Simultaneous Interpolation and Deconvolution Model for the 3-D Reconstruction of Cell Images

Fluorescence microscopy methods are an important imaging technique in cell biology. Due to their depth sensitivity they allow a direct 3-D imaging. However, the resulting volume data sets are undersampled in depth, and the 2-D slices are blurred and noisy. Reconstructing the full 3-D information from these data is therefore a challenging task, and of high relevance for biological applications. We address this problem by combining deconvolution of the 3-D data set with interpolation of additional slices in an integrated variational approach. Our novel 3-D reconstruction model, Interpolating Robust and Regularised Richardson-Lucy reconstruction (IRRRL), merges the Robust and Regularised Richardson-Lucy deconvolution (RRRL) from [16] with variational interpolation. In this paper we develop the theoretical approach and its efficient numerical implementation using Fast Fourier Transform and a coarse-to-fine multiscale strategy. Experiments on confocal fluorescence microscopy data demonstrate the high restoration quality and computational efficiency of our approach.