Background estimation in nonlinear image restoration

One of the essential ways in which nonlinear image restoration algorithms d iffer from linear, convolution-type image restoration filters is their capa bility to restrict the restoration result to nonnegative intensities. The i terative constrained Tikhonov-Miller (ICTM) algorithm, for example, incorpo rates the nonnegativity constraint by clipping all negative values to zero after each iteration. This constraint will be effective only when the resto red intensities have near-zero values. Therefore the background estimation will have an influence on the effectiveness of the nonnegativity constraint of these algorithms. We investigated quantitatively the dependency of the performance of the ICTM, Carrington, and Richardson-Lucy algorithms on the estimation of the background and compared it with the performance of the li near Tikhonov-Miller restoration filter. We found that the performance depe nds critically on the background estimation: An underestimation of the back ground will make the nonnegativity constraint ineffective, which results in a performance that does not differ much from the Tikhonov-Miller filter pe rformance. A (small) overestimation, however, degrades the performance dram atically, since it results in a clipping of object intensities. We propose a novel general method to estimate the background based on the dependency o f nonlinear restoration algorithms on the background, and we demonstrate it s applicability on real confocal images. (C) 2000 Optical Society of Americ a [S0740-3232(00)00803-6].