Cepstral Analysis of Ultrasonic Echoes Measured by an Antenna Array in Order to Obtain Super-Resolution Images of Reflectors

Abstract

The digital focusing aperture (DFA) method is widely used to image reflectors during ultrasonic inspection. The reliability of inspection is determined by the quality of the DFA image—resolution and signal-to-noise ratio. To achieve super-resolution of echo signals, which will lead to lateral super-resolution of reflectors, various methods are used: maximum entropy method, Bernoulli–Gaussian deconvolution, Lucy–Richardson deconvolution, methods of recognition with compression (CS), methods of construction of autoregressive models of signals, etc. To apply these methods, we need to know the impulse response of the ultrasonic inspection system. It can be measured, but you can use methods of  “blind” deconvolution, which are used in image and signal processing. For example: the method of eliminating camera blur at its random displacement, maximum correlated kurtosis deconvolution (MCKD), cepstral analysis, etc. In this paper, a cepstral analysis method for super-resolution or for obtaining information about the impulse response of the system is considered to construct an AR spectrum model to obtain the lateral super-resolution of DFA-images. The performance of the proposed method is confirmed by model experiments.