Background estimation in nonlinear image restoration

Abstract

One of the essential ways in which nonlinear image restoration algorithms differ from linear, convolution-type image restoration filters is their capability to restrict the restoration result to nonnegative intensities. The iterative constrained Tikhonov-Miller (ICTM) algorithm, for example, incorporates the nonnegativity constraint by clipping all negative values to zero after each iteration. This constraint will be effective only when the restored 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 linear Tikhonov-Miller restoration filter. We found that the performance depends critically on the background estimation: An underestimation of the background will make the nonnegativity constraint ineffective, which results in a performance that does not differ much from the Tikhonov-Miller filter performance. A (small) overestimation, however, degrades the performance dramatically, since it results in a clipping of object intensities. We propose a novel general method to estimate the background based on the dependency of nonlinear restoration algorithms on the background, and we demonstrate its applicability on real confocal images.

Parametric Blind Deconvolution for Confocal Laser Scanning Microscopy

“…This reinforces the idea that the background needs to be estimated for every observation volume, and if the object fluorescence is sparse, the estimation could be carried out on the observation. For more details on homogenous or heterogenous background estimation in fluorescence microscopy, the interested reader may refer to the following articles by van Kempen & van Vliet [2000] and Chen, et al [2006].…”

Image filtering in structured illumination microscopy using the Lukosz bound

“…The reconstructions were performed with an implementation of Eqs. (17,20) in which either the Lukosz bound was used as apodization filter Eq. (29) or in which the Lukosz bound was incorporated in the Tikhonov-Miller functional Eq.…”

“…Commonly used filters in SIM image reconstruction are borrowed from the field of image restoration, i.e. methods to extend resolution beyond the diffraction limit by incorporating prior knowledge such as nonnegativity [18], noise models [19], background level [20], and image smoothness [21]. The default filtering technique in SIM is (generalized) Wiener filtering [22][23][24], with a signal-tonoise ratio (SNR) that is assumed constant across the entire spatial frequency range.…”

Scaled Heavy-Ball Acceleration of the Richardson-Lucy Algorithm for 3D Microscopy Image Restoration

“…The background term is a nelement vector. It stands for background emission [3] and can be estimated by preprocessing of the raw image y [4]. From a Bayesian viewpoint, the conditional probability of image y given object x is as follows …”