Phase unwrapping is one of the key steps in InSAR data processing

and its precision directly affects the accuracies of DEM generation or surface deformation monitoring. The phase extracted from a complex SAR interferogram is wrapped because it represents a measure; modulo 2π and multiples of 2π must be added or subtracted. Ideally

when the sampling rate of the image satisfies the Nyquist sampling theorem

phase unwrapping can be achieved by a simple 2D integration. However

phase inconsistencies caused by overlay and shadow appear in the actual data. When the integration path passes through the abovementioned area

the phase error will spread

leading to unwrapping errors. Numerous phase unwrapping algorithms are proposed to solve the above problems. The statistical-cost network-flow algorithm (SNAPHU) is a kind of network flow method that is widely used in InSAR data processing. Based on the SNAPHU algorithm

this study aims to find a phase unwrapping algorithm for airborne SAR interferometry. While applying the SNAPHU to high-resolution airborne InSAR data

if the interferogram has phase inconsistencies caused by lines of trees

then the unwrapped result will show large areas of phase jump along the inconsistencies correspondingly. SNAPHU

which has limitations in managing local phase inconsistencies

is a global optimization algorithm. Local phase inconsistencies can be optimized by a local algorithm. Phase inconsistencies can be described by residues. Local data can be optimized by residue compensation. This paper proposes an airborne unwrapping algorithm combining the residue degradation with the SNAPHU

which has advantages of the local and the global optimum. Residues are degraded to non-residues according to the values of residues and neighboring pixels

and the local data are optimized. The modified SNAPHU algorithm is applied to the degraded image. The proposed algorithm can be divided into three steps.(1) Residue degradation. First

the filtered interferogram is flattened. Residue degradation is applied to the flattened interferogram. This process contains residue detection and compensation. Phase inconsistencies lead to the presence of residues. Phase inconsistencies mean the absolute phase difference between two neighboring pixels exceeding π. Therefore

the pair of pixels in the residue

whose phase is inconsistent

is first located to degenerate the residue

and then a compensation constant C is set to compensate the residue. The residue can be degraded by multiple iterations because the compensation changes the value of phase and the phase difference between the neighboring pixels. A threshold N for the remaining residues is set to balance the accuracy and efficiency. When the number of residues is less than N

the compensation stops to control the degree of degradation.(2) Phase unwrapping of airborne SNAPHU algorithm. In the airborne system

the incidence angle calculated by the original geometric model of SNAPHU is close to zero

which is obviously incorrect

because the height of the platform is far less than the radius of the Earth. Simultaneously

the earth curvature can be ignored to simplify the model with a narrow mapping bandwidth in the airborne system

thus the parameters and the geometric model in the SNAPHU algorithm are modified according to the calibration parameters of the airborne InSAR system. The modified SNAPHU algorithm is employed for phase unwrapping.(3) Median filter. A median filter is applied to the unwrapped result

which effectively reduces phase noise

and the edge information is well preserved. Therefore

a 5×5 median filter is applied to the unwrapped image to obtain the final result. The efficiency and accuracy of the proposed method is tested and validated by using the single-pass dual antenna airborne InSAR data covering Jiangyou

Sichuan areas in 2011. Unwrapping results have a significant error region using SNAPHU directly. A large area of the phase jumping exists. However

error unwrapped regions are significantly shrunk after residue degradation

and phase jumping regions are effectively corrected. After a 5 × 5 median filter

the partial phase noise is removed

and the unwrapping result is smooth. The performances of the improved methods are evaluated by the number of discontinuous points in azimuth and range directions. When the number of discontinuous point is minimal

the anti-phase distortion performance is improved

and the unwrapping quality is high. The residue degradation effectively reduces the number of discontinuous points in the interferogram. The number of discontinuous points in either direction of improved airborne SNAPHU algorithm is lower than that of the simple airborne SNAPHU algorithm. The anti-phase distortion performance and the quality of the unwrapping results are obviously improved. The residue degradation process effectively solves the problem of large unwrapped phase jump and becomes further robust to noise. This algorithm combines the advantages of local and global optimization

which has a good overall performance

and effectively solves the problem of large unwrapped phase jump. Moreover

median filter can effectively reduce the noise and is robust to noise.