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Depth information is the foundation of perception, essential for autonomous driving, robotics, and other source-constrained applications. Promptly obtaining accurate and efficient depth information allows for a rapid response in dynamic environments. Sensor-based methods using LIDAR and RADAR obtain high precision at the cost of high power consumption, price, and volume. While due to advances in deep learning, vision-based approaches have recently received much attention and can overcome these drawbacks. In this work, we explore an extreme scenario in vision-based settings: estimate a depth map from one monocular image severely plagued by grid artifacts and blurry edges. To address this scenario, We first design a convolutional attention mechanism block (CAMB) which consists of channel attention and spatial attention sequentially and insert these CAMBs into skip connections. As a result, our novel approach can find the focus of current image with minimal overhead and avoid losses of depth features. Next, by combining the depth value, the gradients of X axis, Y axis and diagonal directions, and the structural similarity index measure (SSIM), we propose our novel loss function. Moreover, we utilize pixel blocks to accelerate the computation of the loss function. Finally, we show, through comprehensive experiments on two large-scale image datasets, i.e. KITTI and NYU-V2, that our method outperforms several representative baselines.