Combining Windowed Enveloping and the Delay and Sum Algorithm for Photoacoustic Image Reconstruction  
[PERSON]  
State Key Laboratory of Metastable Materials Science & Technology and Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, China; [EMAIL_ADDRESS] (M.F. ); [EMAIL_ADDRESS] (S.G.);[EMAIL_ADDRESS] (J.Z.) Y. Jing  
State Key Laboratory of Metastable Materials Science & Technology and Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, China; fangmy@stumail. However, its simplicity also results in a higher level of side lobes and more pronounced artifacts in the reconstructed images. In recent years, a great deal of research has been conducted to address these issues, leading to the development of several improved algorithms. These enhancements have shown promising results in reducing side lobes and artifacts, contributing to the ongoing evolution of PAI techniques. For instance, [PERSON] and colleagues proposed the Delay Multiply and Sum (DMAS) algorithm, which improves the reconstructed image in terms of contrast and resolution [16; 17]. [PERSON] and colleagues introduced a coherence factor (CF), which integrates the coherence factor (CF) and modified coherence factor (MCF) into the traditional DAS beamforming technique, known as DAS-CF [18; 19; 20]. This combined approach is applied in PAI to mitigate the impact of unwanted off-axis signals on beamforming. Subsequently, the team proposed an improved version of the DMAS algorithm, known as the double-stage DMAS algorithm, which enhances image resolution and side-lobe levels [21; 22]. Compared to the DMAS algorithm, the side-lobe level is reduced by approximately 10 dB. Several other optimization algorithms, which are derived from the DMAS method, have also contributed to improving the quality of the reconstructed images to some extent [23; 24]. There are also some other methods that have made significant contributions to improving the quality of the reconstructed images [25]. Although the aforementioned algorithms have improved the imaging quality, their effectiveness in suppressing the aliasing issue between adjacent microstructures remains limited. However, these methods, like the DAS method, analyze the photoacoustic signal as a single-valued signal. In reality, the acoustic pressure signal is a short pulse lasting for a certain period, composed of both positive and negative amplitudes, forming an N-shaped signal. The duration of this N-shaped signal is related to the size of the source [26]. For a particular pixel within the imaging area, the complete PA signal for that point over the entire imaging time can be obtained through multiple DAS calculations. This signal should also be an N-shaped signal. Furthermore, the N-shaped signals acquired from different pixel points exhibit variations in amplitude and in the timing of their peak values. Thus, the real source points in the imaging region and the pixels with artifacts can be distinguished. [PERSON] and colleagues proposed the Multiple Delay and Sum with Enveloping (multi-DASE) algorithm, which aims to suppress side lobes and artifacts [27]. This method not only computes the initial acoustic pressure signal but also computes the complete signal for each point. The complete signal is then enveloped. By comparing the differences between the envelope signals, the method distinguishes between signal sources and artifacts. This method has shown strong performance in suppressing artifacts. However, when imaging a slightly larger signal source, the interior of the signal source is also suppressed, leading to a reconstructed image that exhibits missing internal structures, thereby causing significant distortion in the final reconstructed result. Furthermore, the larger the volume of the source, the more pronounced this phenomenon becomes. By analyzing this problem, we find that the original N-shaped signal contains abrupt changes.