Point cloud processing is basically a signal processing issue. The huge amount of data which are collected with Terrestrial Laser Scanners or photogrammetry techniques faces the classical questions linked with signal or image processing. Among others, denoising and compression are questions which have to be addressed in this context. That is why, one has to turn attention to signal theory because it is susceptible to guide one's good practices or to inspire new ideas from the latest developments of this field. The literature have been showing for decades how strong and dynamic, the theoretical field is and how efficient the derived algorithms have become. For about ten years, a new technique has appeared: known as compressive sensing or compressive sampling, it is based first on sparsity which is an interesting characteristic of many natural signals. Based on this concept, many denoising and compression techniques have shown their efficiencies. Sparsity can also be seen as redundancy removal of natural signals. Taken along with incoherent measurements, compressive sensing has appeared and uses the idea that redundancy could be removed at the very early stage of sampling. Hence, instead of sampling the signal at high sampling rate and removing redundancy as a second stage, the acquisition stage itself may be run with redundancy removal. This paper gives some theoretical aspects of these ideas with first simple mathematics. Then, the idea of compressive sensing for a Terrestrial Laser Scanner is examined as a potential research question and finally, a denoising scheme based on a dictionary learning of sparse coding is experienced. Both the theoretical discussion and the obtained results show that it is worth staying close to signal processing theory and its community to take benefit of its latest developments.