Simultaneous Deblending and Interpolation using the High-Resolution Radon Transform

Kai Zhuang, Daniel O. Trad

We implement a simultaneous deblending and interpolation method built upon a Radon-based deblending operator to reconstruct randomly sampled blended data into a regularly sampled grid. By interpolating and deblending simultaneously, we eliminate a computationally expensive step in processing by combining it with another required processing step at no extra cost. This is possible because the formulation for sparse deblending that we use is very similar to that of a generic interpolation algorithm using sparse inversion. Our choice of transform operator is also ideal for interpolation for the same reasons it is for deblending: Radon creates both a sparse and accurate mapping of the data into model space. Simultaneous deblending and interpolation enable us to account for all observed data by incorporating the blending operator in conjunction with our sampling operator into the cost function. Our synthetic examples demonstrate that we can effectively perform interpolation and deblending at the same time using a single inversion equation.