Alternation of inverse problem approach and deep learning for lens-free microscopy image reconstruction

A lens-free microscope is a simple imaging device performing in-line holographic measurements. In the absence of focusing optics, a reconstruction algorithm is used to retrieve the sample image by solving the inverse problem. This is usually performed by optimization algorithms relying on gradient computation. However the presence of local minima leads to unsatisfactory convergence when phase wrapping errors occur. This is particularly the case in large optical thickness samples, for example cells in suspension and cells undergoing mitosis. To date, the occurrence of phase wrapping errors in the holographic reconstruction limits the application of lens-free microscopy in live cell imaging. To overcome this issue, we propose a novel approach in which the reconstruction alternates between two approaches, an inverse problem optimization and deep learning. The computation starts with a first reconstruction guess of the cell sample image. The result is then fed into a neural network, which is trained to correct phase wrapping errors. The neural network prediction is next used as the initialization of a second and last reconstruction step, which corrects to a certain extent the neural network prediction errors. We demonstrate the applicability of this approach in solving the phase wrapping problem occurring with cells in suspension at large densities. This is a challenging sample that typically cannot be reconstructed without phase wrapping errors, when using inverse problem optimization alone.