Compressive sensing
First Claim
1. A computerimplemented method for determining optimal sampling grid during seismic data reconstruction, the method comprising:
 a) constructing an optimization model, via a computing processor, given by min_{u}∥
Su∥
_{1 }s.t. ∥
Ru−
b∥
_{2}≦
σ
wherein S is a discrete transform matrix, b is seismic data on an observed grid, u is seismic data on a reconstruction grid, σ
represents noise level in observed data, and matrix R is a sampling operator;
b) defining mutual coherence as
2 Assignments
Litigations
1 Petition
Accused Products
Abstract
Computerimplemented method for determining optimal sampling grid during seismic data reconstruction includes: a) constructing an optimization model, via a computing processor, given by min_{u}∥Su∥_{1}s.t. ∥Ru−b∥_{2}≦σ wherein S is a discrete transform matrix, b is seismic data on an observed grid, u is seismic data on a reconstruction grid, and matrix R is a sampling operator; b) defining mutual coherence as
wherein C is a constant, S is a cardinality of Su, m is proportional to number of seismic traces on the observed grid, and n is proportional to number of seismic traces on the reconstruction grid; c) deriving a mutual coherence proxy, wherein the mutual coherence proxy is a proxy for mutual coherence when S is overcomplete and wherein the mutual coherence proxy is exactly the mutual coherence when S is a Fourier transform; and d) determining a sample grid r_{*}=arg min_{r }μ(r).
5 Citations
6 Claims

1. A computerimplemented method for determining optimal sampling grid during seismic data reconstruction, the method comprising:

a) constructing an optimization model, via a computing processor, given by min_{u}∥
Su∥
_{1 }s.t. ∥
Ru−
b∥
_{2}≦
σ
wherein S is a discrete transform matrix, b is seismic data on an observed grid, u is seismic data on a reconstruction grid, σ
represents noise level in observed data, and matrix R is a sampling operator;b) defining mutual coherence as  View Dependent Claims (2, 3, 4, 5, 6)

1 Specification