Averaging is a popular way to increase the SNR, especially in high resolution MRI. While it is well known that k-space weighted averaging has the potential to further improve SNR and image quality, it requires sophisticated sequence modifications [1]. Here, we show that a part of the advantages of acquisition weighting can also be realized by retrospective k-space filtering of an image acquired with increased spatial resolution.

The contamination caused by the sinc-shape of the spatial response function (SRF) of most imaging sequences not only causes ringing artifacts, but also decreases the SNR due to the predominantly negative signal contributions from distant regions inside the sample. The SRF can be improved by retrospective filtering the k-space data with a Hanning function, but this causes an additional SNR loss which outweighs the SRF gain. Increasing the width of the weighting function beyond the covered k-space (Fig. 1a) reduces the effect of the filter, but even more the associated SNR loss. A simulation of both effects for an experiment with weighting in two dimension shows an optimum for widths around 1.5 (Fig. 1b).

In contrast to acquisition weighting, retrospective filtering can also be applied in the read direction. If the enlarged acquired k-space region is used to prolong the duration of the readouts, an SNR gain up to 28% is possible for low filter width, while for equal readout duration, the maximum gain is around 11% for a filter with of 1.5 again (Fig. 2).

Phantom images were acquired on a 3T Siemens Prisma, using a standard gradient echo sequence. Four repetitions of a high resolution dataset were acquired. Images were reconstructed with several filter widths and compared to unweighted images with the same voxel size. Equal spatial resolutions of weighted and unweighted images were ensured by reducing the k-space region covered in the unweighted experiment until the widths of the SRFs were equal in both experiments. SNR values were obtained and corrected for the differences in scan time.

Additional experiments were performed on a 14.1 T scanner on an isolated mouse brain and on a 9.4 T human scanner on the brain of a human subject.

Figure 1b and 2 compare the measured SNR for varying values of the width of the weighting function, where Fig. 1b displays results for weighting in two phase encode dimensions and Fig. 2 shows the results for weighting in read direction only, where the bandwidth remains equal and the addtional k-space points are sampled by increasing the readout duration. Experimental results agree perfectly with theoretical predictions. Fig. 3 shows a resolution phantom filtered in all three dimension, with and without changing the readout bandwidth to reach equal readout durations. Although weighted and unweighted images have equal spatial resolution and SNRs are corrected for scan time differences, the filtered image has an increased mean SNR by 57% and 38% for equal bandwidth and equal duration, respectively. Figure 4 shows an isolated mouse brain, k-space filtered in three dimensions, showing a time-corrected SNR increase by 40%. The human brain data in Fig. 5 was acquired with an acquisition-weighted gradient echo sequence and thus only can be retrospectively fitered in the read direction. An SNR gain of 30% was still possible by keeping equal bandwidth in weighted and unweighted experiments.An SNR gain up to 57% is possible by retrospective k-space weighting without any loss in spatial resolution by favorably shaping the SRF. Compared to acquisition-weighted imaging, retrospective weighting can not recover all of the possible SNR, but has the advantage of being applicable with most imaging techniques without requiring a specialized pulse sequence. In addition, it can also be applied on the read direction, even on non-averaged images, and allows for fine-adjustment of the spatial resolution after acquisition.