.1 Step by step in one iteration of recovery
	6.5 Summary
	6.A
		6.A.1 Chirp sinusoid
	References
7 Deterministic compressive sensing by chirp codes: a MATLAB® tutorial
	7.1 Introduction
	7.2 Compressive sensing
	7.3 Chirp codes compressive sensing: MATLAB tutorial
		7.3.1 Chirp codes
		7.3.2 The approach for extraction of parameters
			7.3.2.1 Single chirp
			7.3.2.2 Mixture of two chirps
		7.3.3 Bijection between the sets {ri} and {2riT mod K}
		7.3.4 Dechirping yl
		7.3.5 Sensing and recovery
	7.4 Summary
	References
8 Cyber physical systems for healthcare applications using compressive sensing
	8.1 Introduction
	8.2 Related works
	8.3 Proposed work
		8.3.1 Image acquisition
		8.3.2 Pre-processing techniques
		8.3.3 Block division
		8.3.4 Compressive sensing
		8.3.5 Uploading data to cloud
		8.3.6 GUI (graphical user interface)
	8.4 Performance evaluation
		8.4.1 Simulation results
		8.4.2 Experimental results
	8.5 Conclusion and scope for future work
	References
9 Compressive sensing of electrocardiogram
	9.1 Introduction
	9.2 Electrocardiogram
		9.2.1 Historical background
		9.2.2 Heart anatomy
		9.2.3 Conduction system
		9.2.4 Electrophysiology
		9.2.5 Electrocardiogram acquisition
	9.3 Compressive sensing
		9.3.1 Compressive sensing signal acquisition
		9.3.2 Compressive sensed signal reconstruction
			9.3.2.1 Metrics
		9.3.3 CS importance in tele-medicine
	9.4 Compressive sensing approach to ECG
		9.4.1 ECG signal quality
		9.4.2 Body sensor networks and monitoring systems
		9.4.3 Dictionary learning
		9.4.4 ECG signal structure
		9.4.5 Wavelets and compressive sensing
		9.4.6 Signal compression
		9.4.7 Reconstruction algorithms
		9.4.8 Discrete wavelet transform (DWT) vs compressive sensing (CS)
		9.4.9 Hardware implementation
	9.5 Conclusion
	References
10 Multichannel ECG reconstruction based on joint compressed sensing for healthcare applications
	10.1 Introduction
	10.2 Background and related work
		10.2.1 Compressed sensing-based MECG compression
			10.2.1.1 Sensing matrix
				Gaussian random matrix
				Sparse binary matrix
		10.2.2 Compressed sensing based MECG reconstruction
	10.3 Proposed method
	10.4 Results and discussion
		10.4.1 Experimental setup
		10.4.2 Performance metrics
		10.4.3 Performance evaluation
		10.4.4 Healthcare application perspective
		10.4.5 Power saving
	10.5 Conclusion
	References
11 Neural signal compressive sensing
	11.1 Introduction
	11.2 Compressed sensing theory - a brief review
	11.3 Compressive sensing for energy-efficient neural recording
	11.4 Compressive sensing in seizure detection
	11.5 Compressive sensing in Alzheimer's disease
	11.6 Compressive electroencephalography (EEG) sensor design
	11.7 Compressive sensing in neural recording
	11.8 Compressive sensing for fall prevention
	11.9 EEG compressive sensing for person identification
	11.10 Compressive sensing wireless neural recording
	11.11 Compressive sensing in portable EEG systems
	11.12 Compressed and distributed sensing of neuronal activity
	11.13 Summary
	References
12 Level-crossing sampling: principles, circuits, and processing for healthcare applications
	12.1 Introduction
	12.2 Basics of level-crossing sampling
	12.3 Design considerations in level-crossing sampling
		12.3.1 Resolution
		12.3.2 Dynamic range
		12.3.3 Conversion delay
		12.3.4 Timer resolution and number of bits
		12.3.5 Accuracy of the converter
	12.4 Level-crossing analog-to-digital converters
		12.4.1 Floating-window LCADC
		12.4.2 Fixed-window LCADCs
	12.5 Processing of the level-crossing sampled data
	References
13 Compressive sensing of electroencephalogram: a review
	13.1 Introduction
	13.2 Signal acquisition
		13.2.1 Pulse train sampling
		13.2.2 Signal recovery
		13.2.3 Nyquist frequency
		13.2.4 Aliasing
		13.2.5 Sample-hold
	13.3 EEG signals
	13.4 Compressive sensing
		13.4.1 Compressive sensing metrics
	13.5 Applications
		13.5.1 Block sparse Bayesian learning
		13.5.2 Bayesian compressive sensing
		13.5.3 Slepian basis
		13.5.4 Monitoring
		13.5.5 Wireless body area network
		13.5.6 Comparing reconstruction algorithms
		13.5.7 Biometric identification
		13.5.8 Dictionary learning
		13.5.9 General applications
		13.5.10 Hardware implementation
		13.5.11 Feasibility of compressive sensing for EEG signals
	13.6 Conclusion
	References
14 Calibrationless parallel compressed sensing reconstruction for rapid magnetic resonance imaging
	14.1 Introduction
	14.2 Background
	14.3 Proposed method
	14.4 Results and discussion
	14.5 Conclusions
	Acknowledgment
	References
Index