Improved algorithm for Phase Unwrapping with Continuous Submodular Minimization

Abstract

The phase unwrapping is the process of attempting to reconstruct the true phase from modulo 2π phase values. This procedure requires that we have an important congruent constraint i.e. rewrapping unwrapped image should be identical to the original wrapped image. This constraint condition causes a discrete optimization problem. However, many methods have ignored this constraint condition to solve a continuous minimization problem directly, making it difficult to solve the solution correctly. We recently presented new continuous minimum norm method that is based on the Lovász extension. Our method can reach the optimal solution with the congruent constraint condition. Note that in our work, we have taken the subgradient method for minimization, but it is time consuming. In this paper, we introduce the incremental subgradient method to the minimization procedure, which is faster than the subgradient method. To solve the phase unwrapping, first, we also use the Lovász extension to transform the phase unwrapping problem to equivalent continuous minimization problem which consists of the sum of large numbers of component functions. Then we take the incremental subgradient method to solve the minimization problem in which operate on a single component at each iteration, rather than on the entire cost function. On the other hand, we also introduce new minimal function to deal with high lever noise. Several simulations show, compared with the subgradient method, the new algorithm only takes one quarter of (or less) the numbers of iteration for the convergence.