Signal processors and methods for estimating transformations between signals with phase estimation
Signal processing devices and methods estimate transforms between signals, and in particular, utilize techniques for estimating phase between a reference signal and a suspect signal. A phase estimation method estimates the phase of reference signal components in a suspect signal using a point spread function. The method provides a set of feature locations representing a discrete reference signal, applies a transform to the reference signal to provide a set of transformed locations, and then uses a point spread function to sample phase from the suspect signal at discrete sample locations in a neighborhood around the transformed locations. This process provides an estimate of phase of the suspect signal at locations corresponding to the transformed locations.
1. A method of computing an estimate of phase of a transformed signal from a suspect signal, the method comprising:
obtaining a transformed signal at a transformed location, the transformed location being a non-integer location;
sampling the suspect signal at discrete sample locations in a neighborhood around the transformed location of the transformed signal;
using a point spread function at the transformed location to determine point spread function values of the transformed signal at the discrete sample locations; and
combining the sampling and point spread function values to compute an estimate of phase of the transformed signal at the transformed location within the suspect signal.
2. The method of claim 1 wherein the suspect signal comprises an image signal.
3. The method of claim 2 wherein the suspect signal comprises an image signal sampled from an image sensor.
4. The method of claim 1 wherein the transformed signal comprises a set of signal components, and the transformed location comprises locations of the signal components.
5. The method of claim 4 wherein the signal components are frequency components and the locations of the signal components are frequency locations of the frequency components.
6. The method of claim 1 wherein the suspect signal includes a version of a reference signal, and the point spread function is used to determine phase of the version of the reference signal in the suspect signal.
7. The method of claim 6 wherein the phase is used to determine a transformation between the version of the reference signal in the suspect signal and the reference signal.
8. The method of claim 6 wherein the reference signal corresponds to a digital watermark signal embedded in the suspect signal, and the phase is used to detect the digital watermark signal in the suspect signal.
9. A non-transitory computer readable medium, on which is stored instructions, which, when executed by one or more processors, perform a method of computing an estimate of phase of a transformed signal from a suspect signal, the method comprising:
obtaining a transformed signal at a transformed location, the transformed location being a non-integer location;
sampling the suspect signal at discrete sample locations in a neighborhood around the transformed location of the transformed signal;
using a point spread function at the transformed location to determine point spread function values of the transformed signal at the discrete sample locations; and
combining the sampling and point spread function values to compute an estimate of phase of the transformed signal at the transformed location within the suspect signal.
10. A circuit comprising:
a memory for storing phase of a suspect signal;
a transform module for obtaining a transformed coordinate location of a transformed signal; and
a point spread function module for reading, from the memory, selected phase of the suspect signal at locations around a first transformed coordinate location, the first transformed coordinate location being a non-integer location, to provide phase inputs and applying a point spread function at the non-integer location to the phase inputs to transform the phase inputs into a phase estimate at the first transformed coordinate location.
11. The circuit of claim 10 wherein the suspect signal comprises an image signal.
12. The circuit of claim 11 wherein the suspect signal comprises an image signal sampled from an image sensor.
13. The circuit of claim 10 wherein the transformed signal comprises a set of signal components, and the transformed coordinate location comprises a location of a signal component.
14. The circuit of claim 13 wherein the signal components are frequency components and the transformed coordinate location comprises a frequency location of a frequency component.
15. The circuit of claim 10 wherein the suspect signal includes a version of a reference signal, and the point spread function is used to determine phase of the version of the reference signal in the suspect signal.
16. The circuit of claim 15 wherein the phase is used to determine a transformation between the version of the reference signal in the suspect signal and the reference signal.
17. The circuit of claim 15 wherein the reference signal corresponds to a digital watermark signal embedded in the suspect signal, and the phase is used to detect the digital watermark signal in the suspect signal.
18. The circuit of claim 10 wherein the point spread function module comprises a point spread function table and product and sum operators to apply the point spread function to the selected phase.