How to decrease file size of exported plots while keeping labels sharp

Question

When exporting rather complicated plots (especially ListDensityPlot) as a PDF or EPS (for publication, for example), the resulting file size can be quite large. For

Answer 1

If you're dealing with 2D plots, you could combine a rasterized plot with vectorized axes by using Inset. For example

plot2 = ListDensityPlot[data, 
   PlotRange -> {Automatic, Automatic, {0, 1}}, 
   InterpolationOrder -> 0, Axes -> False, Frame -> False, 
   PlotRangePadding -> 0];

plotRange = PlotRange /. AbsoluteOptions[plot2, PlotRange];

plot = Graphics[{
  Inset[Image[plot2], plotRange[[All, 1]], {Left, Bottom}, Scaled[{.96, .96}]],
  Line[{{500, 500}, {700, 700}}]}, 
 Frame -> True, AspectRatio -> 1, 
 PlotRange -> plotRange, PlotRangePadding -> Scaled[.02]]

Export["test.pdf", plot]

produces a .pdf of about 400 KB. The frame, tick marks, and black line are still vectorized, so they stay sharp when zooming in: