  Interferometric phase (InPhase) imaging is an important part of many
present-day coherent imaging technologies. Often in such imaging techniques,
the acquired images, known as interferograms, suffer from two major
degradations: 1) phase wrapping caused by the fact that the sensing mechanism
can only measure sinusoidal $2\pi$-periodic functions of the actual phase, and
2) noise introduced by the acquisition process or the system. This work
focusses on InPhase denoising which is a fundamental restoration step to many
posterior applications of InPhase, namely to phase unwrapping. The presence of
sharp fringes that arises from phase wrapping makes InPhase denoising a
hard-inverse problem. Motivated by the fact that the InPhase images are often
locally sparse in Fourier domain, we propose a multi-resolution windowed
Fourier filtering (WFF) analysis that fuses WFF estimates with different
resolutions, thus overcoming the WFF fixed resolution limitation. The proposed
fusion relies on an unbiased estimate of the mean square error derived using
the Stein's lemma adapted to complex-valued signals. This estimate, known as
SURE, is minimized using an optimization framework to obtain the fusion
weights. Strong experimental evidence, using synthetic and real (InSAR & MRI)
data, that the developed algorithm, termed as SURE-fuse WFF, outperforms the
best hand-tuned fixed resolution WFF as well as other state-of-the-art InPhase
denoising algorithms, is provided.
