What method can be used to recover missing values ​​in a matrix?

Question

Mathematics

There is a matrix (we can say that this matrix corresponds to the image), let's say 1000 by 1000, in which there are several values ​​​​with dimensions (5 - 10 pieces). How to fill in the remaining cells of the matrix using the measurement values.
The first thing that came to mind was to calculate a weighted sum for each missing value, i.e. the closer the measurement is to the estimated value, the greater the contribution of this measurement to the final assessment.
I am sure that there are special approaches for solving such problems.

Answer 1

If there are 5-6 values ​​out of 1.000.000, then there is a very high-quality method - it is called random.

Answer 2

If you are not mistaken, and want to restore the image 1000x1000 by 5-10 pixels, then the answer is obvious - no way.
And if you have approximately 5-10% of the data missing - and it does not matter, in the image, in the measurement, or in some other data - then there are quite a lot and different recovery methods.
Here are a few links that describe the options, some with Python code. It can be useful.
https://gallery.azure.ai/Experiment/Methods-for-ha... https://towardsdatascience.com/the-art-of-cleaning... https://towardsdatascience.com/the-tale- of-missing... https://towardsdatascience.com/working-with-missin... https://www.analyticsvidhya.com/blog/2016/01/guide...