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I am using ArcMap. I have 12 raster layers with coincident pixels, which have different values. I would like to, for each pixel location, pick the pixel from all 12 rasters which have the same value.

I imagine I need to use raster calculator for this, but I am really not sure where to start.

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You can create a Mosaic Dataset, import the rasters and set mosaic operator to max to get max pixel value for overlapping rasters.

A mosaic dataset allows you to store, manage, view, and query small to vast collections of raster and image data. It is a data model within the geodatabase used to manage a collection of raster datasets (images) stored as a catalog and viewed as a mosaicked image.

See What is a Mosaic dataset?

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