## 1 Introduction
#### 2.2.3 Image-Based Navigation
The 2D NAV is generated by adding phase encoding gradients (G\({}_{\text{phase}}\)) to the startup echoes, using a high-low profile order. The number of startup echoes is proportional to the 2D NAV phase encoding resolution, however 10 startup echoes are commonly used which results in accurate respiratory motion estimation of the heart. Whole-heart CMRA from two healthy volunteers using either the conventional diaphragmatic 1D navigator (d1D NAV) with a tracking factor of 0.6 for motion estimation (top row) or 2D NAV (bottom row) with improved coronary vessel sharpness of the distal LAD (arrows) for the 2D NAV approach (**b**). Adapted from [65]. **3. Respiratory Gating Strategies**  
The most commonly used approach for respiratory gating is to limit image acquisition to the most quiescent respiratory phase, which usually is end expiration, and reject data acquired outside of the \"respiratory gating window\". Figure 5 shows a time series of diaphragmatic 1D navigator signals during a scan, including the respiratory gating window (blue lines) within which acquired image data is accepted. This method, called the accept-reject algorithm (ARA) [70,71], is an effective and relatively simple to implement method for reducing the respiratory motion; however, the drawback is that the scan time is inversely proportional to the size of the gating window leading to an even further extended scan time for small gating windows. The magnitude of the diaphragmatic motion is normally around 15-30 mm, however a navigator gating window of 5 mm diaphragmatic motion is often used which leads to a navigator efficiency (the number of accepted navigator positions divided by the total number of navigator acquisitions) of approximately 25%-50%, occasionally resulting in a quadrupled scan time (or more) in the event of irregular breathing or respiratory drift. An alternative to using a fixed respiratory gating window with variable and unpredictable navigator efficiency is to predefine the navigator efficiency, which leads to a variable gating window size but predictable scan time [72]. A retrospective gating method was described by [PERSON] _et al._[73]. The approach involves oversampling data with a certain factor, typically five, during free breathing. For each data point, out of the five acquired samples, the one with the least amount of respiratory motion is used for reconstruction. However, the total scan time becomes greatly increased, proportional to the oversampling factor, and the technique is sensitive to respiratory drift where possibly all five data acquisitions for a certain \(k\)-space point could be acquired with a large displacement relative to other data points. More efficient gating strategies have been proposed, typically involving some sort of ordering scheme whereby \(k\)-space data acquired in the central area of \(k\)-space is gated to a quiescent phase of the respiratory cycle, and vice-versa the outer \(k\)-space lines are acquired in a phase with more respiratory motion. As the central lines contain most of the image energy, motion during their acquisition is more likely to cause motion artifacts. Respiratory ordered phase encoding (ROPE) [74], centrally ordered phase encoding (COPE) [75] and hybrid ordered phase encoding (HOPE) [76] are three such methods which were implemented for 2D cardiac imaging. ROPE was extended to 3D and used for CMRA and shows improvements compared to the ARA [77]. The diminishing variance algorithm (DVA) is a gating technique which does not utilize a predefined gating window, but instead terminates when the acquired navigator variance reaches a certain thresh-hold [78]. First, a complete dataset is acquired allowing navigator positions throughout the whole respiratory cycle. In the following acquisitions the data which has been acquired with the largest navigator values (furthest away from end-expiration) is re-acquired, thus reducing the total variance of the navigator acquisition. This is repeated until the navigator variance reaches a predefined threshold or exceeds a time limit.