## 4 Deconvolution
### Other Models and Applications  
Beyond the specific deconvolution methods explored above, there exists a rich tapestry of other models and applications within the realm of deconvolution. These include emerging techniques, hybrid approaches that combine multiple deconvolutional concepts, or applications in niche areas that have not been as widely explored. This section aims to provide a glimpse into these diverse aspects, highlighting their potential contributions to the broader field of deconvolution. * Wiener Deconvolution
* Blind Deconvolution  
Wiener deconvolution is a deconvolution method based on the criterion of minimum mean square error. It utilizes the statistical properties of signals (such as power spectrum) to design an optimal filter for recovering the convolved signal. Wiener deconvolution performs well at processing signals containing noise. Blind deconvolution estimates the point spread function (PSF) and the original signal through iterative algorithms when the PSF is unknown. For instance, a blind deconvolution method based on generalized Gaussian cyclostationarity (CYCBD \(\beta\)) can be used to extract bearing fault features under non-Gaussian conditions. CYCBD \(\beta\) exhibits higher robustness in the presence of strong non-Gaussian noise and can extract fault features without knowing the fault frequency [147]. When combined with spectral kurtosis, it can be applied to gear fault diagnosis. Under both constant and actual operating speeds, this method outperforms existing blind deconvolution methods, effectively enhancing fault features and improving detection accuracy [148]. To enhance adaptive performance, a method based on maximum autocorrelation kurtosis deconvolution (MACKD) has been developed for detecting abnormal noise in vehicle axles. This method identifies abnormal noise by quantifying periodic impulse components in the signal. Experiments have shown that it outperforms the MCKD and MED methods in feature extraction [149]. Similarly, an improved adaptive multipoint optimal minimum entropy deconvolution adjustment (MOMEDA) fault diagnosis method has been proposed, which improves the effectiveness of signal processing through a grid search optimization algorithm. Combining EEMD and MOMEDA techniques, it can effectively extract feature signals of complex faults in environments with high noise [150]. There is also the periodic component pursuit kurtosis deconvolution (PCPKD) method for the compound fault diagnosis of rolling bearings. It excels at signal period enhancement and multi-frequency component separation, effectively extracting intrinsic periodic components [151]. In addition, optimizations in kurtosis have significantly impacted the performance of model-based methods. The combination of the maximum L-kurtosis deconvolution (MLKD) algorithm and the frequency domain filtering (FDF) algorithm has significant advantages in suppressing outliers and noise, effectively extracting fault features for bearing fault diagnosis [152]. Furthermore, maximum average kurtosis deconvolution (MAKD) is utilized to enhance impact fault features in rotating machinery. MAKD exhibits strong robustness to typical types of interference and is not affected by speed variations or estimation deviations of fault characteristic frequencies [153]. The primary objectives of these deconvolution techniques are to extract useful information from measured signals, recover convolved signals, and estimate unknown system parameters. Each technique is based on different mathematical principles and implementation methods, such as the criterion of minimum mean square error, iterative algorithms, spectral kurtosis, and periodic component pursuit. Although all can be applied in the field of signal processing and structural health monitoring, each technique has its specific application scenarios and advantages. For example, Wiener deconvolution is suitable for processing signals containing noise; blind deconvolution is very useful when the PSF is unknown; and MACKD is particularly suitable for detecting impact faults.