Estimation of the system transfer function for certain linear systems

摘要

The pupil image function (PIF) matrix of a plenoptic imaging system is calibrated, taking advantage of the low rank of the PIF matrix. In one approach, the low rank is utilized by identifying a subspace for the PIF matrix and then estimating the PIF matrix within that subspace. This can lead to a significant reduction in the number of calibration patterns used to estimate the PIF matrix.

主权项

1. A method implemented on a computer system comprising a programmable processor and memory, the method for producing an estimate  of a system transfer matrix A for a linear system, wherein the linear system is characterized by y=Ax+e, where x is an input vector, e is a noise vector and y is the output vector resulting from input vector x, the method comprising:
selecting a set of calibration inputs Xcal=[x1, . . . xm] where each of the xm is an input vector that is a calibration pattern; applying the calibration inputs Xcal to the linear system; observing the calibration outputs Ycal resulting from the calibration inputs Xcal according to Y=AX+E, where Ycal−=[y1, . . . , ym] where each of the ym is an output vector resulting from the corresponding input calibration pattern xm, and E−=[e1, . . . , em] where each of the em is a noise vector; identifying, by the computer system, a subspace of A, assuming that a column span of A equals a row span of A; calculating, by the computer system, an estimate  within the subspace of A, the estimate  calculated from the calibration outputs Ycal and calibration inputs Xcal and subject to a constraint that a row span of the estimate  equals a column span of the estimate Â; observing outputs Y1 produced by the linear system; and based on solving an inverse problem for the calculated estimate Â, estimating, by the computer system, corresponding inputs X1 that produced the outputs Y1.