Learning filters to produce sparse image representations in terms of overcomplete dictionaries has emerged as a powerful way to create image features for many different purposes. Unfortunately, these filters are usually both numerous and non-separable, making their use computationally expensive. In this paper, we show that such filters can be computed as linear combinations of a smaller number of separable ones, thus greatly reducing the computational complexity at no cost in terms of performance. This makes filter learning approaches practical even for large images or 3D volumes, and we show that we significantly outperform state-of-the-art methods on the tubular structure extraction task, in terms of both accuracy and speed. Moreover, our approach is general and can be used on generic convolutional filter banks to reduce the complexity of the feature extraction step.