Synthetic radar image recognition and classification are areas of interest for both the military and civilian communities. These tasks have significance in automatic target recognition, air traffic control, and remote sensing. Equivalent problems of recognition and classification are also of interest for the ultrasonic and sonar imaging communities, for which numerous algorithms such as neural networks, wavelets, fuzzy logic, mean-square error-matching templates, and feature base classifications have been used.

The architecture of a photorefractive two-beam coupling joint Fourier processor.

Although the processors involved in these techniques are claimed to be real time, they require an extensive amount of time for calculations, making it very difficult to track targets with them in real time. Moreover, these techniques require a digital workstation for data processing in real time. Furthermore, synthetic aperture radar (SAR) image information is blurred by the radar ambiguity function, which relates the uncertainty between the target range and its range rate. Unfortunately, accuracy in the measurement of one of these quantities usually comes at the expense of the other.

Although the role of the ambiguity function in image blurring is similar to that of the point-spread function in optical imaging, its effect is much more severe. The above facts make it hard to recognize SAR images compared to optical images, which have resolution within a few micrometers. SAR images are dominated by a few strong scattering centers. These scattering centers play the role as fingerprint identification of SAR images.

Dynamic Range Compression

Dynamic Range Compression/Expansion, known as companding (compressing-expanding), is a well-established principle for recovering signals embedded in high noise. Dynamic Range Compression/Expansion nonlinearity, when it is applied to a noisy signal, improves the signal-to-noise (SNR) ratio in areas where the signal is low compared to the noise, and reduces the SNR in areas where the signal is higher than the noise level. This principle has been used for improving the quality of acoustic signals in the 50s and is extensively used for noise reduction in tape recording, which is limited by “tape hiss,” or high-frequency random noise. Noise reduction systems like “Dolby” and “dbx” help to solve this problem by pre-emphasizing (compression) the high frequencies before recording onto tape in order to make them higher in amplitude than the tape hiss noise with which they compete, and then upon playback, a matched de-emphasis filter (expansion) is employed.

In Fourier processing, applying dynamic range compression: (1) enhances the SNR where the SNR is low; (2) increases the noise frequency, which leads to spreading the noise over a larger area in the other domain – this consequently has a significant affect on SNR enhancement in the image plane; and (3) enhances the high frequencies relative to the low frequencies. This is an essential functionality for the recovery of high-frequency intensity in blurred signals, or for enhancing the high frequencies relative to low frequencies for increasing the discrimination capability of pattern recognition. These three advantages of applying dynamic range compression on noisy signals in spectral domain lead to significant improvement of processed data relative to noise.

Two-Beam Coupling-Joint Fourier Processor

In the architecture of a photorefractive two-beam coupling-joint Fourier processor, a signal beam passes through the SLM, which is addressed by a joint image of signal and reference information (see figure). The joint image then is Fourier transformed via a lens to pump a spectrally variant reference beam. The reference beam is shaped through a beam profiler. A beam profiler is a spatial light modulator (SLM) addressed either by an expected spectrum of the joint spectrum or adaptively addressed by the joint spectra envelope through direct measurement. The beam profiler is essential for reducing the extremely high beam ratio constraint required to achieve dynamic range compression. The deflected output from the crystal is Fourier transformed to produce the joint spectra processed image.

There are three techniques for enhancing the scattering centers of a SAR image: (1) applying a pure dynamic range compression on the image’s Fourier spectrum, (2) raising the image to a certain power, and (3) applying both the dynamic range compression and the power-law enhancement simultaneously. The high frequencies are significantly enhanced compared to the low frequencies. It is clear that there is significant enhancement of high frequencies relative to the low frequencies as the power increases. Further enhancement in high frequencies can be achieved by applying the dynamic range compression. The beam ratios for dynamic range compression have been reduced as the power increased.

The enhancement in the images’ scattering centers was more prominent when dynamic range compression was implemented. The combination of power-law enhancement and dynamic range compression did not lead to significant enhancement in the scattering center compared to implementing dynamic range compression. Although the combination of power-law and dynamic range compression did not lead to any significant advantage over just implementing dynamic range compression for enhancement of the scattering centers, the combination is more effective in removing the clutter surrounding the target.

The 128×128 SAR images were set within 256×256 zeros arrays. The images were raised to a certain power and then Fourier transformed. The Fourier transform data was terminated via a 128x128 window, and the two-beam coupling dynamic range compression was applied on the spectrum. Applying power-law enhancement showed not only an enhancement in the scattering center, but also improved the signal-to-clutter. Implementation of dynamic range compression with low-pass filtering alone without power-law enhancement produced some enhancement in the target’s scattering centers and signal-to-clutter ratio. The enhancement of the scattering centers due to solely dynamic range compression implementation was always better than that due solely to power-law enhancement, while the signal-to-clutter ratio was the opposite.

However, when the power-law and the dynamic range compression enhancements were applied simultaneously, both of the scattering centers and the signal-to-clutter ratio improves as the power-law enhancement increases. The results show what could effectively happen to the input impulse response on clutter reduction and scattering centers enhancement for both of the matching template and the input target if the nonlinear processor is replaced by a linear processor: 1) Enhances the signal to noise ratio where the signal is lower than the noise, (2) Increases the noise frequencies, which consequently leads for spreading the noise over a larger area in the spatial domain, and (3) Enhances the intensity of the high frequencies compared to the low frequencies.

These three effects demonstrate that dynamic range compression in the Fourier domain significantly improves the signal-to-noise ratio and is more effective than conventional dynamic range compression. Applying power-law scattering center enhancement has two effects: it enhances the target’s high frequencies relative to its lower frequencies, and it increases the clutter’s frequencies so that it spreads over a large area in the spatial domain. Although power-law enhancement of the scattering center is an expansion process that leads to a signal-to-noise reduction, it is not applied to SAR images since the clutter is disjoint of the target.

The advantages of using this procedure (i.e. the power-law enhancement) are that it: (a) enhances the signal-to-clutter Fourier spectrum energy, which facilitates the preconditions for further enhancement in the signal-to-noise ratio through applying dynamic range compression on the Fourier spectrum, and (b) converts the clutter to very high spatial frequencies, the major part of which can be blocked or filtered out with little loss in the scattering centers spectrum.

This article was written by Bahareh Hajisaeed and John Kierstead of Solid State Scientific Corp., Hollis, NH; and Jed Khoury and Charles L. Woods of the Optoelectronic Technology Branch at Hanscom Air Force Base, MA. For more information, visit

RF & Microwave Technology Magazine

This article first appeared in the August, 2009 issue of RF & Microwave Technology Magazine.

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