Sparse Radon transform with dual gradient ascent method

Yujin Liu, Zhimin Peng, William Symes, and Wotao Yin

Soceity of Exploration Geophysicists (SEG) annual meeting, Houston, TX 2013

Overview

The Radon transform suffers from the typical problems of loss of resolution and aliasing that arise as a consequence of in- complete information, such as limited aperture and discretiza- tion. Sparseness in Radon domain, which is equivalent to as- suming 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 geo- physics is reweighted least-squares inversion (IRLS) method. As IRLS method needs to compute the weighting function it- eratively 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 com- pressive 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 pro- vide results with higher resolution than CGG method after a few iterations, which is also of great potential in other seismic applications.

Citation

Y. Liu, Z. Peng, W. Symes, and W. Yin, Sparse Radon transform with dual gradient ascent method, Extended abstract for SEG annual meeting, Houston, TX 2013.


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