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I have a bunch of georeferenced TIFF images created in QGIS. The person creating them saved them as uncompressed (around 1 GB each).
I would like to compress them as LZW to save space.

How can I do that in a programmatic way (e.g. batch)?

I am open to QGIS or R approches. Please consider I do not know how Georeferencing information are attached to an image (e.g. I have seen somewhere references to a world file, but I do not know what it is).

You can do this using the command line tool gdal_translate. This is available for Windows, Linux, and Mac OSs (you don't state your OS).

Running:

gdalinfo none.tif

will show the info on the file, including the compression type and the locations:

Driver: GTiff/GeoTIFF
Files: none.tif
Size is 204, 228
Coordinate System is:
GEOGCS["WGS 84",
 DATUM["WGS_1984",
 SPHEROID["WGS 84",6378137,298.257223563,
 AUTHORITY["EPSG","7030"]],
 AUTHORITY["EPSG","6326"]],
 PRIMEM["Greenwich",0],
 UNIT["degree",0.0174532925199433],
 AUTHORITY["EPSG","4326"]]
Origin = (96.546435160745574,17.535114346013060)
Pixel Size = (0.004491576420598,-0.004491576420598)
Metadata:
 AREA_OR_POINT=Area
Image Structure Metadata:
 INTERLEAVE=PIXEL
Corner Coordinates:
Upper Left ( 96.5464352, 17.5351143) ( 96d32'47.17"E, 17d32' 6.41"N)
Lower Left ( 96.5464352, 16.5110349) ( 96d32'47.17"E, 16d30'39.73"N)
Upper Right ( 97.4627168, 17.5351143) ( 97d27'45.78"E, 17d32' 6.41"N)
Lower Right ( 97.4627168, 16.5110349) ( 97d27'45.78"E, 16d30'39.73"N)
Center ( 97.0045760, 17.0230746) ( 97d 0'16.47"E, 17d 1'23.07"N)
[etc]

it doesn't mention a compression type, because it doesn't have one. If your GeoTIFFs aren't compressed they should also not say anything. Note the spatial information is stored in geoTIFF chunks and is output as a bounding box corner set. Great.

Let's compress it. Uncompressed file is 4.7Mb:

$ ls -hs none.tif 
4.7M none.tif

Run this:

$ gdal_translate none.tif lzw.tif -co COMPRESS=LZW
Input file size is 204, 228
0...10...20...30...40...50...60...70...80...90...100 - done.

and get

$ ls -hs lzw.tif 
1.6M lzw.tif

1.6Mbytes in LZW compressed form. Again gdalinfo shows:

$ gdalinfo lzw.tif 
Driver: GTiff/GeoTIFF
Files: lzw.tif
Size is 204, 228
Coordinate System is:
GEOGCS["WGS 84",
 DATUM["WGS_1984",
 SPHEROID["WGS 84",6378137,298.257223563,
 AUTHORITY["EPSG","7030"]],
 AUTHORITY["EPSG","6326"]],
 PRIMEM["Greenwich",0],
 UNIT["degree",0.0174532925199433],
 AUTHORITY["EPSG","4326"]]
Origin = (96.546435160745574,17.535114346013060)
Pixel Size = (0.004491576420598,-0.004491576420598)
Metadata:
 AREA_OR_POINT=Area
Image Structure Metadata:
 COMPRESSION=LZW
 INTERLEAVE=PIXEL
Corner Coordinates:
[etc]

Note the COMPRESSION=LZW message.

Loop over your files using your command line interpreter loop functions.

You might also be able to do this via the gdalUtils package in R which will run these command line commands via a shell.

Indeed for my test file:

library(gdalUtils)
gdal_translate(
 src_dataset="none.tif",
 dst_dataset="lzwR.tif",
 co="COMPRESS=LZW")

results in a byte-for-byte identical output file.

In addition to @Spacedman's answer, you can set up a loop in R to compress tiffs using LZW with the writeRaster function in the raster package, which still uses GDAL. The options argument allows you to apply LZW compression.

In this example, the file is not overwritten but rather has an "_LZW" appended to the original name. To just overwrite the original file you can omit the paste0 function in writeRaster and just use the file iterator (ie., rfiles[i]). You could also paste a directory path into the file name to aim the compressed files to a different directory. If the tif files are multi-band then you would use stack rather than raster to read the data.

library(raster)
setwd("C:/...")
rfiles <- list.files(getwd(), "tif$")
 for(i in 1:length(rfiles)) 
 r <- raster::raster(rfiles[i])
 raster::writeRaster(r, paste0(gsub(pattern = "\.tif$", "", 
 rfiles[i]), "_LZW", ".tif"), overwrite=TRUE, 
 options="COMPRESS=LZW")