Phase unwrapping is the most critical step in the processing of synthetic aperture radar interferometry. The phase obtained by SAR interferometry is wrapped over a range from -
to
.
Phase unwrapping must be
performed to obtain the true phase. The least square approach attains the
unwrapped phase by minimizing the difference between the discrete partial
derivatives of the wrapped phase and the discrete partial derivatives of
the unwrapped solution. The least square solution will result in discrete
version of the Poisson's partial differential equation.
Solving the discretized Poisson's equation with the classical method of
Gauss-Seidel relaxation has extremely slow convergence. In this paper we have
used Wavelet techniques which overcome this limitation by transforming
low-frequency components of error into high frequency components which
consequently can be removed quickly by using the Gauss-Seidel relaxation method.
In Discrete Wavelet Transform (DWT) two operators, decomposition (analysis) and
reconstruction (synthesis), are used. In the decomposition stage an image is
separated into one low-frequency component (approximation) and three
high-frequency components (details). In the reconstruction stage, the image
is reconstructed by synthesizing the approximated and detail components.
We tested our algorithm on both simulated and real data and on both unweighted
and weighted forms of discretized Poisson's equation. The experimental results
show the effectiveness of the proposed method.
