  Fluorescence microscopy plays an important role in biomedical research. The
depth-variant point spread function (PSF) of a fluorescence microscope produces
low-quality images especially in the out-of-focus regions of thick specimens.
Traditional deconvolution to restore the out-of-focus images is usually
insufficient since a depth-invariant PSF is assumed. This article aims at
handling fluorescence microscopy images by learning-based depth-variant PSF and
reducing artifacts. We propose adaptive weighting depth-variant deconvolution
(AWDVD) with defocus level prediction convolutional neural network (DelpNet) to
restore the out-of-focus images. Depth-variant PSFs of image patches can be
obtained by DelpNet and applied in the afterward deconvolution. AWDVD is
adopted for a whole image which is patch-wise deconvolved and appropriately
cropped before deconvolution. DelpNet achieves the accuracy of 98.2%, which
outperforms the best-ever one using the same microscopy dataset. Image patches
of 11 defocus levels after deconvolution are validated with maximum improvement
in the peak signal-to-noise ratio and structural similarity index of 6.6 dB and
11%, respectively. The adaptive weighting of the patch-wise deconvolved image
can eliminate patch boundary artifacts and improve deconvolved image quality.
The proposed method can accurately estimate depth-variant PSF and effectively
recover out-of-focus microscopy images. To our acknowledge, this is the first
study of handling out-of-focus microscopy images using learning-based
depth-variant PSF. Facing one of the most common blurs in fluorescence
microscopy, the novel method provides a practical technology to improve the
image quality.
