If you do something really simple like a Gaussian blur (which is a type of convolution), it might be possible to find the inverse convolution (de-convolution) and restore the original image with some accuracy.
One method is the Lucy-Richardson deconvolution [1], which is an iterative algorithm, and here [2] is the best practical example I could find right away. Unfortunately the text is not in English, but the illustrations and formulae might be enough to give some intuition of the process.
Yes this is possible before JPEG compression, because convolution removes fairly little information but once you compress using JPEG you remove the frequency components that make it reversible.
One method is the Lucy-Richardson deconvolution [1], which is an iterative algorithm, and here [2] is the best practical example I could find right away. Unfortunately the text is not in English, but the illustrations and formulae might be enough to give some intuition of the process.
[1] https://en.wikipedia.org/wiki/Richardson%E2%80%93Lucy_deconv...
[2] https://habr.com/en/post/136853/