The gradient-consensus Richardson–Lucy (GC-RL) deconvolution algorithm is a novel approach to contrast restoration in high-resolution microscopy imaging without excessive noise amplification. We evaluate this method in this work, focusing on the impact of the noise level of the input image, of imperfections and deviations in image formation from the ideal incoherent case, and of using undersampled input data. The gain in spectral signal to noise ratio (SSNR) is larger when the noise level of the raw image is lower. We also find a positive impact on SSNR gain from using an optical transfer function (OTF) in the deconvolution that has a decreased spatial frequency response compared to the ideal incoherent OTF. A simple upsampling scheme, embedded in the GC-RL deconvolution, is demonstrated to be suitable for undersampled data. We show our results on simulated data, on fluorescence microscopy data, and on brightfield microscopy data of a breast tumour section. The GC-RL method has potential for whole slide imaging technology to retrieve diagnostically relevant image features at the smallest length scales from scanned images at lower resolution, providing a gain in throughput and data storage requirements.

Richardson-Lucy (RL) deconvolution optimizes the likelihood of the object estimate for an incoherent imaging system. It can offer an increase in contrast, but converges poorly, and shows enhancement of noise as the iteration progresses. We have discovered the underlying reason for this problematic convergence behaviour using a Cramér Rao Lower Bound (CRLB) analysis. An analytical expression for the CRLB diverges for spatial frequency components that approach the diffraction limit from below. The resulting mean noise variance per pixel diverges for large images. These results imply that a regular optimum of the likelihood does not exist, and that RL deconvolution is necessarily ill-convergent.