David C. Munson

A tomographic formulation of spotlight-mode synthetic aperture radar

Spotlight-mode synthetic aperture radar (spotlight-mode SAR) synthesizes high-resolution terrain maps using data gathered from multiple observation angles. This paper shows that spotlight-mode SAR can be interpreted as a tomographic reeonstrution problem and analyzed using the projection-slice theorem from computer-aided tomograpy (CAT). The signal recorded at each SAR transmission point is modeled as a portion of the Fourier transform of a central projection of the imaged ground area. Reconstruction of a SAR image may then be accomplished using algorithms from CAT. This model permits a simple understanding of SAR imaging, not based on Doppler shifts. Resolution, sampling rates, waveform curvature, the Doppler effect, and other issues are also discussed within the context of this interpretation of SAR.

A generalization of median filtering using linear combinations of order statistics

We consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence. Assuming a constant signal in white noise, the coefficients in the linear combination are chosen to minimize the output MSE for several noise distributions. It is shown that the optimal order statistic filter (OSF) tends toward the median filter as the noise becomes more impulsive. The optimal OSF is applied to an actual noisy image and is shown to perform well, combining properties of both the averaging and median filters. A more general design scheme for applications involving nonconstant signals is also given.

The Effect of Median Filtering on Edge Estimation and Detection

In this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images. Where possible, a quantitative statistical comparison is made for a number of filters defined with two-dimensional geometries; in some cases one-dimensional analyses are required to illustrate certain points. Noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis, and it is found that median prefiltering improves the performance of both thresholding and zero-crossing based edge detectors.

A signal processing view of strip-mapping synthetic aperture radar

The authors derive the fundamental strip-mapping SAR (synthetic aperture radar) imaging equations from first principles. They show that the resolution mechanism relies on the geometry of the imaging situation rather than on the Doppler effect. Both the airborne and spaceborne cases are considered. Range processing is discussed by presenting an analysis of pulse compression and formulating a mathematical model of he radar return signal. This formulation is used to obtain the airborne SAR model. The authors study the resolution mechanism and derive the signal processing relations needed to produce a high-resolution image. They introduce spotlight-mode SAR and briefly indicate how polar-format spotlight processing can be used in strip-mapping SAR. They discuss a number of current and future research directions in SAR imaging. >

Generation of a random sequence having a jointly specified marginal distribution and autocovariance

We consider the problem of generating a random sequence with a specified marginal distribution and autocovariance. The proposed scheme for generating such a sequence consists of a white Gaussian noise source input to a linear digital filter followed by a zero-memory nonlinearity (ZMNL). The ZMNL is chosen so that the desired distribution is exactly realized and the digital filter is designed so that the desired autocovariance is closely approximated. Both analytic results and examples are included. The proposed scheme should prove useful in simulations involving non-Gaussian processes.

Image reconstruction from frequency-offset Fourier data

Motivated by the ability of synthetic-aperture radar and related imaging systems to produce images of surprisingly high quality, we consider the problem of reconstructing the magnitude of a complex signal f from samples of the Fourier transform of f located in a small region offset from the origin. It is shown that high-quality speckle reconstructions are possible so long as the phase of f is highly random. In this case, the quality of the reconstruction is insensitive to the location of the known Fourier data, and edges at all orientations are reproduced equally well. A large number of computer examples are presented demonstrating these attributes. Methods for improving image quality are also briefly discussed.

Optimal and suboptimal error spectrum shaping for cascade-form digital filters

Error spectrum shaping (ESS) can significantly reduce finite-wordlength error in recursive fixed-point digital filters. Most past work on ESS has focused on second-order filters. In this paper, expressions for the ESS coefficients minimizing the roundoff error are derived for high-order filters composed of cascaded second-order sections. A comparison of the noise gains is made between optimal and suboptimal ESS structures and the section-optimal structure; the ESS structures perform well in comparison. A heuristic section-ordering strategy, based on ideas underlying ESS, is proposed and deemed useful, particularly for elliptic filters.

Noise reduction strategies for digital filters: Error spectrum shaping versus the optimal linear state-space formulation

The noise reduction performance of error spectrum shaping (ESS) structures and of the optimal linear state-space (LSS) structure are compared for second-order digital filter sections. It is shown that optimal direct form 1 and direct form 2 ESS realizations have a higher signal-to-noise ratio than the optimal LSS structure. In practice, suboptimal ESS structures with simple hardware implementations are of greater interest. Several of these implementations are considered and optimal values for the ESS coefficients in these structures are derived. For filters with zeros at z = -1, it is shown that some of the simple ESS structures can outperform the optimal LSS structure. For elliptic filters, it is shown that several of the suboptimal ESS structures perform poorly, but that others still perform well.

SAR Image Autofocus By Sharpness Optimization: A Theoretical Study

Synthetic aperture radar (SAR) autofocus techniques that optimize sharpness metrics can produce excellent restorations in comparison with conventional autofocus approaches. To help formalize the understanding of metric-based SAR autofocus methods, and to gain more insight into their performance, we present a theoretical analysis of these techniques using simple image models. Specifically, we consider the intensity-squared metric, and a dominant point-targets image model, and derive expressions for the resulting objective function. We examine the conditions under which the perfectly focused image models correspond to stationary points of the objective function. A key contribution is that we demonstrate formally, for the specific case of intensity-squared minimization autofocus, the mechanism by which metric-based methods utilize the multichannel defocusing model of SAR autofocus to enforce the stationary point property for multiple image columns. Furthermore, our analysis shows that the objective function has a special separble property through which it can be well approximated locally by a sum of 1-D functions of each phase error component. This allows fast performance through solving a sequence of 1-D optimization problems for each phase component simultaneously. Simulation results using the proposed models and actual SAR imagery confirm that the analysis extends well to realistic situations.

Narrow-band recursive filters with error spectrum shaping

Earrrs due to Finite wordlength can be quite large in narrowband recursive digital filters. It has been shown that these errors may be considerably reduced by using a technique known as error spectrum shaping (ESS), which utilizes quantizer feedback. In this letter we first derive closed-formn bounds on the amplitude of zero-input limit cycles in ESS filters. An expression is then derived for the mean squared roundoff error (MSE) in a inultiplierless ROM/ACC type implementation, including the effects of scaling and finite wordlength ROM.