Shearlets and sparse representation for microresistivity borehole image inpainting

Microresistivity image logs from wireline tools commonly include nonmeasured gaps corresponding to the spaces between electrode-carrying pads in contact with the borehole wall. The missing data impede the development of automated processes that seek to provide objective and reproducible geologic analysis. Geologic features often manifest themselves as curvilinear objects representing a variety of discontinuities, such as layer boundaries and fractures, which lend themselves to sparse representation. Missing data may be inpainted by thresholding or minimizing the norm of their representation in a fitting dictionary. Curvelets have been found to provide good sparse approximation for these features, but shearlets are shown to be more computationally efficient. Results from a mix of synthetic and field image logs indicate more accurate reconstruction of sharp high-contrast edges.