From diversity and denoising to phase imaging

Many imaging techniques,e.g., magnetic resonance imaging (MRI), yield phase images. In these, each pixel retrieves the phase up to a modulo2π rad ambiguity, i.e., the phase wrapped around the principal interval [−π π(. Phase unwrapping (PU) is, then, a crucial operation to obtain absolute phase, which is what embodies physical information. If the phase difference between neighbor pixels is less than π rad, then, phase unwrapping can be obtained unambiguously. This, however, is not always the case.E.g., in MRI, where absolute phase can be proportional to temperature, we often face neighbor phase differences much larger thanπ rad. The PU problem is even more challenging for noisy images. This paper proposes a diversity approach, which consists of usin g two (or more) images of the same scene acquired with differen t frequencies. Diversity grants an enlargement of the ambigu ity interval [−π π(, thus, allowing to unwrap images with high phase rates. Furthermore, this paper presents a multi-reso lution technique to make denoising. We formulate the problem with a maximum a posteriori Markov random field (MAP-MRF) rationale, and apply energy minimization techniques basedon graph cuts. We illustrate the performance of the algorithm by showing experimental results, and argue that it is, as far aswe know, state-of-the art competitive.