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Modern magnetic resonance (MR) applications require high-speed acquisitions. One of the possible ways to accelerate the process is to acquire the data along a k-space trajectory at sub-Nyquist rate and then reconstruct the image by an iterative non-linear reconstruction algorithm. The choice of k-space trajectory and its parameters has a large influence on the image quality. For physicians it is more important to optimize the reconstructed image and thus the trajectory for diagnostic tasks than creating aesthetically pleasing images. Task-specific model observers have been proposed in order to replace the time-consuming and costly human observer experiments. Very recently, we have developed a novel model observer for signal-known-statistically tasks, which can also measure several image quality factors such as noise, blur and contrast without reference images. In this paper, we discuss the image quality for several k-space trajectories in a pilot study. We find that traditionally used measures such as RMSE or PSNR do not correlate with the diagnostic image quality. Alternative measures are brought through our newly developed model observers.