Anomalies, such as jumps and glitches, frequently occur in the time-series data from astronomical observatories. These anomalies, arising from instrument errors and various other factors, must be accurately identified and addressed during data processing. Traditional anomaly detection methods often use Fourier transforms, which are effective for smooth, continuous signals but struggle with jagged, anomaly-laden data. Wavelet transforms offer a potential alternative by using wavelets that are localized in both time and frequency, which provides more detailed information about localized features. To explore the effectiveness of this alternative, this project developed an anomaly detection algorithm based on wavelet transforms and evaluated its effectiveness.

In this project, the Mallet-Zhong discrete wavelet transform and Lipschitz regularity were used to develop an algorithm capable of identifying anomalies in time-series data and providing insights into their type and duration. The algorithm is also flexible, relying on two parameters: the anomaly threshold and the alpha threshold, which can be tuned to detect various sizes and types of anomalies. Additionally, the accuracy of the algorithm was extensively evaluated, revealing optimal threshold values that minimize and alpha threshold values that minimizes both false positives and false negatives, while successfully detecting anomalies as small as 8 times the white noise level.

This project’s findings have demonstrated that wavelet transforms offer a promising alternative to Fourier transforms for anomaly detection. However, future work is needed to evaluate the viability, accuracy, and speed of wavelet-based algorithms and compare their performance with that of existing Fourier-based methods.