Accelerating seismic interpolation with a gradient projection method based on tight frame property of curvelet
Jingjie Cao 1 4 Yanfei Wang 2 Benfeng Wang 3
+ Author Affiliations
- Author Affiliations
1 Shijiazhuang University of Economics, Shijiazhuang, Hebei 050031, China.
2 Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, PO Box 9825, Beijing 100029, China.
3 State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China.
4 Corresponding author. Email: cao18601861@163.com
Exploration Geophysics 46(3) 253-260 https://doi.org/10.1071/EG14016
Submitted: 11 February 2014 Accepted: 24 June 2014 Published: 6 August 2014
Abstract
Seismic interpolation, as an efficient strategy of providing reliable wavefields, belongs to large-scale computing problems. The rapid increase of data volume in high dimensional interpolation requires highly efficient methods to relieve computational burden. Most methods adopt the L1 norm as a sparsity constraint of solutions in some transformed domain; however, the L1 norm is non-differentiable and gradient-type methods cannot be applied directly. On the other hand, methods for unconstrained L1 norm optimisation always depend on the regularisation parameter which needs to be chosen carefully. In this paper, a fast gradient projection method for the smooth L1 problem is proposed based on the tight frame property of the curvelet transform that can overcome these shortcomings. Some smooth L1 norm functions are discussed and their properties are analysed, then the Huber function is chosen to replace the L1 norm. The novelty of the proposed method is that the tight frame property of the curvelet transform is utilised to improve the computational efficiency. Numerical experiments on synthetic and real data demonstrate the validity of the proposed method which can be used in large-scale computing.
Key words: curvelet transform, gradient projection method, inverse problems, L1 norm regularisation, wavefield interpolation.
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