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US 7,689,056 B2Granted
Frame multi-resolution analysis in any number of dimensions
AssigneeUniversity of Houston System
InventorsEmmanouil I. Papadakis, Donald J. Kouri, David K. Hoffman, Ioannis A Kakadiaris, Grigoriy Gogoshin
Life of this patent
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Abstract
A non-separable multiresolution structure based on frames by radial scaling functions is disclosed, which are minimally supported in the frequency. Resulting frame multiwavelets are also disclosed which can be isotropic. The construction can be carried out in any number of dimensions and for a variety of dilation matrices.
Claims24
A method for frame multi-resolution analysis implemented on a computer comprising the steps of:
- using the computer to perform steps comprising:
- constructing isotropic, non-separable ideal windows in a dimension greater than 1;
- translating and dilating the ideal windows using translation and dilation operators;
- constructing isotropic, non-separable filters from the ideal windows of the previous step, where the filters are selected from the group consisting of isotropic, non-separable low pass filters, isotropic, non-separable high pass filters and isotropic, non-separable filters that cover a desired frequency range or plurality of desired frequency ranges;
- constructing isotropic, non-separable frame scaling functions;
- and
- producing associated isotropic, non-separable wavelets from the isotropic, non-separable filters and the isotropic, non-separable scaling functions, where the wavelets and filters filter and resolve or decompose multidimensional signals, data, information, or images into a plurality of non-overlapping sub-bands derived from the signals, data, information or images and corresponding to resolution levels improving analysis efficiency and improving analysis of more complex multidimensional signals, data, information or images.
4 more elements
A method for analyzing data implemented on a computer comprising the steps of:
- using the computer to perform steps comprising:
- constructing at least one isotropic, non-separable wavelet including:
- isotropic, non-separable filters having at least one ideal isotropic, non-separable window translated and dilated as necessary using translation and dilation operators, where the filters are selected from the group consisting of isotropic, non-separable low pass filters, isotropic, non-separable high pass filters and isotropic, non-separable filters that cover a desired frequency range or plurality of desired frequency ranges;
- isotropic frame scaling functions, where translations of the frame scaling functions form a frame;
- and
- resolving or decomposing multidimensional signals, data, information, or images into a plurality of non-overlapping sub-bands corresponding to resolution levels, where the at least one isotropic, non-separable wavelet improves analysis efficiency and improves analysis of more complex multidimensional signals, data, information or images.
3 more elements
A system for processing signals implemented on a computer comprising:
- a computer including a processing unit having encoded thereon a completely isotropic, non-separable ideal filter for frame multi-resolution analysis software including:
- software encoding isotropic, non-separable wavelets adapted to resolve a multidimensional signal into a plurality of non-overlapping sub-bands or resolution levels, where the wavelets are derived from:
- isotropic, non-separable ideal windows or filters in a dimension greater than 1,
- isotropic, non-separable low pass filters, isotropic, non-separable high pass filters and isotropic, non-separable filters that cover a desired frequency range or plurality of frequency ranges;
- and
- isotropic, non-separable frame scaling functions where translations of the frame scaling functions form a frame;
- where at least one of the wavelets resolves or decomposes multidimensional signals, data, information, or images into the plurality of non-overlapping sub-bands or resolution levels and improves analysis efficiency and analysis of more complex multidimensional signals, data, information or images.
4 more elements
Dependencies are inferred from the claim text.