Multiresolution Network Flow Phase Unwrapping

Phase Unwrapping is a key step in deriving topographic information from Interferometric SAR. Several recent methods are based on a minimum cost network flow approach. In this paper we develop a new, computationally efficient, “divideand-conquer” strategy for phase unwrapping. INTRODUCTION The well-studied Interferometric Synthetic Aperture Radar (InSAR) problem for DEM generation involves the derivation of topographic information from radar phase. The topography is proportional to the full phase, whereas the measured phase is modulo 2 , necessitating the process of recovering full phase values via phase unwrapping. In general, the presence of noise, phase discontinuities, and the sheer size of the problem make phase-unwrapping challenging. Our research is motivated by recent work[1, 2] which models the phase unwrapping problem as a discrete optimization problem. We define (i; j) and (i; j) as the unwrapped and wrapped phase functions respectively, where the indices i; j live in a rectangular M N grid. Our measured phase obeys (i; j) =W( (i; j)) = (i; j) + 2 n(i; j) (1) where n(i; j) are integers such that < (i; j) and W is the wrapping operator. We define the residuals kq = ki;j;d = 1 2 d (i; j) W( d (i; j)) (2) for each individual arc q = fi; j; dg, where d is the discrete difference operator along direction d 2 fx; yg. If we let q = i;j;d = W( d (i; j)), then the phase unwrapping problem can be formulated as min Xq cqjkqj (3) such that all simple loop integrals be zero: ka + kb + kc + kd = 1 2 [ a + b + c + d] (4) 0Funding acknowledgment: Research supported by the Canadian Centre for Remote Sensing, the Canadian International Development Agency, and the Canadian Natural Science & Engineering Research Council. −3 −2 −1 0 1 2 3 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 −6 −4 −2 0 2 4 6 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100