Wavelet processing applied to the estimation of continuously distributed objects

Teresa L. P. Dixon

doi:10.1117/12.217572

1 September 1995 Wavelet processing applied to the estimation of continuously distributed objects

Teresa L. P. Dixon

Proceedings Volume 2569, Wavelet Applications in Signal and Image Processing III; (1995) https://doi.org/10.1117/12.217572
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

This paper uses a wavelet transform approach to actively image an object continuously distributed in range and velocity. It is shown that by transmitting a high resolution, i.e. large time-bandwidth product, signal into the environment and operating on the echo with a wavelet transform, an estimate of the delay-time-scale representation or wideband spreading function of the object can be obtained in the wavelet domain. The wideband spreading function (WBSF) is a characterization of the time-varying propagation and scattering associated with the channel being imaged. It is shown that the linear operator that acts on the wideband spreading function to form the echo is in the form of an inverse wavelet transform and the adjoint operator is in the form of a forward wavelet transform. Thus, the wavelet transform is a natural transform for the investigation of wideband spreading functions. By combining information extracted from wavelet estimates of the WBSF associated with independently located sensors, it is possible to estimate vectors which describes the physical characteristics of the object in the channel. Specifically, the support curve of the WBSF in the wavelet domain can be directly related to the projections of these vectors along the line of sight of each of the sensors. Therefore, it is necessary to obtain a wavelet estimate of the WBSF which highly resolves the support curve. The wavelet transform estimate is shown to be limited by the resolution capabilities of the auto-wavelet transform of the transmitted signal therefore establishing the need for high resolution transmit signals. Results of wavelet transform estimates of the WBSF of a rough, rotating sphere using wideband and narrowband signals are compared and discussed.

Citation Download Citation

Teresa L. P. Dixon "Wavelet processing applied to the estimation of continuously distributed objects", Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, (1 September 1995); https://doi.org/10.1117/12.217572

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KEYWORDS

Wavelets

Wavelet transforms

Optical spheres

Signal processing

Signal attenuation

Scattering

Sensors

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