Frequency‐domain shot‐record migration can produce higher quality images than Kirchhoff migration but typically at a greater cost. The computing cost of shot‐record migration is the product of the number of shots in the survey and the expense of each individual migration. Many attempts to reduce this cost have focused on the speed of the individual migrations, trying to achieve a better trade‐off between accuracy and speed. Another approach is to reduce the number of migrations. We investigate the simultaneous migration of shot records using frequency‐domain shot‐record migration algorithms. The difficulty with this approach is the production of so‐called crossterms between unrelated shot and receiver wavefields, which generate unwanted artifacts or noise in the final image. To reduce these artifacts and obtain an image comparable in quality to the single‐shot‐per‐migration result, we have introduced a process called phase encoding, which shifts or disperses these crossterms. The process of phase encoding thus allows one to trade S/N ratio for the speed of migrating the entire survey. Several encoding functions and two application strategies have been tested. The first strategy, combining multiple shots per migration and using each shot only once, reduces computation in direct relation to the number of shots combined. The second strategy, performing multiple migrations of all the shots in the survey, provides a means to reduce the crossterm noise by stacking the resulting images. The additional noise in both strategies may be tolerated if it is no stronger than the inherent seismic noise in the migrated image and if the final image is achieved with less cost.

Frequency-domain shot-record migration can produce higher quality images than Kirchhoff migration but typically at a greater cost. The computational cost of shot-record migration is the product of the number of shots in the survey and the expense of each individual migration. Many attempts to reduce this cost have focused on the speed of the individual migrations, trying to achieve a better trade-off between accuracy and speed. Another approach is to reduce the number of migrations. We investigate the simultaneous migration of shot records using frequency-domain shot-record migration algorithms. The difficulty with this approach is the production of so-called cross terms between unrelated shot and receiver wavefields, which generate unwanted artifacts or noise in the final image. To reduce these artifacts and obtain an image comparable in quality to the single-shot-per-migration result, we have introduced a process called phase encoding which shifts or disperses these cross terms. The process of phase encoding thus allows one to trade signal-to-noise ratio for the speed of migrating the entire survey. Several encoding functions and two application strategies have been tested. The first strategy, combining multiple shots per migration and using each shot only once, provides a reduction in computation directly related to the number of shots combined. The second strategy, performing multiple migrations of all the shots in the survey, provides a means to reduce the cross-term noise through stacking the resulting images. The additional noise in both strategies may be tolerated if it is no stronger than the inherent seismic noise in the migrated image, and if the final image is achieved with less cost.

We develop an algorithm for the minimum Lp-norm solution to the two-dimensional phase unwrapping problem. Rather than its being a mathematically intractable problem, we show that the governing equations are equivalent to those that describe weighted least-squares phase unwrapping. The only exception is that the weights are data dependent. In addition, we show that the minimum Lp-norm solution is obtained by embedding the transform-based methods for unweighted and weighted least squares within a simple iterative structure. The data-dependent weights are generated within the algorithm and need not be supplied explicitly by the user. Interesting and useful solutions to many phase unwrapping problems can be obtained when p< 2. Specifically, the minimum L0-norm solution requires the solution phase gradients to equal the input data phase gradients in as many places as possible. This concept provides an interesting link to branch-cut unwrapping methods, where none existed previously.

From the Publisher:Spotlight-mode Synthetic Aperture Radar: A Signal Processing Approach describes an important mode of synthetic aperture radar (SAR) imaging, known as spotlight-mode SAR. By treating the subject via the principles of signal processing, this book allows those individuals who are not schooled in the specialized (and sometimes confusing) language of radar imaging to gain accessibility to the critical ideas of SAR relatively quickly. An understanding of basic signal processing concepts (Fourier transforms, convolution, filtering, etc.) is the only required background. The first two chapters of the book develop a rigorous theoretical framework for spotlight-mode SAR, using a paradigm based on three-dimensional tomographic concepts. Following that, a chapter is devoted to the various signal processing steps that are required for robust spotlight-mode image formation via the polar-reformatting algorithm. Numerous examples, derived from simulated as well as real spotlight-mode imagery, are employed to clearly demonstrate the important concepts. Chapter 4 then discusses the effects of phase errors on spotlight-mode SAR imagery, and describes various algorithms for automatic phase error correction, also known as autofocus. The widely used technique of Phase Gradient Autofocus (PGA) is analyzed in depth and a variety of results from actual SAR imagery are shown. The final chapter discusses the subject of interferometry from spotlight-mode SAR imagery. This important topic is currently the subject of extensive research and development efforts across the international SAR community. Spotlight-mode Synthetic Aperture Radar: A Signal Processing Approach is intended for a variety of audiences. Engineers and scientists working in the field of remote sensing, but who do not have experience with SAR imaging, will find an easy entrance into what can seem at times a very complicated subject. Experienced radar engineers will find that the book describes several modern areas of SAR pr

Two-dimensional (2D) phase unwrapping continues to find applications in a wide variety of scientific and engineering areas including optical and microwave interferometry, adaptive optics, compensated imaging, and synthetic-aperture-radar phase correction, and image processing. We have developed a robust method (not based on any path-following scheme) for unwrapping 2D phase principal values (in a least-squares sense) by using fast cosine transforms. If the 2D phase values are associated with a 2D weighting, the fast transforms can still be used in iterative methods for solving the weighted unwrapping problem. Weighted unwrapping can be used to isolate inconsistent regions (i.e., phase shear) in an elegant fashion.

The phase gradient autofocus (PGA) technique for phase error correction of spotlight mode synthetic aperture radar (SAR) imagery is examined carefully in the context of four fundamental signal processing steps that constitute the algorithm. We demonstrate that excellent results over a wide variety of scene content, and phase error function structure are obtained if and only if all of these steps are included in the processing. Finally, we show that the computational demands of the fun PGA algorithm do not represent a large fraction of the total image formation problem, when mid to large size images are involved.< >

A spotlight synthetic aperture radar digital processor has been implemented on an nCUBE 2 parallel supercomputer at Sandia National Laboratories. The digital processor consists of three principal components: a polar reformatter, a two-dimensional fast Fourier transformation code, including Taylor weighting (1) for side-lobe reduction, and a phase gradient autofocus (2) code. Several components of the digital processor have also been implemented on other parallel computers including a CM-2, an Intel iPSC/860 , and a Cray Y-MP/1. The performance of the radar processor on all of these machines is dis- cussed.

Inspired by the work of Lane and Bates on automatic multidimensional deconvolution [ J. Opt. Soc. Am. A4, 180 ( 1987)], we have developed a systematic approach and an operational code for performing the deconvolution of multiply-convolved two-dimensional complex data sets in the absence of noise. We explain, in some detail, the major algorithmic steps, where noise or numerical errors can cause problems, our approach in dealing with numerical rounding errors, and where special noise-mitigating techniques can be used toward making blind de-convolution practical. Several examples of deconvolved imagery are presented, and future research directions are noted.

Near-real-time digital formation of large synthetic aper ture radar (SAR) images requires the computational throughput that only a dedicated special processor or a massively parallel computer can offer. This article documents the implementation of digital spotlight SAR processing components on three commercially avail able massively parallel computers: the Connection Ma chine (CM-2), the nCUBE 2, and the Intel iPSC/860. The three basic spotlight SAR processing components, the polar reformatter, the two-dimensional fast Fourier transformation, and autofocus, are briefly discussed to provide a technical background for the implementation issues that apply to massively parallel computers. As pects of the SAR components that can exploit features of a SIMD or MIMD architecture are also presented. Finally, timing test results on various computers are provided for evaluation and comparison.