MoDL: Model Based Deep Learning Architecture for Inverse Problems
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We introduce a model-based image reconstruction framework with a convolution neural network (CNN) based regularization prior. While CNN based image recovery methods are ideally suited for inverse problems with a convolutional structure, deep learning architectures for problems that do not have a convolutional structure (e.g., parallel MRI, structured illumination microscopy) are less obvious. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with the arbitrary structure. Since the forward model is explicitly accounted for, a much smaller network with fewer parameters is sufficient to capture the image information. In addition, this strategy enables the re-use of the learned network in acquisition schemes with slightly different parameter settings (e.g., different image size, undersampling patterns) and allows one to account for the imperfections of the acquisition scheme. The main difference of the framework from existing model based schemes is the sharing of the network weights across iterations and channels, which provides benefits including considerably lower demand for training data, reduced risk of overfitting, and reconstruction algorithms with significantly reduced memory footprint.
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