TES pulse signal data processing method based on PCA-gradient descent joint algorithm

[Background] The Transition-Edge Sensor (TES) offers high energy resolution, a broad spectral response range, and high collection efficiency, making it an ideal tool for X-ray spectroscopy. The Shanghai High repetitioN rate XFEL and Extreme light facility (SHINE) plans to employ a hundred-pixel TESs-based spectrometer for high-precision measurements. The conventional signal processing method for TESs, the Optimal Filtering method, is able to realize the intrinsic high energy resolution of the device, however, its application faces limitations such as the requirement for pulse templates adaptable to a dynamic operating range and separate noise data collection, which increases system complexity and resource consumption. [Purpose] This study aims to develop a signal processing method for TES-based devices that can obtain high energy resolution results, and is optimized for processing efficiency and resource usage in multi-pixel applications. [Methods] The proposed method was designed to combine Principal Component Analysis (PCA) and gradient descent analysis. The processing was applied directly to the digitized TES pulse waveforms acquired in X-ray measurement experiments. Firstly, waveforms of all pulses were aligned in time with cross-correlation time delay estimation. Then PCA was used to autonomously extract the primary shape features of the aligned signal pulses. Subsequently, gradient descent was employed on these PCA-derived features to get projections from the pulse data along an optimal vector. Lastly, the energy represented by each pulse was calibrated based on the known energy points and the spectrum could be obtained in histogram. [Results] Tests on a dataset showed that the energy resolution achieved by our PCA-gradient descent joint algorithm was comparable to that of the traditional OF method. Furthermore, our method demonstrated greater robustness to noise variations. [Conclusions] The developed method provides an efficient and adaptive alternative for TES signal processing. It exhibits strong potential for application in the high-precision spectroscopy measurements planned with the TES array at SHINE, offering a streamlined workflow without compromising performance.