Bandlimited Frequency-Constrained Iterative Methods
Variable aperture sampling reconstruction matrices have a history of being computationally intensive due to the need to compute a full matrix inverse. In the field of remote sensing, several spaceborne radiometers and scatterometers, which have irregular sampling and variable apertures, use iterativ...
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MDPI AG
2025-01-01
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| Series: | Remote Sensing |
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| Online Access: | https://www.mdpi.com/2072-4292/17/2/236 |
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| author | Harrison Garrett David G. Long |
| author_facet | Harrison Garrett David G. Long |
| author_sort | Harrison Garrett |
| collection | DOAJ |
| description | Variable aperture sampling reconstruction matrices have a history of being computationally intensive due to the need to compute a full matrix inverse. In the field of remote sensing, several spaceborne radiometers and scatterometers, which have irregular sampling and variable apertures, use iterative techniques to reconstruct measurements of the Earth’s surface. However, many of these iterative techniques tend to over-amplify noise features outside the reconstructable bandwidth. Because the reconstruction of discrete samples is inherently bandlimited, solving a bandlimited inverse can focus on recovering signal features and prevent the over-amplification of noise outside the signal bandwidth. To approximate a bandlimited inverse, we apply bandlimited constraints to several well-known iterative reconstruction techniques: Landweber iteration, additive reconstruction technique (ART), Richardson–Lucy iteration, and conjugate gradient descent. In the context of these iterative techniques, we derive an iterative method for inverting variable aperture samples, taking advantage of the regular and irregular content of variable apertures. We find that this iterative method for variable aperture reconstruction is equivalent to solving a bandlimited conjugate gradient descent algorithm. |
| format | Article |
| id | doaj-art-92fa1c32084c44629585805a3b6a928c |
| institution | Kabale University |
| issn | 2072-4292 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Remote Sensing |
| spelling | doaj-art-92fa1c32084c44629585805a3b6a928c2025-01-24T13:47:49ZengMDPI AGRemote Sensing2072-42922025-01-0117223610.3390/rs17020236Bandlimited Frequency-Constrained Iterative MethodsHarrison Garrett0David G. Long1Electrical and Computer Engineering Department, Brigham Young University, Provo, UT 84602, USAElectrical and Computer Engineering Department, Brigham Young University, Provo, UT 84602, USAVariable aperture sampling reconstruction matrices have a history of being computationally intensive due to the need to compute a full matrix inverse. In the field of remote sensing, several spaceborne radiometers and scatterometers, which have irregular sampling and variable apertures, use iterative techniques to reconstruct measurements of the Earth’s surface. However, many of these iterative techniques tend to over-amplify noise features outside the reconstructable bandwidth. Because the reconstruction of discrete samples is inherently bandlimited, solving a bandlimited inverse can focus on recovering signal features and prevent the over-amplification of noise outside the signal bandwidth. To approximate a bandlimited inverse, we apply bandlimited constraints to several well-known iterative reconstruction techniques: Landweber iteration, additive reconstruction technique (ART), Richardson–Lucy iteration, and conjugate gradient descent. In the context of these iterative techniques, we derive an iterative method for inverting variable aperture samples, taking advantage of the regular and irregular content of variable apertures. We find that this iterative method for variable aperture reconstruction is equivalent to solving a bandlimited conjugate gradient descent algorithm.https://www.mdpi.com/2072-4292/17/2/236iterative inversebandlimitedresolution enhancementvariable aperturesconjugate gradient descent |
| spellingShingle | Harrison Garrett David G. Long Bandlimited Frequency-Constrained Iterative Methods Remote Sensing iterative inverse bandlimited resolution enhancement variable apertures conjugate gradient descent |
| title | Bandlimited Frequency-Constrained Iterative Methods |
| title_full | Bandlimited Frequency-Constrained Iterative Methods |
| title_fullStr | Bandlimited Frequency-Constrained Iterative Methods |
| title_full_unstemmed | Bandlimited Frequency-Constrained Iterative Methods |
| title_short | Bandlimited Frequency-Constrained Iterative Methods |
| title_sort | bandlimited frequency constrained iterative methods |
| topic | iterative inverse bandlimited resolution enhancement variable apertures conjugate gradient descent |
| url | https://www.mdpi.com/2072-4292/17/2/236 |
| work_keys_str_mv | AT harrisongarrett bandlimitedfrequencyconstrainediterativemethods AT davidglong bandlimitedfrequencyconstrainediterativemethods |