Estimation of channelized features in geological media using sparsity constraint

In this thesis, a new approach is studied for inverse modeling of ill-posed problems with spatially continuous parameters that exhibit sparseness in an incoherent basis (e.g. a Fourier basis). The solution is constrained to be sparse in the transform domain and the dimension of the search space is effectively reduced to a low frequency subspace to improve estimation efficiency. The solution subspace is spanned by a subset of a discrete cosine transform (DCT) basis containing low-frequency elements. The methodology is related to compressive sensing, which is a recently introduced paradigm for estimation and perfect reconstruction of sparse signals from partial linear observations in an incoherent basis. The sparsity constraint is applied in the DCT domain and reconstruction of unknown DCT coefficients is carried out through incorporation of point measurements and prior knowledge in the spatial domain. The approach appears to be generally applicable for estimating spatially distributed parameters that are approximately sparse in a transformed domain such as DCT. The suitability of the proposed inversion framework is demonstrated through synthetic examples in characterization of hydrocarbon reservoirs.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Jafarpour, Behnam

Advisor dc:contributor.advisor

• William T. Freeman and Vivek K. Goyal.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/43040

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/43040