This paper studies the Speech Enhancement based on Deep Neural Networks. The proposed architecture gradually follows the signal transformation during enhancement by means of a visualization probe at each network block. Alongside the process, the enhancement performance is visually inspected and evaluated in terms of regression cost. This progressive scheme is based on Residual Networks. During the process, we investigate a residual connection with a constant number of channels, including internal state between blocks, and adding progressive supervision. The insights provided by the interpretation of the network enhancement process leads us to design an improved architecture for the enhancement purpose. Following this strategy, we are able to obtain speech enhancement results beyond the state-of-the-art, achieving a favorable trade-off between dereverberation and the amount of spectral distortion.