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

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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 radial super-resolution of CFA-image of reflectors, various methods are used: maximum entropy method, Bernoulli—Gauss 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 radial super-resolution of CFA images. The performance of the proposed method is confirmed by model experiments.

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About the authors

Evgeny G. Bazulin

ECHO+ Research and Production Center LLC

Author for correspondence.
Email: bazulin@echoplus.ru
Russian Federation, 8, Tvardovsky St., Moscow, 123458

A. A. Krylovich

Moscow Power Engineering Institute

Email: bazulin@echoplus.ru
Russian Federation, 14, Krasnokazarmennaya St., Moscow, 111250

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Supplementary files

Supplementary Files
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2. Fig. 1. Obtaining radial super-resolution by extrapolating the echo spectrum using the AR model.

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3. Fig. 2. Initial echoes (a) and their cepstr (b).

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4. Fig. 3.

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5. Fig. 4. Ideal impulse response s (t) (red graph), impulse response estimate s^ (t) (black graph) - (a); modulus of spectrum s (t) (red graph), modulus of s^ (t) (black graph) - (b); modulus of original echoes (blue graph), extrapolation result using s (t) (red graph) and extrapolation result using s^ (t) (black graph) - (c).

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6. Fig. 5. Impulse responses (a), modulus (b) and phase (c) of their spectra obtained during antenna array acceptance (plots in red) and after cepstral analysis (plots in black).

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7. Fig. 6. Result of echo processing after AR spectrum model construction when inverse filtering is performed using the measured impulse response (red graphs) and the one obtained after cepstral analysis (black graphs).

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8. Fig. 7. Echoes of 33 shots after building an AR model of the spectrum while performing inverse filtering using the measured impulse response (a) and the one obtained after cepstral analysis (b).

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9. Fig. 8. CFA images of two transverse-wave BCOs reconstructed from the measured echoes (a), from the echoes after building an AR model of the spectrum while performing inverse filtering using the measured impulse response (b) and obtained after cepstral analysis (c).

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10. Fig. 9. Impulse response (a) and spectrum modulus (b) obtained during antenna array acceptance (red coloured lines) and after cepstral analysis (black coloured lines).

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11. Fig. 10. CFA images of the transverse wave crack model reconstructed from the measured echoes (a), from the echoes after building an AR spectrum model by performing inverse filtering using the measured impulse response (b) and obtained after cepstral analysis (c).

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12. Fig. 11. CFA-CF images of the crack model, similar to those in Fig. 10b and c, reconstructed on the transverse wave.

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13. Fig. 12. CFA images of the longitudinal wave crack model reconstructed from the measured echoes (a), from the echoes after building the AR spectrum model by inverse filtering using the measured impulse response (b) and obtained after cepstral analysis (c).

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14. Fig. 13. CFA-CF images of the crack model, similar to those in Fig. 12b and c, reconstructed on the longitudinal wave.

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