Does this progressive image compression exists? I want to know if this progressive image compression that I have in mind exists and it it does I want know its name and/or get some references about it.

The algorithm consists of converting one high resolution image in multiple low resolution images (all of the same size, not like in wavelet transform) with the following properties:


If you have one of them, any of them, you can reconstruct a low resolution approximation to the original image.
You can compose many of those in any order to get better approximations to the original image.
If you combine all low resolution images you get the original image or a very good approximation of it without perceptible artifacts.
Algorithm is real-time, i.e. it can display a meaningful partial reconstruction of the original image at any time of the reconstruction process (independently of received sub-images and their order).


Does this algorithm exits? Is it possible at all?

I know about image reconstruction techniques, but those use similar but different images to reconstruct a higher resolution one and the result is always noisy and full of artifacts. This is not I am asking for.
I believe that the Stationary Wavelet Transform (SWT) meets your requirements:
https://en.wikipedia.org/wiki/Stationary_wavelet_transform

1) Any given level of coefficients could be used to reconstruct the original image by running normal reconstruction but assuming zeros for the other levels.

2) Each level of coefficients stores data about a different range of spatial frequencies in the original image, and thus they can be recombined arbitrarily.

3) Unless you quantize when or after you perform the transform, the SWT is lossless.

4) I haven't done any processing time evaluation, but optimized libraries are available: https://www.mathworks.com/help/wavelet/ug/discrete-stationary-wavelet-transform-swt.html

In general though, unless you require translation invariance, you would benefit from the downsampling in the more common Discrete Wavelet Transform (DWT). The downsampling results in smaller images which requires less space to store and time to process. No information is lost by this downsampling as the frequency filters in the DWT filter out and then store (in the higher resolution levels) the frequencies that then get lost in the downsampling. The lower frequencies simply need fewer samples to be accurately reconstructed (https://en.wikipedia.org/wiki/Nyquist_frequency).