Text extraction is an important problem in image processing with applications from optical character recognition to autonomous driving. Most of the traditional text segmentation algorithms consider separating text from a simple background (which usually has a different color from texts). In this work we consider separating texts from a textured background, that has similar color to texts. We look at this problem from a signal decomposition perspective, and consider a more realistic scenario where signal components are overlaid on top of each other (instead of adding together). When the signals are overlaid, to separate signal components, we need to find a binary mask which shows the support of each component. Because directly solving the binary mask is intractable, we relax this problem to the approximated continuous problem, and solve it by alternating optimization method. We show that the proposed algorithm achieves significantly better results than other recent works on several challenging images.