Blurring reduces noise/entropy so that JPEG compresses better. You can use a bilateral filter (Photoshop: Surface Blur; GIMP: Selective Gaussian Blur) for larger amount of smoothing while preserving edges.
Image Posterization
This is actually called image quantization. pngquant[1] and pngnq[2] are two specialized open-source tools for automatically selecting the best palettes to represent the image with least perceptual error.
Selective JPEG Compression
JPEGmini[3] automatically selects areas of interest with custom perceptual metrics and preserves quality within those areas while optimizing out other areas. I tested the sample image in the article: JPEGmini obtained 6.7% decrease in size without manually selecting the mask.
[1]: http://pngquant.org/
[2]: http://pngnq.sourceforge.net/
[3]: http://www.jpegmini.com/main/shrink_photo https://news.ycombinator.com/item?id=2940505
JPEGmini seems to go partway with selective compression, but it seems like there's room to improve the actual compression algorithm to do things like gaussian smoothing instead of just truncating the high-frequency components to reduce filesize.
But JPEG is a pretty crude algorithm designed mainly to be computationally cheap [to match the capabilities of computer hardware in 1992 when it was created]. Trying to make better encoders within the limits of what JPEG decoders can handle is quite limiting, and yields only marginal improvements.
It’s possible to do much better if we’re willing to accept more CPU time spent in encoding/decoding using fancier algorithms. Unfortunately it’s really hard to get traction for anything else, because the whole world already has JPEG decoders built into everything. For instance JPEG 2000, designed to be a general purpose replacement with many improvements over JPEG, is now 13 years old but used only in niche applications, such as archiving very high resolution images.
But for use cases where you control the full stack, better compression is quite viable. Video game engines for instance devote considerable attention to image compression formats.
This is what JPEGmini is doing, perceptual compression metric.
gaussian smoothing instead of just truncating the high-frequency components
Gaussian smoothing does remove high-frequency components.
demo: http://o-0.me/RgbQuant/
For PNG, always run your images through ImageOptim (http://imageoptim.com) before committing your work.
And for large PNGs, ImageAlpha (http://pngmini.com) lets you reduce bit depth, keep transparency and maintain a decent image quality.
Why only PNG?
The files worked fine elsewhere, so I think it was an decoder bug not an invalid file, but I had to avoid optimizing JPEG files to avoid the problem.
This was about two years ago, so I don't recall version numbers or phone models.
The article should be called "Image Compression Tricks". I don't think any of the techniques are considered advanced in today's technology.
It's possible to pick posterization levels more fitting the image:
http://pngmini.com/lossypng.html#posterization (https://github.com/pornel/mediancut-posterizer)
I again wish there was an Imagemagick/Graphicsmagick script to do this.