We develop a texture analysis framework to assist radiologists in interpreting high-resolution computed tomography (HRCT) images of the lungs of patients affected with interstitial lung diseases (ILD). Novel texture descriptors based on the Riesz transform are proposed to analyze lung texture without any assumption on prevailing scales and orientations. A global classification accuracy of 78.3% among five lung tissue types is achieved using locally-oriented Riesz components. Comparative performance analysis with features derived from optimized grey-level co-occurrence matrices showed an absolute gain of 6.1% in classification accuracy. The adaptability of the Riesz features is demonstrated by reconstructing templates according to the first principal components of the lung textures. The balanced performance achieved among the various lung textures suggest that the proposed methods can complement human observers in HRCT interpretation, and opens interesting perspectives for future research.