Hyperspectral (HS) imaging retrieves information from data obtained across a wide spectral range of spectral channels. The object to reconstruct is a 3D cube, where two coordinates are spatial and the third one is spectral. We assume that this cube is complex-valued, i.e. characterized spatially frequency varying amplitude and phase. The observations are squared magnitudes measured as intensities summarized over the spectrum. The HS phase retrieval problem is formulated as a reconstruction of the HS complex-valued object cube from Gaussian noisy intensity observations. The derived iterative algorithm includes the original proximal spectral analysis operator and the sparsity modeling for complex-valued 3D cubes. The efficiency of the algorithm is confirmed by simulation tests.