Deep neural networks recognize objects by analyzing local image details and summarizing their information along the inference layers to derive the final decision. Because of this, they are prone to adversarial attacks. On the other hand, human eyes recognize objects based on their global structures and semantic cues, instead of local image textures. In this work, we propose to develop a structure-oriented progressive low-rank image completion method to remove unneeded texture details from the input images and shift the bias of deep neural networks towards global object structures and semantic cues. We formulate the problem into a low-rank matrix completion problem with progressively smoothed rank functions to avoid local minimums. Our experimental results demonstrate the proposed method is able to successfully remove the insignificant local image details while preserving important global object structures.