O ct 2 01 8 Solving Inverse Problems With Multi-scale Deep Convolutional Neural Networks

We propose multi-scale deep convolutional neural networks (MDCNN) as a general purpose solution for image(s)-to-image(s) inverse problems. Deep convolutional neural networks (DCNN)[1] have shown great potential for general and highly variable tasks across many image-based domains, especially successful for pixel-to-pixel applications in which the input images and the output images are similar[2, 3]. Here, we present this generalized framework to solve inverse problems with a traditional DCNN architecture enabling residual connections between the encapsulated layers of a pair of encoder and decoder, trained in a end-to-ends fashion from direct or indirect measurements to multi-scale reconstructions, no longer constrained by the choice of the mathematical formulations and the implementation of the reconstruction algorithms. The expediency of this framework is demonstrated by benchmarking predicted retrieval with a classic transport of intensity equation (TIE)[4] scheme, showing a performance on par with existing solvers.By predicting phases from a single astigmatism image, which is not feasible by other methods for its inner complexity, MDCNN shows good potential for application independent generalization, demonstrates the possibility to solve inversion problems unconstrained by complex mathematical formulas and complicated reconstruction algorithms. Furthermore, utilizing the capability of multi-channel input inherited from DCNN, MDCNN is able to address the stalling and non-uniqueness problems arising from single measurements, showing good robustness against parameters even when the mathematical nature is not evident. This opens a way for a large variety of new applications in a wide range of inverse problems, especially in the places where phase imaging or structure retrieval is an issue. The core idea of our architecture is, learning to solve inverse problems through big data, rather than coding explicit reconstruction algorithms from the mathematical formulas that characterized inverse problems. Previous works has targeted much more on how can we reconstruct rather than what we can reconstruct. Our strategy offers a shift of this paradigm.