Hyperspectral (HS) imaging retrieves information from data obtained across a broad spectral range of spectral channels. The object to reconstruct is a 3D cube, where the 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 spectra. HS phase retrieval is formulated as a reconstruction of an HS complex-valued object cube from Gaussian noisy intensity observations. The considered observation model, projections of the object on the sensor plane, includes varying delay operators such that identical but mutually phase-shifted broadband copies of the object are interfering at the sensor plane. The derived iterative algorithm includes an original proximity spectral analysis operator and sparsity modeling for complex-valued 3D cubes. It is demonstrated that the HS phase retrieval problem can be resolved without random phase coding of wavefronts typical for the conventional phase retrieval techniques. The performance of the new algorithm for phase imaging is demonstrated in simulation tests and in the processing of experimental data.