Utilization of Fourier domain real zeros in the phase retrieval problem.

A problem encountered in a number of disciplines is the phase retrieval problem: given only the magnitude of the Fourier transform of some object and some constraints about the object, reconstruct the object. This is equivalent to reconstructing the phase of the Fourier transform, hence the name phase retrieval. Common object constraints are compact support, real-valued, and non-negativity. For objects with pact support, the phase retrieval problem has been successfully characterized by utilizing the zeros of the analytic extension of the Fourier transform into the complex plane. All possible solutions can be generated in theory from these zeros. In practice most phase retrieval algorithms instead utilize an iterative approach which iterates between the spatial and frequency domains, successively satisfying the constraints in both. Such algorithms are simple to implement, but have been shown empirically to suffer from stagnation problems where the program continues to iterate but does not get closer to a solution. In this thesis we show that utilizing a subset of the zeros of the Fourier transform analytic extension, referred to as real zeros since they are the intersections of these zeros with the real plane, can improve existing phase retrieval algorithms. This is possible because: (1) these real zeros locations can be estimated from the Fourier magnitude data and thus represent information that is known; and (2) these real zeros locations determine the endpoints of the so-called branch cuts in the Fourier phase (curves across which there is a 2$\pi$ ambiguity). We show that the constraints imposed on the Fourier phase by the real zeros can be utilized to recover from specific stagnation conditions that are caused by the iterative algorithms generating a reconstruction that has real zeros in erroneous locations. We also develop an algorithm for estimating the Fourier phase values using the real zero locations, and show that when this phase estimate is combined with the known Fourier magnitude data to generate an initial guess for the iterative algorithms, the final reconstruction is improved.Ph.D.Applied SciencesEngineeringMathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/129092/2/9319648.pd

AUTOMATED LOCATION OF ICE REGIONS IN RADARSAT SAR IMAGERY

A supervised classification algorithm has been developed to automatically remove regions of ice from consideration by ship detection and wind vector estimation algorithms. The output from the classifier is then put through a series of rule-based modifications to eliminate erroneous classifications that do not have the correct spatial relationships. Performance analysis on RADARSAT ScanSAR Wide imagery shows a 7% mis-classification rate with the classification algorithm, all of which are corrected by the subsequent set of spatial rules

Tropical Cyclone Winds Retrieved From Synthetic Aperture Radar

This paper describes algorithms used to retrieve high-resolution wind fields in tropical cyclone conditions from synthetic aperture radar (SAR) data acquired at C-band with either co-polarization or cross-polarization. Wind directions are estimated from the orientation of wind-induced streaks visible in SAR images using a simple tropical cyclone flow field. Wind speeds are retrieved from the normalized radar cross section taking into account imaging geometry and SAR-retrieved wind direction using a geophysical model function. The algorithms are validated by comparing outputs to a set of SAR images acquired under tropical cyclone conditions. The simulated wind fields are compared to co-located results from the QuikSCAT scatterometer as well as to wind speeds measured by the Stepped Frequency Microwave Radiometer (SFMR) during reconnaissance flights through individual storms. Comparison of QuikSCAT winds to SAR co-polarization data shows that winds can be retrieved with a root mean square error of 17.6° for wind directions and 4.6 m s–1 for wind speeds. Comparison of SAR wind speeds to SFMR data result in a root mean square error of 5.7 m s–1 for co-polarization data and 3.8 m s–1 for cross-polarization data. SAR cross-polarization data are significantly better suited for SAR wind retrieval under tropical cyclone conditions at wind speeds above approximately 20 m s–1

Tropical cyclone winds retrieved from c-band cross-polarized synthetic aperture radar

This paper presents a geophysical model function (GMF) that has been developed to describe the relation of the ocean surface wind with the normalized radar cross section (NRCS) at C-band cross polarization (cross-pol). Synthetic aperture radar (SAR) images have been simultaneously collected at copolarization (co-pol) and cross-pol at moderate to high wind speeds. Using the SAR co-pol retrieved wind fields and an uncertainty estimate of the retrieved wind speeds, the cross-pol dependencies of the NRCS are investigated with respect to wind, incidence angle, and polarization pairs. For wind speeds above 10 m/s, there is a significant dependence of the NRCS on wind speed. However, the SAR cross-pol data are also significantly affected by the noise floor and crosstalk between the channels. Estimates of the noise floor are determined and removed from the NRCS. Three GMFs are developed: the first is for transmission at horizontal (H) polarization and the second at vertical (V) polarization. A third GMF accounts for wind direction dependence. Validation of the GMFs is conducted by comparison with collocated Stepped Frequency Microwave Radiometer (SFMR) data. The resulting bias of -0.7 m/s and standard deviation of 3.7 m/s demonstrate the excellent performance for these GMFs for wind speed retrieval between 10 and 35 m/s. Furthermore, comparisons show that SAR cross-pol retrieved wind speeds are of similar quality as those of SFMR and are significantly better in the moderate to high wind speed regime than SAR co-pol retrieved winds

THE ALASKA SAR DEMONSTRATION: RADARSAT-1 EXPERIENCE AND ENVISAT PLANS

Information Service (NESDIS) ENVISAT project is focused on a pre-operational demonstration of wind and vessel position products using, predominately, the Wide-Swath Mode of the ENVISAT Advanced Synthetic Aperture Radar (ASAR). The necessary scientific algorithms, data management techniques, and product production and dissemination procedures are being prototyped using Canadian RADARSAT-1 SAR data. A near real-time demonstration of SAR product production, the Alaska SAR Demonstration (AKDEMO) has been underway since October 1999 for the waters surrounding Alaska. Wind speed, wind vector (with 180 degree ambiguity) and vessel position products are generated within about 6 hours of satellite acquisition and provided to operational agencies for evaluation and validation. Wind validation is accomplished by comparing SAR-derived winds with model output in Alaska and with buoy measurements from the NOAA moored meteorological buoys in the Atlantic off the U.S. East Coast. For validation of vessel positions, fishery observer reports are being paired with SAR-derived positions to ascertain vessel detection success. ENVISAT data will first be taken over the U.S. East Coast buoys to test and validate the wind algorithm. The vessel detection algorithm will be tailored for the ENVISAT ASAR imagery and tested as well. Once the algorithms ar