Principles of Modern Radar - Volume 2 1891121537

8.5 InSAR Processing Steps 365ξ takes on higher values for sharp correlation peaks than for diffuse peaks. ξ can then bethresholded to eliminate unreliable tie point candidates.Now that tie points have been identified and their relative position in each imageestimated, the slave image must be transformed to align with the master. A typical approachcomputes an affine transformation wherein the warping function is a 2-D polynomial thatmaps tie points in the slave image to the corresponding locations in the master image. Asystem of equations can be established using the tie point displacements previously foundand solved to give the warping function. This procedure is effective at compensating globaltranslations, rotations, skews, and scale changes and works well in relatively flat regions.However, in the second (fine grain) registration stage, it is more common to use a localwarping procedure, such as a thin-plate spline method, which can account for nonlineardistortions [32].In general, the image warping function will require shifting slave image data byfractional pixels, so resampling (interpolation) is required to produce values on the samecoordinate grids for both images. Resampling of b[l,m] can be done with any number ofinterpolation methods. A typical choice that provides adequate quality with relatively lowcomputation for coarse registration is a simple bilinear interpolator. High-fidelity systemsmay require higher-order interpolators for good results. For fine registration using thinplatespline methods, the spline is itself the interpolating kernel, so that the two steps ofwarping and resampling can be combined.Numerous additional details and extensions for InSAR image registration are describedin the literature. Some global skews and translations can be corrected in theoriginal data collection and image formation. A multiresolution, iterative approach maybe necessary if misalignments are severe or tie point generation is difficult. Registrationtechniques have been suggested that use subbanding of the image data to estimate registrationerrors without cross-correlation or interpolation computations [35]. Despite theadditional Fourier transforms required, it is claimed that these techniques can achieve registrationaccuracies of a few hundredths of a resolution cell with reduced computationalcomplexity8.5.2 Estimation of the Wrapped Interferometric Phase DifferenceOnce the two images are registered, the wrapped phase ˜φ ab [l,m] must be computed.Because the clutter within a given resolution cell of one image is typically modeled asa random process, the interferogram is also a random process. The maximum likelihoodestimator of the wrapped phase map is the phase of an averaged interferogram [20,36]:{ N} {∑N}∑˜φ ab [l,m] = arg a[l,m]b ∗ [l,m] = arg I ab [l,m] (8.33)n=1The N interferogram samples averaged in this equation can be obtained by dividing theSAR data bandwidth into N subbands, forming degraded-resolution images from each,and averaging the interferograms or by local spatial averaging of a single full-bandwidthinterferogram. The latter technique is most commonly used, typically with a 3 × 3, 5 × 5,or 7 × 7 window. Error sources limiting the accuracy of IPD estimation are discussed inSection 8.6.Interferogram flattening is often implemented at this point. In this stage, the wrappedreference DEM or flat earth phase function ˜φ refab [l,m] is subtracted from ˜φ ab and the resultn=1