Abstract
Abstract in Undetermined
We introduce Gaussian wave packets in pursuit of representations of functions, in which the representation is invariant under translation, modulation, scale,
rotation and anisotropic dilation. Properties of both continuous and discrete representations are discussed. For the discrete (two-dimensional) case, we develop fast
algorithms for the application of the analysis and synthesis operators. A main objective for using Gaussian wave packets is to obtain sparse approximations of functions.
However, due to the many invariance properties, the representations will have a high
degree of redundancy. Therefore, we also introduce sparse methods for highly redundant representations, that employ some of the analytic properties of Gaussian wave
packet for gaining computational efficiency.
We introduce Gaussian wave packets in pursuit of representations of functions, in which the representation is invariant under translation, modulation, scale,
rotation and anisotropic dilation. Properties of both continuous and discrete representations are discussed. For the discrete (two-dimensional) case, we develop fast
algorithms for the application of the analysis and synthesis operators. A main objective for using Gaussian wave packets is to obtain sparse approximations of functions.
However, due to the many invariance properties, the representations will have a high
degree of redundancy. Therefore, we also introduce sparse methods for highly redundant representations, that employ some of the analytic properties of Gaussian wave
packet for gaining computational efficiency.
Original language | English |
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Pages (from-to) | 146-181 |
Journal | Journal of Fourier Analysis and Applications |
Volume | 18 |
DOIs | |
Publication status | Published - 2012 |
Subject classification (UKÄ)
- Mathematics
- Computer Vision and Robotics (Autonomous Systems)
Free keywords
- Gaussian wave packets · Sparse representations · Fast algorithms · Compression