## 1 Introduction
Notwithstanding these technical developments, the relatively long breath-hold durations of approximately 20-25 s may be difficult to achieve in patients with CAD which is why free-breathing motion compensated CMRA approaches are typically favoured. A generic CMRA sequence is shown in Figure 2, where the segmented k-space data acquisition is synchronized with the ECG to minimize cardiac motion related artifacts [25]. Various magnetization preparation pulses such as T2 prep [26] and fat suppression [27] are used to improve visualization of the coronary lumen, and respiratory motion compensation is employed to suppress respiratory motion artifacts. There are essentially three separate processes for respiratory motion compensation which can be used separately or in concert in CMRA to reduce respiratory motion artifacts: (i) motion estimation, (ii) gating and (iii) correction. The focus of this review is to describe these motion compensation  
Figure 2: Schematics of ECG-triggered CMRA sequence. One k-space data segment is acquired (ACQ) following a time delay (trigger delay) after the R-wave to minimize cardiac motion artifacts. Typically the trigger delay is adjusted to coincide with the mid-diastolic rest period and the center of k-space. Preparation pulses (PP) can be used to improve visualization of the coronary arteries by suppressing signal from surrounding tissues, including epicardial fat and myocardium. Respiratory motion compensation (RMC), including motion estimation, gating and correction, is typically performed prior to ACQ, although gating and correction may be also being performed retrospectively. processes. However, it is worth noting that there are alternative methods to minimize motion artifacts in MRI, for example by signal averaging or using motion insensitive _k_-space trajectories such as radial [28,29] or spiral [30] sampling. **2. Respiratory Motion Estimation**  
Most respiratory compensation strategies rely on some sort of motion estimation information as input to the gating or correction algorithms. There are a number of ways in which motion estimation can be achieved, from external monitoring devices to MRI based techniques, so called respiratory navigators. _2.1. External Devices_  
The most commonly used external respiratory monitoring device in cardiovascular MRI is the respiratory bellows [31,32], which measures pressure differences between the abdomen and a tightly wrapped belt to establish whether the respiratory cycle is in inspiration or expiration. Other techniques to perform respiratory motion estimation with external devices include measuring the electric impedance between ECG leads [33] or the more recently developed ultra wideband electromagnetic sensor [34]. The advantage of utilizing external devices for respiratory motion estimation is that the motion information may be obtained with a very high temporal resolution due to the low dimensionality of the measurements. Therefore, external devices can be useful in conjunction with simple respiratory gating such as the accept/reject algorithm which will be described in the following section. An additional advantage of external devices is that they are independent of the MRI acquisition and can be acquired in parallel with the CMRA, which is particularly important for steady-state MRI sequences. Nevertheless, for high-resolution imaging such as CMRA, external devices alone may be insufficient to adequately compensate for the respiratory motion. This is because they typically only provide relative information about respiration, which can be used to determine the respiratory phase (inspiration or expiration) but not any absolute motion information, such as displacement, rotation, _etc_. Therefore, its usefulness for the purpose of respiratory motion correction is very limited. _2.2. Respiratory Navigators_  
Respiratory navigators are integrated into the MRI pulse sequence and can be used to monitor the respiratory displacement and deformation of the heart and surrounding tissues and organs.