## Modern Signal ProcessingRockmore, Daniel Nahum Rockmore, Daniel N. Rockmore, Dennis M. Healy, Jr, Healy, Jr. (Dennis M.) Signal processing is everywhere in modern technology. Its mathematical basis and many areas of application are the subject of this book, based on a series of graduate-level lectures held at the Mathematical Sciences Research Institute. Emphasis is on challenges in the subject, particular techniques adapted to particular technologies, and certain advances in algorithms and theory. The book covers two main areas: computational harmonic analysis, envisioned as a technology for efficiently analysing real data using inherent symmetries; and the challenges inherent in the acquisition, processing and analysis of images and sensing data in general [EMDASH] ranging from sonar on a submarine to a neuroscientist's fMRI study. |

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### Contents

Engineering Applications of the MotionGroup Fourier Transform | 63 |

Fast XRay and Beamlet Transforms for ThreeDimensional Data | 79 |

Fourier Analysis and Phylogenetic Trees | 117 |

Diffuse Tomography as a Source of Challenging Nonlinear Inverse | 137 |

An Invitation to Matrixvalued Spherical Functions | 147 |

Image Registration for MRI | 161 |

The Mathematics of JPEG 2000 | 185 |

Integrated Sensing and Processing for Statistical Pattern Recognition | 223 |

Sampling of Functions and Sections for Compact Groups | 247 |

The CooleyTukey FFT and Group Theory | 281 |

Signal Processing in Optic Fibers | 301 |

The Generalized Spike Process Sparsity and Statistical Independence | 317 |

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### Common terms and phrases

algebra algorithm antenna applications Assume band-limited basis bit array bitplane bitstream chain classifier code-block coder coefficients compact compression compute continuum beamlets corresponding data cube defined denote dimensional disk disk algebra distribution dyadic cube elements encoded entropy coding equation example Figure filter finite Fourier transform frequency harmonic analysis IEEE image registration integrals invariant inverse JPEG Lemma Lie group line codes line segments linear lossless 2-ports LSDB matching circuits matching problem Math mathematical medical imaging minimize Nehari nonlinear norm nucleotide operator optical fibers optimization orthogonal parameters pixel plane polynomials power mismatch probability PROOF properties ramp process representation result sampling scattering matrix Section sensor signal processing significant simple spike process slant stack space spherical functions statistical statistical independence subbitplane sublevel sets subset subspace substitution matrices taxa techniques Theorem theory tion tomography variables vector voxel wavelet transform X-ray transform