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Recent frameworks for image denoising have demonstrated that it can be more productive to recover an image from a smoothed version of some geometric feature of the image rather than denoise the image directly. Improvements can be found both with respect to image quality metrics as well as the preservation of fine details. The challenge in working with this data is that mathematically sound mechanisms developed for handling natural image data do not necessarily apply, and this data itself can be quite ill behaved. In this work we learn both ‘geometric’ or nonlinear higher order features and corresponding regularizers. These approaches show improvement over recent modelbased deep learning (DL) image denoising methods both with respect to image quality metrics as well as the preservation of fine features. Furthermore, the proposed approach for enhancing DL architectures by incorporating geometrically-inspired features is motivated by and has the potential to feed back into mathematically sound models for solving a variety of problems in image processing. 

Iron overload, a complication of repeated blood transfusions, can cause tissue damage and organ failure. The body has no regulatory mechanism to excrete excess iron, so iron overload must be closely monitored to guide therapy and measure treatment response. The concentration of iron in the liver is a reliable marker for total body iron content and is now measured noninvasively with magnetic resonance imaging (MRI). MRI produces a diagnostic image by measuring the signals emitted from the body in the presence of a constant magnetic field and radiofrequency pulses. At each pixel, the signal decay constant, T2*, can be calculated, providing insight about the structure of each tissue. Liver iron content can be quantified based on this T2* value because signal decay accelerates with increasing iron concentration. We developed a method to automatically segment the liver from the MRI image to accurately calculate iron content. Our current algorithm utilizes the active contour model for image segmentation, which iteratively evolves a curve until it reaches an edge or a boundary. We applied this algorithm to each MRI image in addition to a map of pixelwise T2* values, combining basic image processing with imaging physics. One of the limitations of this segmentation model is how it handles noise in the MRI data. Recent advancements in deep learning have enabled researchers to utilize convolutional neural networks to denoise and reconstruct images. We used the Trainable Nonlinear Reaction Diffusion network architecture to denoise the MRI images, allowing for smoother segmentation while preserving fine details.