Depth image super-resolution (SR) is a technique that utilizes signal processing technology to enhance the resolution of a low-resolution (LR) depth image. Generally, the external database or high-resolution (HR) images are needed for acquiring the priori information to support the SR reconstruction. To overcome the limitation, a depth image SR method which does not need the reference of any external images is proposed. In the paper, a high-quality edge map is firstly constructed using a sparse coding method, which uses a dictionary learned from the original images themselves at different scales. Then, the high-quality edge map is used to guide the interpolation for depth images by a modified joint trilateral filter. During the interpolation, some information of gradient and structural similarity (SSIM) are added to preserve the detailed information and suppress the noise. The proposed method not only can preserve the sharpness of image edge, but also can avoid the dependence on database. Experimental results show the proposed method is superior to some state-of-the-art depth image SR methods.