Let the vector, U0, contain the input patch gray levels (or area coverages) for controlling DMA on the photoconductor for cyan separation shown in Table 9.1.

The vector x contains the normalized values of the measurements, the vector xd contains the tone values of the desired reference TRC. Both vectors are shown as a function of the patch gray level.

a. Find the derivatives at the patch values and the gain matrix for pole values equal to 0.4. Use Equation 9.45 to find the gain matrix.

b. Obtain the inverted tone values for (i.e., U(k)) iterations, k¼1, 2, . . . , 9.
Plot them with respect to iteration number, k.

c. Using end points 0 and 255 and a suitable curve fitting algorithm complete the full inverse TRC. Plot the inverted TRC. Mark the values of the reference vector, xd, and the normalized values of the measurements, x, corresponding to the patch gray levels.

d. Complete steps a through c for the new reference tone values.