Existing deep learning-based speech denoising approaches require clean speech signals to be available for training. This paper presents a deep learning-based approach to improve speech denoising in real-world audio environments by not requiring the availability of clean speech signals in a self-supervised manner. A fully convolutional neural network is trained by using two noisy realizations of the same speech signal, one used as the input and the other as the output of the network. Extensive experimentations are conducted to show the superiority of the developed deep speech denoising approach over the conventional supervised deep speech denoising approach based on four commonly used performance metrics and also based on actual field-testing outcomes.