This paper presents an extension of the spatio-spectral ("3D") image reconstruction algorithm called PAINTER (Polychromatic opticAl INTErferometric Reconstruction software). The algorithm is able to solve large scale problems and relies on an iterative process, which alternates estimation of polychromatic images and of complex visibilities. The complex visibilities are not only estimated from squared moduli and closure phases, but also from differential phases, which helps to constrain the polychromatic reconstruction. Alternative methods to construct the specific differential phases used in PAINTER are proposed. Simulations on synthetic data illustrate the specificities of the proposed methods.