Strong gravitational is a natural phenomenon that produces distorted images of distant galaxies due to massive galaxies or clusters, called deflectors or lenses, lying along the line of sight. Due to the mass of the deflector, and as a result of general relativity, the light coming from galaxies at the background follows a path that appears to us as bent, thus forming magnified and sheared images. The spectacular images of gravitational lens systems give us information about a wealth of cosmological and physical processes, from the expansion of the Universe to the nature of dark matter. The study of strong gravitational lenses requires being able to extract information from images of such systems. When faced with this task, many problems arise. First, there is the problem of finding them. So far, only a few hundreds of strong gravitational lens systems are known, but future surveys are expected to bring hundreds of thousands new systems to be found amongst billions of light sources. The second problem is to be able to identify lensed features and separate them from the light profile of the foreground deflector. The third problem is to be able to reconstruct the image of a lensed background source as if it had been unaffected by lensing. The last problem is the reconstruction of the deflector's mass distribution. In practice, the last two problems have to be solved as one. Recovering the light distribution of the source requires being able to invert the distortion by the gravitational lens, which depends on its mass distribution. In turn, the lens mass distribution is constrained by the distortions applied to the source's image. In this thesis I propose to address these problems with the tools provided by sparse inverse problem solving with a particular emphasis on the problem of separating lens and source luminosity profiles. The problem of separating two overlapping light profiles is known as deblending. I introduce three new techniques for the deblending of strong gravitational lenses that exploit different properties of lens systems and that each contribute to solving the problems of strong lens finding and modelling. The first technique allows the general subtraction of galaxies light profiles in large survey in order to facilitate the search for strong gravitational lenses. The second technique allows to separate lens and source light profiles based on their difference in colour and the sparsity of a galaxy's light profile in the wavelet. This technique allows in particular to remove most of the light from foreground galaxy clusters, which facilitates the identification of lensed galaxies in view of the modelling of the cluster's mass distribution. Finally, I show that lensing itself can be used to separate the unperturbed light profile of a lens galaxy from the distorted profile of a lensed source. This technique involves the joint reconstruction of the source in its own referential based again on sparsity. At this stage, the joint reconstruction and separation is performed at fixed mass model, but this work paves the way for the development of a free form lens mass distribution reconstruction technique in the near future, based on the combination of these separation and reconstruction techniques.