How does Google’s Page Speed lossless image compression work?

If you’re really interested in the technical details, check out the source code:

• png_optimizer.cc
• jpeg_optimizer.cc
• webp_optimizer.cc

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For PNG files, they use OptiPNG with some trial-and-error approach

// we use these four combinations because different images seem to benefit from
// different parameters and this combination of 4 seems to work best for a large
// set of PNGs from the web.
const PngCompressParams kPngCompressionParams[] = {
  PngCompressParams(PNG_ALL_FILTERS, Z_DEFAULT_STRATEGY),
  PngCompressParams(PNG_ALL_FILTERS, Z_FILTERED),
  PngCompressParams(PNG_FILTER_NONE, Z_DEFAULT_STRATEGY),
  PngCompressParams(PNG_FILTER_NONE, Z_FILTERED)
};

When all four combinations are applied, the smallest result is kept. Simple as that.

(N.B.: The optipng command line tool does that too if you provide -o 2 through -o 7)

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For JPEG files, they use jpeglib with the following options:

 JpegCompressionOptions()
     : progressive(false), retain_color_profile(false),
       retain_exif_data(false), lossy(false) {}

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Similarly, WEBP is compressed using libwebp with these options:

  WebpConfiguration()
      : lossless(true), quality(100), method(3), target_size(0),
        alpha_compression(0), alpha_filtering(1), alpha_quality(100) {}

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There is also image_converter.cc which is used to losslessly convert to the smallest format.