Borehole microresistivity images are an important source of high resolution information with broad application in geology and petrophysics. They contain large volumes of data which (for reasons of efficiency and reproducibility) makes it desirable to automate aspects of quantitative analysis such as feature extraction. One of several hurdles to be addressed in this challenge is the typically incomplete circumferential coverage of measurements from wireline tools (often less than 70%). Robust estimates of the missing information have been obtained by decomposing the measured parts into sparse representations of their morphological components using dictionaries of multi-scale, multi-orientation transforms; reconstructing these representations recovers missing information to an extent dependent on the dictionaries. In clastic rock formations the most useful transforms are found to be curvelets, which have been used to reconstruct a broad range of attributes including common continuous curvilinear features such as partial and full sinusoids, as well as textural elements. The method has been tested on full-coverage data from small diameter wells artificially obscured to simulate partial coverage. For images dominated by curvilinear features, reconstruction accuracy is 92% for 50% coverage loss (typical in 12.25 inch diameter wells), and at 30% loss (typical in 8.5 inch wells) images are almost indistinguishable from the original unobscured images for all apparent dip angles below near-vertical, regardless of degree of feature parallelism (or lack thereof). Successful reconstruction of near-vertical features (including those with complex boundaries such as breakouts) is more dependent on coverage loss, but in these cases the results are consistent with judgments made by human interpreters. The utility of these inpainted images is further enhanced by visualizations that improve on the universally-used static and dynamically normalized image displays by (for example) rendering wide dynamic range data without introducing unwanted artefacts. The image inpainting and visualization methods described are enablers for automated feature recognition.