Method of generating matrix factors for a finite-dimensional linear transform
US7454084B2 · kind B2 · utility
Assignee
Inventors
Key dates
| Filing date | May 14, 2007 |
| Grant date | Nov 18, 2008 |
| Priority date | — |
| Expiry date | May 14, 2027 |
Classification
- Technology area (CPC H)Electricity
- CPC primaryH04N19/42
- WIPO fieldAudio-visual technology
- WIPO sectorElectrical engineering
Abstract
A method of generating matrix factors for a finite-dimensional linear transform using a computer. The linear transform is represented by data values stored in a linear transformation matrix having a nonzero determinant. In one aspect, a first LU-decomposition is applied to the linear transformation matrix. Four matrices are generated from the LU-decomposition, including a first permutation matrix, a second permutation matrix, a lower triangular matrix having a unit diagonal, and a first upper triangular matrix. Additional elements include a third matrix Â, a signed permutation matrix Π such that A=ΠÂ, a permuted linear transformation matrix A′, a second upper triangular matrix U1, wherein the second upper triangular matrix satisfies the relationship Â=U1A′. The permuted linear transformation matrix is factored into a product including a lower triangular matrix L and an upper triangular matrix U. The linear transformation matrix is expressed as a product of the matrix factors.
Source: USPTO / EPO open patent data. Objective bibliographic and citation counts.