We present methods used to measure the information in an astronomical image, in both a statistical and a deterministic way. We discuss the wavelet transform and noise modeling, and describe how to measure the information and the implications for object detection, filtering, and deconvolution. The perspectives opened up by the range of noise models, catering for a wide range of eventualities in physical science imagery and signals, and the new two-pronged but tightly coupled understanding of the concept of information have given rise to better quality results in applications such as noise filtering, deconvolution, compression, and object (feature) detection. We have illustrated some of these new results in this article. The theoretical foundations of our perspectives have been sketched out. The practical implications, too, are evident from the range of important signal processing problems which we can better address with this armoury of methods. The results described in this work are targeted at information and at relevance. While we have focused on experimental results in astronomical image and signal processing, the possibilities are apparent in many other application domains.