Mark A. Richards

A Beginner's Guide to Interferometric SAR Concepts and Signal Processing [AESS Tutorial IV]

Interferometric synthetic aperture radar (IFSAR, also abbreviated as InSAR) employs pairs of high resolution SAR images to generate high quality terrain elevation maps using phase interferometry methods. IFSAR provides an all-weather, day/night capability to generate measurements of terrain elevation on a dense grid of sample points with accuracies of ones of meters. Both spaceborne and airborne IFSAR systems are in use. In this paper we present a tutorial introduction to the concepts, techniques, and applications of IFSAR. After a brief introduction to digital elevation models (DEMs) and digital terrain elevation data (DTED), the fundamental IFSAR equation relating interferometric phase measurements to terrain elevation is derived from simple geometric considerations. The central section of the paper describes the major algorithmic steps required to form an IFSAR terrain map. Finally, variations of IFSAR for mapping terrain elevation or reflectivity changes are briefly described. A Web site at users.ece.gatech.edu/~mrichard/AESSJFSAR.htm provides access to color versions of many of the IFSAR images included in this paper.

Coherent integration loss due to white Gaussian phase noise

We develop a simple analytic expression for the change in coherent weighted integration gain due to a white Gaussian error or noise in the phase of the integrated samples. Our expression is shown by simulation to be very accurate for any reasonable value of phase noise standard deviation. The result is useful in estimating the performance impact on coherent signal processing systems of oscillator noise, residual motion compensation errors, and other system imperfections that are manifested primarily as phase errors.

Iterative noncoherent angular superresolution (radar)

In noncoherent scanning or imaging sensors, the angular resolution, theta , is limited by the aperture size, D, to the value theta infinity lambda /D, where lambda is the wavelength. A method is proposed for improving the effective angular resolution by three to eight times by postdetection processing of the aperture-limited signal. The technique derives from modeling the detected signal as the desired high-resolution equivalent signal degraded by convolution with the antenna pattern or point-spread function of the physical sensor. The resolution is therefore increased by deconvolving the real-aperture data. This deconvolution, or inverse filtering, approach is inherently numerically unstable. A constrained iterative deconvolution algorithm was adapted to obtain well-behaved results exhibiting true superresolution, and a fast algorithm was developed to overcome the computational burden of the iterative approach. Examples using both simulated and real millimeter-wave radar data is shown.<<ETX>>

On hardware implementation of the split-radix FFT

An algorithm for computing length-2/sup M/ discrete Fourier transforms (DFTs), called the split-radix FFT, has recently been developed. The split-radix algorithm has fewer multiplies than the radix-8 Cooley-Tukey algorithm, and many fewer additions that the minimum-multiply algorithms. It is shown that it involves significantly more butterfly computations than the radix-4 Cooley-Tukey algorithms which have butterflies of similar complexity. Consequently, the split-radix algorithm is advantageous for hardware in which a multiplier/accumulator is the basic processor, as might be the case with some VLSI implementations. In addition, the split-radix algorithm has varying numbers of butterflies in successive stages, complicating the design of efficient multiprocessor implementations. A few simple strategies for balancing the computational load among the stages are considered, and their average efficiencies are computed. >

Helium speech enhancement using the short-time Fourier transform

Speech produced in a hyperbaric helium-oxygen atmosphere suffers a variety of distortions which render it virtually unintelligible. This paper describes a new system for helium speech enhancement based on a short-time Fourier transform signal representation. The algorithm is robust, allows nonlinear warping of the spectral envelope, and includes provisions for generating the enhanced speech at a reduced sampling rate. Noise reduction by spectral subtraction can be included, and the algorithm is amenable to real-time implementation on an array processor. A review of helium speech phenomena is included to motivate the design, and a new result for the behavior of formant bandwidths is given. The results of formal intelligibility tests are reviewed, These tests show an improvement in intelligibility from about 40 to 70 percent. The tests also show that the noise reduction scheme is detrimental to intelligibility, but fail to conclusively resolve the importance of a non-linear formant frequency shift.

Application of Deczky's program for recursive filter design to the design of recursive decimators

The IEEE Press book Programs for Digital Signal Processing includes a program due to Deczky for the least-p design of recursive filters with simultaneous magnitude and group delay constraints. This correspondence outlines a method for generalizing the algorithm to enable it to design linear phase recursive decimators. An example is given.

Iterative deconvolution algorithm with quadratic convergence

Deconvolution is an important problem in many branches of physics and engineering, and many different algorithms have been considered for deconvolving two signals. Iterative algorithms based on the method of successive approximations have become popular for signal deconvolution because of the flexibility that they allow for the incorporation of signal constraints into the restoration. One of the limitations with these iterative algorithms, however, is that they achieve only a linear rate of convergence. In this paper an accelerated iterative deconvolution algorithm is presented that is based on the idea of updating the observation equation after each iteration. With this approach it is shown that the modified iterative algorithm achieves a quadratic rate of convergence. Although with this new algorithm there is a significant increase in the convergence rate, the incorporation of signal constraints into the iteration is more difficult than with the algorithms based on the method of successive approximation.

Obtaining a 35x Speedup in 2D Phase Unwrapping Using Commodity Graphics Processors

Graphics processing units (GPUs) are a powerful tool for numerical computation. The GPU architecture and computational model are uniquely designed for high-resolution high-speed grid-based calculations. This capability can be utilized to accelerate certain classes of compute-intensive radar signal processing algorithms. Characteristics of a problem well-suited for computation on a GPU include high levels of data parallelism, low control logic, uniform boundary conditions, and well-defined input and output. We describe the implementation of two-dimensional multigrid least-squares weighted phase unwrapping on a GPU and demonstrate a large speedup over C and MATLAB implementations. Details of the GPU computation are provided. Background information on the GPU architecture and its applicability to general-purpose computation is discussed.

VSIPL: an object-based open standard API for vector, signal, and image processing

VSIPL, the Vector, Signal, and Image Processing Library, is an open standard application programmers interface (API) for signal and image processing. Defined by a consortium of industry, government, and academic representatives, VSIPL is gaining widespread acceptance as a de facto standard in the embedded signal processing world. The primary goal of the API is to increase the portability of vector signal processing, matrix signal processing, and image processing applications. We present an overview of the design, features, and availability of the VSIPL API.

Fast reconstruction of linearly distorted signals

A product expansion of the inverse operator is used to derive a class of iterative algorithms that have a pth-order rate of convergence. Compared to the linear algorithm, the number of iterations required to obtain a given reconstruction is reduced from p/sup n/ to n. The primary difference between these algorithms and the linear algorithm is that they update both the estimate of x and the operator D, rather than the estimate alone. Several methods that may be used to incorporate linear and nonlinear constraints are also proposed. Finally, some examples of linear inverse problems are presented and the differences in rates of convergence for the linear and the pth-order algorithms are compared. >