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 modulo-2π 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 than π rad. The PU problem is even more challenging for noisy images. This paper proposes a diversity approach, which consists of using two (or more) images of the same scene acquired with different frequencies. Diversity grants an enlargement of the ambiguity interval [−π π(, thus, allowing to unwrap images with high phase rates. Furthermore, this paper presents a multi-resolution technique to make denoising. We formulate the problem with a maximum a posteriori Markov random field (MAP-MRF) rationale, and apply energy minimization techniques based on graph cuts. We illustrate the performance of the algorithm by showing experimental results, and argue that it is, as far as we know, state-of-the art competitive.