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In this article we describe a novel enhancement method for images containing filamentous structures. Our method combines a gradient sparsity constraint with a filamentous structure constraint for effective removal of clutter and noise from the background. The method is applied and evaluated on three types of data: confocal microscopy images of neurons, calcium imaging data and images of road pavement. We found that images enhanced by our method preserve both the structure and the intensity details of the original object. In the case of neuron microscopy, we find that the neurons enhanced by our method are better correlated with the original structure intensities than the neurons enhanced by well-known vessel enhancement methods. Experiments on simulated calcium imaging data indicate that both the number of detected neurons and the accuracy of the derived calcium activity improved. Applying our method to real calcium data, more regions exhibiting calcium activity in the full field of view were found. In road pavement crack detection, smaller or milder cracks were detected after using our enhancement method.