Robust hermite transform based on the L-estimate principle

Hermite transform has been used In various signal processing applications due to many desirable properties. Particularly, when compared with the trigonometric functions, Hermite functions provide better computational localization in both signal and transform domains. Therefore, this transform has been applied in image compression, tomography, biomedical applications, etc. However, the performance of the Hermite transform may be degraded in the presence of impulse noise, which appears in real applications, for instance, during signal transmission. In such cases, an L-estimation approach is used to mitigate the noise effect. In this paper, the L-estimation approach is applied to the Hermite transform. The goal is to improve signal processing results in the cases of noisy signals for which Hermite transform gives suitable representation. The proposed solution is tested under pure impulse and under combination of the impulse and Gaussian noise, showing improved results in both cases.