The essential difference of non-linear image restoration algorithms with linear image restoration filters is their capability to restrict the restoration result to non-negative intensities. The iterative constrained Tikhonov-Miller algorithm (ICTM) algorithm, for example, incorporates the non- negativity constraint by clipping each iteration of its conjugate gradient descent algorithm. This constraint will only be effective when the restored intensities have near zero values. Therefore the background estimation will have an influence on the effectiveness of the non-negativity constraint of these non-linear restoration algorithms. We have investigated the effect of the background estimation on the performance of the ICTM, Carrington, and Richardson-Lucy algorithms and compared it to the performance of the linear Tikhonov-Miller restoration filter. We found that an underestimation of the background will make the non-negativity constraint ineffective which results in a performance that does not differ much from the performance obtained by the linear restoration filter. An overestimation of the background however is even more dramatic since it results in a clipping of object intensities. We show that this will dramatically deteriorate the performance of the non-linear restoration algorithms. We propose a novel method to estimate the background based on the dependency of non-linear restoration algorithms on the background.
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