Square Root Compression and Noise Effects in Digitally Transformed Images
We report on a particular example of noise and data representation interacting to introduce systematic error into scientific measurements. Many instruments collect integer digitized values and apply nonlinear coding, in particular square root coding, to compress the data for transfer or downlink; th...
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| Language: | English |
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IOP Publishing
2022-01-01
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| Series: | The Astrophysical Journal |
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| Online Access: | https://doi.org/10.3847/1538-4357/ac7f3d |
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| author | Craig E. DeForest Chris Lowder Daniel B. Seaton Matthew J. West |
| author_facet | Craig E. DeForest Chris Lowder Daniel B. Seaton Matthew J. West |
| author_sort | Craig E. DeForest |
| collection | DOAJ |
| description | We report on a particular example of noise and data representation interacting to introduce systematic error into scientific measurements. Many instruments collect integer digitized values and apply nonlinear coding, in particular square root coding, to compress the data for transfer or downlink; this can introduce surprising systematic errors when they are decoded for analysis. Square root coding and subsequent decoding typically introduces a variable ±1 count value-dependent systematic bias in the data after reconstitution. This is significant when large numbers of measurements (e.g., image pixels) are averaged together. Using direct modeling of the probability distribution of particular coded values in the presence of instrument noise, one may apply Bayes’ theorem to construct a decoding table that reduces this error source to a very small fraction of a digitizer step; in our example, systematic error from square root coding is reduced by a factor of 20 from 0.23 to 0.012 count rms. The method is suitable both for new experiments such as the upcoming PUNCH mission, and also for post facto application to existing data sets—even if the instrument noise properties are only loosely known. Further, the method does not depend on the specifics of the coding formula, and may be applied to other forms of nonlinear coding or representation of data values. |
| format | Article |
| id | doaj-art-07d8fd82452e4bcdae55c0016388c1d4 |
| institution | OA Journals |
| issn | 1538-4357 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal |
| spelling | doaj-art-07d8fd82452e4bcdae55c0016388c1d42025-08-20T02:19:47ZengIOP PublishingThe Astrophysical Journal1538-43572022-01-01934217910.3847/1538-4357/ac7f3dSquare Root Compression and Noise Effects in Digitally Transformed ImagesCraig E. DeForest0https://orcid.org/0000-0002-7164-2786Chris Lowder1https://orcid.org/0000-0001-8318-8229Daniel B. Seaton2https://orcid.org/0000-0002-0494-2025Matthew J. West3https://orcid.org/0000-0002-0631-2393Southwest Research Institute , 1050 Walnut Street, Suite 300 Boulder, CO 80302, USA ; deforest@boulder.swri.eduSouthwest Research Institute , 1050 Walnut Street, Suite 300 Boulder, CO 80302, USA ; deforest@boulder.swri.eduSouthwest Research Institute , 1050 Walnut Street, Suite 300 Boulder, CO 80302, USA ; deforest@boulder.swri.eduSouthwest Research Institute , 1050 Walnut Street, Suite 300 Boulder, CO 80302, USA ; deforest@boulder.swri.eduWe report on a particular example of noise and data representation interacting to introduce systematic error into scientific measurements. Many instruments collect integer digitized values and apply nonlinear coding, in particular square root coding, to compress the data for transfer or downlink; this can introduce surprising systematic errors when they are decoded for analysis. Square root coding and subsequent decoding typically introduces a variable ±1 count value-dependent systematic bias in the data after reconstitution. This is significant when large numbers of measurements (e.g., image pixels) are averaged together. Using direct modeling of the probability distribution of particular coded values in the presence of instrument noise, one may apply Bayes’ theorem to construct a decoding table that reduces this error source to a very small fraction of a digitizer step; in our example, systematic error from square root coding is reduced by a factor of 20 from 0.23 to 0.012 count rms. The method is suitable both for new experiments such as the upcoming PUNCH mission, and also for post facto application to existing data sets—even if the instrument noise properties are only loosely known. Further, the method does not depend on the specifics of the coding formula, and may be applied to other forms of nonlinear coding or representation of data values.https://doi.org/10.3847/1538-4357/ac7f3dAstronomy data reductionMeasurement error modelCoronagraphic imagingDirect imaging |
| spellingShingle | Craig E. DeForest Chris Lowder Daniel B. Seaton Matthew J. West Square Root Compression and Noise Effects in Digitally Transformed Images The Astrophysical Journal Astronomy data reduction Measurement error model Coronagraphic imaging Direct imaging |
| title | Square Root Compression and Noise Effects in Digitally Transformed Images |
| title_full | Square Root Compression and Noise Effects in Digitally Transformed Images |
| title_fullStr | Square Root Compression and Noise Effects in Digitally Transformed Images |
| title_full_unstemmed | Square Root Compression and Noise Effects in Digitally Transformed Images |
| title_short | Square Root Compression and Noise Effects in Digitally Transformed Images |
| title_sort | square root compression and noise effects in digitally transformed images |
| topic | Astronomy data reduction Measurement error model Coronagraphic imaging Direct imaging |
| url | https://doi.org/10.3847/1538-4357/ac7f3d |
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