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Extracting a DEM without low vegetation cover in a flooding area using LiDAR data

I've been struggling with this for the past few days. I want to create a DEM of a flood control area, which is covered in low/intermediate-height vegetation (pioneers and reed mostly). The point cloud data with x,y,z comes from airborne LiDAR and I've been able to load it into QGIS by conversion and translation and managed to create a DSM. From false-colored images, I know the locations where the vegetation is present. Is there a way to get an actual DEM of the area by removing the low/intermediate-vegetation? My aim is to obtain a DEM to analyze the flooding area, so an increase in the accuracy of the elevation data would be very useful.

I use QGIS 3.16 and the LiDAR data I received is in headerless .txt format. I've tried LAStools and converted the LiDAR .txt into .las, but the las2dem is not working somehow. As you can probably tell, I'm very much a beginner in QGIS. Any help would be greatly appreciated!