  We introduce a framework for the reconstruction of the amplitude, phase and
polarisation of an optical vector-field using calibration measurements acquired
by an imaging device with an unknown linear transformation. By incorporating
effective regularisation terms, this new approach is able to recover an optical
vector-field with respect to an arbitrary representation system, which may be
different from the one used in calibration. In particular, it enables the
recovery of an optical vector-field with respect to a Fourier basis, which is
shown to yield indicative features of increased scattering associated with
tissue abnormalities. We demonstrate the effectiveness of our approach using
synthetic holographic images as well as biological tissue samples in an
experimental setting where measurements of an optical vector-field are acquired
by a fibre endoscope, and observe that indeed the recovered Fourier
coefficients are useful in distinguishing healthy tissues from lesions in early
stages of oesophageal cancer.
