According to the standard cosmological model, the Gaussian adiabatic perturbations that occurred in the early universe produced a pure Gaussian component in the cosmic microwave background (CMB). However, some models also suggest the formation of topological defects such as "cosmic strings" which would have imprinted a non-Gaussian component in the CMB superimposed to the standard Gaussian component. This overall CMB signal may be probed by radio-interferometers through incomplete and noisy Fourier measurements. The aim of the project is to develop and test algorithms for the detection of cosmic strings from such interferometric data of the CMB. In this work, we show that this problem can be address in a compressed sensing perspective. In this context, we propose and test two algorithms which take into account prior information on the string signal. The performance are then assessed by comparing the reconstructions obtained with these methods and the ones obtained with a very common algorithm in radio-astronomy called CLEAN.