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- W55207904 abstract "In my dissertation, I study AM-FM transforms and their applications in signal and image processing. I introduce two novel classes of AM-FM transforms: (i) multidimensional continuous AM-FM transforms and (ii) multidimensional discrete orthogonal FM transforms.To study continuous AM-FM transforms, I focus on the use of curvilinear coordinate systems and how image structure can be characterized by the components of the Instantaneous Frequency Gradient Tensor (IFGT). Using the IFGT, I derive the Ordinary Differential Equations (ODEs) that describe image flowlines, the trajectories of the ODEs when a point on the image moves with the instantaneous frequency vector acting as its particle velocity. I study the diagonalization of the ODEs of multidimensional Frequency Modulation along the IFGT eigenvector coordinate system and suggest that separable transforms can be computed along these coordinates. For such separable transforms, there is a reduction in dimensionality in our requirements for representing the spectra. To compute continuous AM-FM transforms, I study the use of the mean-component approximation and how it can be used to estimate appropriate coordinate systems for efficiently representing images for which there is an underlying curvilinear coordinate system. In an application to latent fingerprint analysis, I use the instantaneous frequency magnitude and the amplitude of the estimated fundamental AM-FM harmonic to extract minutiae points.For discrete, orthogonal FM transforms, I derive all the necessary conditions for designing multidimensional orthogonal transforms. Then, I focus on studying orthogonal FM transforms that arise from permutations. I use algebraic methods to derive the number of distinct FM transforms that can be computed for signals of any finite number of dimensions, prove certain invariance properties of the FM spectra, and use these theoretical results to develop algorithms for computing FM transforms. FM transforms are shown to provide better rate-distortion performance than baseline JPEG. In a related topic, I also study the use of merge sorting algorithms for encoding arbitrary permutations for efficient lossless coding. In the development of the theory of orthogonal discrete FM transforms, the author has benefited from discussions and supporting material provided by Nikos Sidiropoulos, John Havlicek and Alan Bovik." @default.
- W55207904 created "2016-06-24" @default.
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- W55207904 date "1998-01-01" @default.
- W55207904 modified "2023-09-28" @default.
- W55207904 title "Am-fm transforms with applications" @default.
- W55207904 hasPublicationYear "1998" @default.
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