Getting points with lowest value and exact location for each cell?

I have an assignment to create a simplified depth scheme. The calculation has to be done for a large area automatically.

There are depth points every 0.5 meters (marked black in the picture). By using “point to raster” function I can generate a raster layer with defined size cells (e.g. 4x4 m) and also request to calculate lowest (shallowest) values for each cell.

Then I can create points layer from the raster generated before, which results is a layer of depth every 4 m (points in red) with lowest values. However the points are generated in the center of the cell. They do not represent the actual place within the cell with lowest value (yellow points).

How can I get the points with lowest value and exact location for each cell?

• If you don't mind me asking, what is the application of this? I don't see why the 4m raster matters when you already have the values in the points. Do you really need to average across all potential configurations of 81 point neighborhoods? – jbchurchill Sep 16 '16 at 13:15
• I have raw data with points every 0.5 meters. Earlier it was enough to show just minimum depth's values in grid of 4x4 meters. But now our client also wants to see a map with exact places of minimum depths. – Viaceslav Jurkin Sep 19 '16 at 8:04