  Next-generation radio interferometric telescopes will exhibit non-coplanar
baseline configurations and wide field-of-views, inducing a w-modulation of the
sky image, which in turn induces the spread spectrum effect. We revisit the
impact of this effect on imaging quality and study a new algorithmic strategy
to deal with the associated operator in the image reconstruction process. In
previous studies it has been shown that image recovery in the framework of
compressed sensing is improved due to the spread spectrum effect, where the
w-modulation can act to increase the incoherence between measurement and
sparsifying signal representations. For the purpose of computational
efficiency, idealised experiments were performed, where only a constant
baseline component w in the pointing direction of the telescope was considered.
We extend this analysis to the more realistic setting where the w-component
varies for each visibility measurement. Firstly, incorporating varying
w-components into imaging algorithms is a computational demanding task. We
propose a variant of the w-projection algorithm for this purpose, which is
based on an adaptive sparsification procedure, and incorporate it in compressed
sensing imaging methods. This sparse matrix variant of the w-projection
algorithm is generic and adapts to the support of each kernel. Consequently, it
is applicable for all types of direction-dependent effects. Secondly, we show
that for w-modulation with varying w-components, reconstruction quality is
significantly improved compared to the setting where there is no w-modulation
(i.e. w=0), reaching levels comparable to the quality of a constant, maximal
w-component. This finding confirms that one may seek to optimise future
telescope configurations to promote large w-components, thus enhancing the
spread spectrum effect and consequently the fidelity of image reconstruction.
