Abstract
The phase extraction neural network (PhENN) [Optica 4, 1117 (2017)] is a computational architecture, based on deep machine learning, for lens-less quantitative phase retrieval from raw intensity data. PhENN is a deep convolutional neural network trained through examples consisting of pairs of true phase objects and their corresponding intensity diffraction patterns; thereafter, given a test raw intensity pattern, PhENN is capable of reconstructing the original phase object robustly, in many cases even for objects outside the database where the training examples were drawn from. Here, we show that the spatial frequency content of the training examples is an important factor limiting PhENN's spatial frequency response. For example, if the training database is relatively sparse in high spatial frequencies, as most natural scenes are, PhENN's ability to resolve fine spatial features in test patterns will be correspondingly limited. To combat this issue, we propose "flattening" the power spectral density of the training examples before presenting them to PhENN. For phase objects following the statistics of natural scenes, we demonstrate experimentally that the spectral pre-modulation method enhances the spatial resolution of PhENN by a factor of 2.
Highlights
The use of machine learning architectures is a relatively new trend in computational imaging and rapidly gaining popularity
The examples presented to phase extraction neural network (PhENN) during training establish the spatial frequency content that is stored in the network weights contributing to the retrieval operation Eq (2)
We have found the Negative Pearson Correlation Coefficient (NPCC) to generally result in better Deep Neural Networks (DNNs) training in the problems that we examined, especially for objects that are spatially sparse [3]
Summary
The use of machine learning architectures is a relatively new trend in computational imaging and rapidly gaining popularity. The examples presented to PhENN during training establish the spatial frequency content that is stored in the network weights contributing to the retrieval operation Eq (2). This means that high spatial frequencies are inherently under-represented in PhENN training. Compounded by the nonlinear suppression of the less popular spatial frequencies due to PhENN nonlinearities, as mentioned above, this results in low-pass filtering of the estimates and loss of fine detail Even though we have not tried extensively beyond phase retrieval, pre-processing of training examples by spectral manipulation might have merit for several other challenging imaging problems
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