Probability of error as an image metric for the assessment of tomographic reconstruction of dense-layered binary-phase objects

Each image metric represents different characteristics of images. For instance, similarity metrics, e.g. Structural Similarity Index Metric (SSIM) or Pearson Correlation Coefficient (PCC), utilize correlation between two images to calculate similarity between them; error metrics, e.g. Mean Absolute Error (MAE) or Root-Mean Squared Error (RMSE), compute the pixel-wise error between them according to different norms. As each of them highlights different aspects, a choice of the metric for an application may depend upon characteristics of the images. In this paper, we will show some tomographic reconstructions of dense-layered binary-phase objects, and as the objects are binary, we propose Probability of Error (PE) as an image metric for the assessment of the reconstructions in contrast to other metrics that are not constrained to the range of values. PE is equivalent to Bit-Error Rate (BER) in digital communications as both of the signals of interest are binary, and we are interested to a bit-wise deviation of the reconstructions of their corresponding ground truth images.

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