Piecewise smooth regularization of data is disclosed. One example is a system where input data is received, the input data being associated with a certainty function indicative of confidence of each data element in the input data. Guide data including information indicative of presumed piecewise smoothness of the input data is received. A joint edge-aware filter is applied, based on the guide data, to the input data to provide filtered data. The joint edge-aware filter is applied, based on the guide data, to the certainty function to provide filtered certainty. A normalized convolution algorithm is applied to the filtered data and the filtered certainty to provide output data indicative of a piecewise smooth regularization of the input data.
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