Robert L. Morrison

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.

MCA: A Multichannel Approach to SAR Autofocus

We present a new noniterative approach to synthetic aperture radar (SAR) autofocus, termed the multichannel autofocus (MCA) algorithm. The key in the approach is to exploit the multichannel redundancy of the defocusing operation to create a linear subspace, where the unknown perfectly focused image resides, expressed in terms of a known basis formed from the given defocused image. A unique solution for the perfectly focused image is then directly determined through a linear algebraic formulation by invoking an additional image support condition. The MCA approach is found to be computationally efficient and robust and does not require prior assumptions about the SAR scene used in existing methods. In addition, the vector-space formulation of MCA allows sharpness metric optimization to be easily incorporated within the restoration framework as a regularization term. We present experimental results characterizing the performance of MCA in comparison with conventional autofocus methods and discuss the practical implementation of the technique.

MULTICHANNEL ESTIMATION OF COIL SENSITIVITIES IN PARALLEL MRI

We consider the problem of estimating receiver coil sensitivity functions in parallel MRI. By exploiting the multichannel nature of the problem, where multiple acquisitions of the same image function are obtained with different sensitivity weightings, we obtain a subspace-based framework for directly solving for the sensitivity functions. The proposed approach does not rely on the sum-of-squares assumption used in existing estimation schemes; this assumption tends to be violated towards the center of the image, thus leading to errors in the sensitivity estimates. Our approach eliminates this problem, producing superior sensitivity estimates in comparison to the sum-of-squares technique. In addition, the proposed restoration procedure is non-iterative, computationally efficient, and applicable both to cases where pilot scans are available or where auto-calibration data are collected with each scan. We present experimental results using actual and simulated data to assess the performance of our approach in comparison with existing methods

Multichannel Autofocus Algorithm for Synthetic Aperture Radar

The autofocus problem in synthetic aperture radar (SAR) is considered, where phase errors in the acquired signal data result in imagery that is improperly focused. We present a new non-iterative approach to SAR autofocus, termed the multichannel autofocus (MCA) algorithm, that allows the image focusing operator to be determined directly using a linear algebraic formulation. Specifically, we exploit the multichannel redundancy of the defocusing operation to create a linear subspace framework, where the unknown perfectly-focused image can be expressed in terms of a known basis expansion. By invoking an additional assumption on the underlying image support, the framework becomes sufficiently constrained so that a unique focusing filter can be solved for. The MCA approach is found to be computationally efficient and robust, and does not require prior assumptions about the characteristics of the SAR scene; the performance of previous SAR autofocus techniques relies upon the accuracy of priors such as sharpness metrics or dominant point scatterers. We present experimental results characterizing the performance of MCA in comparison with conventional autofocus methods, and discuss the practical implementation of the technique.

Avoiding local minima in entropy-based SAR autofocus

This paper explores the problem of avoiding local minima solutions in entropy-based synthetic aperture radar (SAR) autofocus. These autofocus algorithms correct defocused SAR images by determining the phase error estimate that produces the image with minimum entropy. However, the optimization strategy may converge to local minima solutions that correspond to incorrect image restorations. We propose two methods for reducing the likelihood of achieving such solutions. The first is a novel wavelet-based decomposition technique that determines the neighborhood of the global entropy minimum. A second strategy is the application of simulated annealing techniques to the optimization. We explore the performance of these methods using simulated SAR data, and provide a justification for how they work. Worst case phase errors in which the phase is random and uncorrelated between elements are considered.

Reduction of Spatial Sampling Requirement in Sound-Based Synthesis

We study the problem of synthesizing the sound field at arbitrary locations and times from the recordings of an array of audio sensors. Given prior estimates of the locations and frequencies of the sound sources, such as those obtained using adaptive source localization, we characterize the spatio-temporal support of the sound field spectrum. This characterization allows the spatial sampling requirements to be reduced in comparison to when no prior estimates of the sources are utilized. We derive an adaptive interpolation kernel, based on the estimated spectral support, to reconstruct the sound-field function using measurements from sensors on a coarse spatial-sampling grid. Simulation results demonstrate the gain achieved in reduced sampling requirements by using the proposed adaptive interpolation approach.