Sparse Radon transform with dual gradient ascent method

The Radon transform suffers from the typical problems of loss of resolution and aliasing that arise as a consequence of incomplete information, such as limited aperture and discretization. Sparseness in Radon domain, which is equivalent to assuming smooth amplitude variation in the transition between known and unknown (missing) data, is a valid and useful prior information (Trad et al., 2003). The most commonly used method to solve sparsity-promotion inverse problems in geophysics is reweighted least-squares inversion (IRLS) method. As IRLS method needs to compute the weighting function iteratively at the outer loop of conjugate gradient iteration, the computational cost is very expensive. In this abstract, we adopt the dual gradient ascent methods, developed in compressive sensing into geophysics and compare them with an updated version of IRLS, namely conjugate guided gradient method (CGG). Numerical tests show that the dual gradient ascent method with Nesterov’s acceleration (DGAN) can provide results with higher resolution than CGG method after a few iterations, which is also of great potential in other seismic applications.