In order to improve the accuracy and robustness of the Canny algorithm in processing noise images, we propose a low rank matrix recovery method based on truncated singular value, and present a more accurate dual noiseconvex optimization model and a method of solving the optimization model. We use the classical Canny edge detection method on the decomposed principal component without redundant information, and thus transform the edge detection of the image into the edge detection of the principal component. This method can effectively eliminate the impulse noise and Gaussian noise while preserving the edge information better. To verify its effectiveness, we conduct experiments under different noise concentrations and mixed noises, and the results show that the edge detection algorithm based on lowrank matrix recovery can better preserve the complete edge information and improve the accuracy and robustness of edge detection methods.