Interpolation of potential-field data by Projection Onto Convex Sets algorithm with generalized exponential threshold and based on Discrete Cosine Transform

Data filling or interpolation is a fundamental and vital problem of potential-field data processing. Some data cannot be measured when some places are unable to reach, such as rivers, or cliffs. If we want to acquire the missing data for better subsequent processing, we need to interpolate or fill in the missing data. Hence, this article introduces the Discrete Cosine Transform (DCT) method into the Projection Onto Convex Sets (POCS) algorithm to tackle this problem, and a generalized exponential threshold attenuation method is also given. Finally, model tests and practical applications show that the POCS algorithm with generalized exponential threshold and based on DCT has the advantages of high accuracy, small filling or interpolating traces and the noise standard of the filled data are closer to real situation.