Overlapping ArrayPlot with Grid

Question

There is one 2D List of data, like {{2,3,0},{1,0,0},{0,0,1}}, which I'd like to plot in the form of the following image (drawn with Adobe Illustrator):

Which has the following properties:

1. Every small grid is colored corresponding to their number, like ArrayPlot
2. For every number above a certain threshold, say 1, will be written on their grid, as shown. I would not want every number to be written and then hidden by coloring the grid with the same color, as the data I have is both large in dimension and sparse.
3. This is essentially an overlapping of ArrayPlot and a partially shown Grid, but I couldn't figure out how to not draw every number.

So how can this be done with standard Mathematica functions?

Answer 1

a = {{2, 3, 0}, {1, 0, 0}, {0, 0, 1}}; 

ArrayPlot[Rescale[1 - a], 
 Mesh -> All,
 Epilog -> MapIndexed[If[# >= 1, Text[Style[#, Large], #2 - .5], {}] &, 
   Reverse /@ Transpose@a, {2}]]