Sinusoidal signal models are a useful representation of local image structure, as sinusoid phase describes symmetry separately from strength and orientation. Existing models consist of one or two oriented sinusoids, calculated using the 0th to 3rd order Riesz transforms. We propose an expanded signal model consisting of a larger number of oriented sinusoids. The model parameters are estimated using higher-order Riesz transforms and a novel application of super-resolution theory. Image features consisting of multiple lines or edges can be analysed using the method, which compares favourably to existing approaches.