Single-image haze removal is challenging due to its ill-posed nature. The breadth of real-world scenarios makes it difficult to find an optimal dehazing approach that works well for various applications. This article addresses this challenge by utilizing a novel robust quaternion neural network architecture for single-image dehazing applications. The architecture's performance to dehaze images and its impact on real applications, such as object detection, is presented. The proposed single-image dehazing network is based on an encoder-decoder architecture capable of taking advantage of quaternion image representation without interrupting the quaternion dataflow end-to-end. We achieve this by introducing a novel quaternion pixel-wise loss function and quaternion instance normalization layer. The performance of the proposed QCNN-H quaternion framework is evaluated on two synthetic datasets, two real-world datasets, and one real-world task-oriented benchmark. Extensive experiments confirm that the QCNN-H outperforms state-of-the-art haze removal procedures in visual quality and quantitative metrics. Furthermore, the evaluation shows increased accuracy and recall of state-of-the-art object detection in hazy scenes using the presented QCNN-H method. This is the first time the quaternion convolutional network has been applied to the haze removal task.