Different signals from the various sensors of the same scene form an ensemble. Distributed compressed sensing (DCS) rests on a new concept called the joint sparsity of the ensemble. JSM‐1 is a model that describes the joint sparsity by one dictionary. Previously, the generalisation of JSM‐1 was proposed where the signal ensemble depends on two dictionaries. Its compressed sensing (CS) version is considered: generalised DCS (GDCS). Instead of using random projections (random Gaussian (rGauss)), a gradient method with Barzilai–Borwein stepsize (GBB) is developed to optimise the projections in the GDCS. It enhances the reconstruction performance of the GDCS. It is verified by some experiments on the synthesised signals.