  Deep learning (DL) is a powerful tool in computational imaging for many
applications. A common strategy is to reconstruct a preliminary image as the
input of a neural network to achieve an optimized image. Usually, the
preliminary image is acquired with the prior knowledge of the imaging model.
One outstanding challenge, however, is the degree to which the actual imaging
model deviates from the assumed model. Model mismatches degrade the quality of
the preliminary image and therefore affect the DL predictions. Another main
challenge is that since most imaging inverse problems are ill-posed and the
networks are over-parameterized, DL networks have flexibility to extract
features from the data that are not directly related to the imaging model. To
solve these challenges, a two-step-training DL (TST-DL) framework is proposed
for real-time computational imaging without physics priors. First, a single
fully-connected layer (FCL) is trained to directly learn the model. Then, this
FCL is fixed and concatenated with an un-trained U-Net architecture for a
second-step training to improve the output image fidelity, resulting in four
main advantages. First, it does not rely on an accurate representation of the
imaging model since the model is directly learned. Second, real-time imaging
can be achieved. Third, the TST-DL network is trained in the desired direction
and the predictions are improved since the first step is constrained to learn
the model and the second step improves the result by learning the optimal
regularizer. Fourth, the approach accommodates any size and dimensionality of
data. We demonstrate this framework using a linear single-pixel camera imaging
model. The results are quantitatively compared with those from other DL
frameworks and model-based iterative optimization approaches. We further extend
this concept to nonlinear models in the application of image
de-autocorrelation.
