Weak NP-Hardness for the 2-D L⁰-Norm InSAR Phase Unwrapping

Two-dimensional phase unwrapping (PU) is an essential step in interferometric synthetic aperture radar (InSAR) analysis. Although the L-0-norm PU method is desired, it is nondeterministic polynomial (NP)-hard. Thus, many PU meth-ods have been proposed to find near-optimal solutions of the L-0-norm. As PU is an ill-posed problem, it is difficult to choose the method with the most accurate solution unless reference data are available. In this letter, we prove that the NP-hardness of the L-0-norm is weak, suggesting that the alpha-approximation algorithm of the L-0-norm can be devised, that is, the obtained near-optimal solutions can be within a factor of alpha of the L-0-norm optimal value. The primary contribution of the proof is that the alpha value of each obtained PU solution can be considered as a new index to assess the PU performance without using reference data. The validity and effectiveness of the alpha-based index have been verified using simulated and acquired interferometric datasets and three PU methods.