Is there a method to extract a random sample from a population that matches the distribution of another sample?

Question

So. I have a satellite image with pixels representing a physical parameter which is expressed as radiance. Every pixel has a value. I selected a number of pixels that matched certain criteria. Therefore, the selected pixels are not a random sample from the population, but a systematic sample. Is there a method to extract a second sample from the same population, but ensure that this sample has the same probability distribution as the systematic sample? I have considered rejection sampling, but as far as I understand, it would generate a sample given a certain pdf, rather than extract a sample given the parameters from a reference sample (the systematic sample).

My other approach was to divide the systematic sample into S equal extent strata and count the number of observations in each stratum. Then, I extracted random samples from the population within each stratum specified from the systematic sample, respecting the number of samples found initially in each stratum. My hope is that as S increases, the distribution of the 'random sample' would get closer to the distribution of the systematic sample. I suppose that if I identify the percentiles from the systematic sample and get the same amount of samples in each percentile the results would be alike. Does this approach makes sense? Is there a way to prove these allegations mathematically? Is there any reference discussing this topic?

Please correct me if any terms are non-sense, I'm not very literate in statistics.