In this paper, we propose a new synthetic aperture radar (SAR) image detection algorithm based on the de-noising algorithm via the sparse representation and a new morphology edge detector. Firstly, we apply the Shearlet transform to the SAR image to get the sparse representation of it. Then, morphological edge detector with direction is applied to directional sub-band coefficients of the Shearlet which are recovered by the iterative de-noising process. Finally, the completed SAR image edge is obtained by merging each sub-band edge using Dempster–Shafer evidence theory. By completely using the directional sub-bands of the Shearlet transform, the proposed algorithm overcomes the disadvantages of transform detection algorithms which are very unrobust to noise and can also generate inaccurate edges. The experimental results demonstrate the effectiveness and superiority of our proposed algorithm in terms of the edge positioning accuracy, integrity, and the number of false edge points.