# Coregistration and Spatial Compounding of
## 1 Introduction  
Cardiovascular imaging is essential for phenotyping the structure and function of the mammalian heart and vascular system. Preclinical studies generally rely on mice to model arrhythmias, myocardial infarction and other conditions [1; 2; 3]. However, imaging the mouse heart is challenged by the small size of internal structures and the very fast beating rate (400-600 beats per minute) [4]. Gating is used in high-resolution magnetic resonance imaging (MRI) and x-ray computed tomography (CT) to overcome the big difference between the beating frequency and the temporal resolution of these modalities [5; 6]. This is achieved by either triggering the acquisition of data after detection of a physiological event (prospective gating) or by continuous acquisition and subsequent data correlation with the cardiac cycle (retrospective gating). Self-gated cardiac imaging methods are particularly valuable for small rodents as they do not require additional electrocardiogram (ECG) readings, but they generally lead to long acquisition times [7]. On the other hand, real-time imaging modalities have been used for visualizing the heart dynamics. Pulse-echo ultrasound (US) is widely used for in vivo cardiovascular imaging in rodents [4; 8] and intravital microscopy has facilitated single cell tracking in cardiac tissues [9].  
Recently, volumetric optoacoustic (OA) tomography (OAT) has been suggested as a particularly suitable modality for imaging the murine heart in vivo [10]. OAT provides high-contrast images of optical absorption within biological tissues with a single laser pulse [11; 12; 13], thus avoiding the need of image compounding. High frame rates in the order of 100 Hz have then been achieved for four-dimensional (real-time three-dimensional) imaging of the heart [14]. This has facilitated the visualization of transient events, such as arrhythmias [15] or the perfusion of a contrast agent [16]. By measuring the time of arrival of a bolus of indocyanine green (ICG) in the right and left ventricles, respectively, it was possible to estimate the pulmonary transit time (PTT), defined as the time it takes for blood to travel though the pulmonary circulation. It was shown that this physiological parameter changes in mice subjected to myocardial infarction [16; 17] or chronic hypoxic stress [15], thus defining new capabilities in cardiovascular research. Fully exploiting the cardiac imaging capacities of volumetric OAT may however require acquisition of independent image sequences. For example, the effective field of view (FOV) scales with the achievable resolution and generally needs to be enhanced to cover the entire heart and surrounding regions, which can be done e.g., by stitching the images acquired by scanning the spherical array used for collecting OA signals [18]. Also, estimation of the bio-distribution of spectrally-distinctive substances such as oxygenated and deoxygenated hemoglobin requires acquisition of images corresponding to several excitation wavelengths. Synchronization of sequential acquisitions of cardiac images is challenged by the fast murine heart rate, and alternative methods must be developed for cardiac gating.  
Herein, we investigate on the capabilities of Fourier analysis of four dimensional data as a self-gated cardiac imaging approach for co-registration of independent volumetric OA image sequences of the heart. We investigate on the feasibility of stitching heart images acquired at different scanning positions and multi-spectral un-mixing of cardiac data based on this methodology. We discuss on the potential implications in cardiovascular research and other fields.