preface to the sparse edition
notations
chapter 1 sparse representations
1.1 computational harmonic analysis
1.1.1 the fourier kingdom
1.1.2 wavelet bases
1.2 approximation and processing in bases
1.2.1 sampling with linear approximations
1.2.2 sparse nonlinear approximations
1.2.3 compression
1.2.4 denoising
1.3 time-frequency dictionaries
1.3.1 heisenberg uncertainty
1.3.2 windowed fourier transform
1.3.3 continuous wavelet transform
1.3.4 time-frequency orthonormal bases
1.4 sparsity in redundant dictionaries
1.4.1 frame analysis and synthesis
1.4.2 ideal i)ictionary approximations
1.4.3 pursuit in dictionaries
1.5 inverse problems
1.5.1 diagonal inverse estimation
1.5.2 super-resolution and compressive sensing
1.6 travel guide
1.6.1 reproducible computational science
1.6.2 book road map
chapter 2 the fourier kingdom
2.1 linear time-invariant filtering
2.1.1 impulse response
2.1.2 transfer functions
2.2 fourier integrals
2.2.1 fourier transform in l1(r)
2.2.2 fourier transform in l2(r)
2.2.3 examples
2.3 properties
2.3.1 regularity and decay
2.3.2 uncertainty principle
2.3.3 totalvariation
2.4 two-dimensional fourier transform
2.5 exercises
chapter 3 discrete revolution
3.1 sampling analog signals
3.1.1 shannon-whittaker sampling theorem
3.1.2 aliasing
3.1.3 general sampling and linear analog conversions
3.2 discrete time-invariant filters
3.2.1 impulse response and transfer function
3.2.2 fourier series
3.3 finite signals
3.3.1 circular convolutions
3.3.2 discrete fourier transform
3.3.3 fast fourier transform
3.3.4 fast convolutions
3.4 discrete image processing
3.4.1 two-dimensional sampling theorems
3.4.2 discrete image filtering
3.4.3 circular convolutions and fourier basis
3.5 exercises
chapter 4 time meets frequency
4.1 time-frequency atoms
4.2 windowed fourier transform
4.2.1 completeness and stability
4.2.2 choice of window
4.2.3 discrete windowed fourier transform
4.3 wavelet transforms
4.3.1 real wavelets
4.3.2 analytic wavelets
4.3.3 discrete wavelets
4.4 time-frequency geometry of instantaneous frequencies
4.4.1 analytic instantaneous frequency
4.4.2 windowed fourier ridges
4.4.3 wavelet ridges
4.5 quadratic time-frequency energy
4.5.1 wigner-ville distribution
4.5.2 interferences and positivity
4.5.3 cohen's class
4.5.4 discrete wigner-ville computations
4.6 exercises
chapter 5 frames
chapter 6 wavelet zoom
chapter 7 wavelet bases
chapter 8 wavelet packet and local cosine bases
chapter 9 approximations in bases
chapter 10 compression
chapter 11 denoising
chapter 12 sparsity in redundant dictionaries
chapter 13 inverse problems
appendix mathematical complements
bibliography
index