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| PHOStronics:
We are a student interested in learning how the sequence of query voltages is chosen to optimally extract information, especially in the case of a non single-valued signal. Can you explain a bit more on how these sequences are determined? |
| SJL-Instruments:
This requires some understanding of statistics. Essentially, given all the samples collected so far, you can compute the differential entropy reduction given one additional sample collected as a function of the next query voltage. This is the Fisher information. Maximizing this quantity gives the optimal choice of query voltage. This is a greedy algorithm and only locally maximizes the information gained per trigger. It generally does not give the globally optimal voltage sequence, but the FPGA/MCU does not have enough processing power to perform a global optimization in real-time. |
| PHOStronics:
Do you have books/resources you can recommend on the topic, or does the algorithm you are using have a name? We do not yet understand enough about statistics to understand how you can determine which sample locations may be optimal in reducing the error, and it seems like a very fascinating problem. I guess we would start by reading up on Fisher information, and see if we can find some relevant information there |
| SJL-Instruments:
Usually we try to give the simplest explanation possible, but in this case there isn't really one. You do need to get an intuitive understanding of Gaussian process regression and maximum-likelihood estimation. We tried many simpler algorithms as well, but all of them perform poorly on at least some subset of possible signals. The fancy stats is actually necessary in general. There isn't a name for this algorithm - we derived it specifically for this application. |
| joeqsmith:
--- Quote ---We found a simple, bias-free way to remove 90% of the speckle. Essentially, we just enforce monotonicity on each CDF. In detail, any neighboring pair of points that are in the wrong order are set to their average. This might need to be repeated a few times until the entire CDF is monotonic. --- End quote --- From what I can tell, the latest manual makes no mention of this. So, if CDF(0) > CDF(1), both CDF(0 &1) are set to the average of CDF (0&1). We then check the new value of CDF(1) with CDF(2). Once all are checked, we repeat this entire process until they are in order. Then we calculate the new PDF. For example, CDF 0, 0.1, 0.05, 0.2 Final CDF is 0, 0.075, 0.075, 0.2, PDF is then calculated from final CDF. |
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