Spatially varying regularization of deconvolution in 3D microscopy

Confocal microscopy has become an essential tool to explore biospecimens in 3D. Confocal microcopy images are still degraded by out-of-focus blur and Poisson noise. Many deconvolution methods including the Richardson-Lucy (RL) method, Tikhonov method and split-gradient (SG) method have been well received. The RL deconvolution method results in enhanced image quality, especially for Poisson noise. Tikhonov deconvolution method improves the RL method by imposing a prior model of spatial regularization, which encourages adjacent voxels to appear similar. The SG method also contains spatial regularization and is capable of incorporating many edge-preserving priors resulting in improved image quality. The strength of spatial regularization is fixed regardless of spatial location for the Tikhonov and SG method. The Tikhonov and the SG deconvolution methods are improved upon in this study by allowing the strength of spatial regularization to differ for different spatial locations in a given image. The novel method shows improved image quality. The method was tested on phantom data for which ground truth and the point spread function are known. A Kullback-Leibler (KL) divergence value of 0.097 is obtained with applying spatially variable regularization to the SG method, whereas KL value of 0.409 is obtained with the Tikhonov method. In tests on a real data, for which the ground truth is unknown, the reconstructed data show improved noise characteristics while maintaining the important image features such as edges.