| US 7,577,307 B2 | ||
| Fast adaptive lifting lossless wavelet transform | ||
| Hsieh S. Hou, Rancho Palos Verdes, Calif. (US) | ||
| Assigned to The Aerospace Corporation, El Segundo, Calif. (US) | ||
| Filed on Apr. 12, 2005, as Appl. No. 11/104,703. | ||
| Prior Publication US 2006/0228031 A1, Oct. 12, 2006 | ||
| Int. Cl. G06K 9/36 (2006.01); G06K 9/46 (2006.01); G06F 17/14 (2006.01) | ||
| U.S. Cl. 382—240 [382/232; 382/239; 708/400] | 4 Claims |
| 1. A lifting wavelet transform for transforming an input into an adaptive highpass output and an adaptive lowpass output,
the lifting wavelet transform useful for transforming data into transform data being the adaptive highpass output and the
adaptive lowpass output and for communicating the same over a communication data link, the lifting wavelet transform comprising,
a three lifting stage wavelet transform for transforming an input into a third highpass output and a third lowpass output,
and
an adaptive lifting stage for processing the third highpass output and the third lowpass output into an adaptive highpass
output, the adaptive lifting stage comprising a [P(z)/C2] adaptive predictor process for providing an adaptive predictor output from the third lowpass output and comprising an adder
for subtracting the adaptive predictor output to the third highpass output into the adaptive highpass output, the third lowpass
output being an adaptive lowpass output,
wherein,
a first order difference is a difference between a cubic interpolation and a linear interpolation of two successive samples
of the third lowpass output,
a second order difference is the difference between two consecutive first order differences,
a third order difference is the difference between two consecutive second order differences, and
the adaptive prediction output is equal to the sum of the first order difference and one quarter of the third order difference,
the [P(z)/C2] adaptive predictor process in the adaptive lifting stage is a third linear combination of the third lowpass output at the
index sample time z,
P(z) is a filter function characterized by a polynomial for generating the adaptive predictor output,
C is a constant, and
C2 is the constant C squared.
|