Two-dimensional wavelet analysis with directional frames is well-adapted and efficient for detecting oriented features in images but, for (quasi-)isotropic components, it is unnecessarily redundant. Using wavelets with variable angular selectivity leads to a prohibitive computing cost in the continuous wavelet formalism. We propose a solution based on a multiresolution analysis in the angular variable (transferred from a biorthogonal analysis on the line), in addition to the usual multiresolution in scale. The resulting scheme is efficient and competitive with traditional methods. Some applications are given to image denoising.