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Frequency-Constrained QR: Signal and Image Reconstruction.

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Title: Frequency-Constrained QR: Signal and Image Reconstruction.
Authors: Garrett, Harrison1 (AUTHOR) hcgarret@byu.edu, Long, David G.1 (AUTHOR) long@ee.byu.edu
Source: Remote Sensing. Feb2025, Vol. 17 Issue 3, p464. 19p.
Subjects: Sampling theorem, Signal-to-noise ratio, Microwave imaging, Signal reconstruction, Image reconstruction
Abstract: Because a finite set of measurements is limited in the amount of spectral content it can represent, the reconstruction process from discrete samples is inherently band-limited. In the case of 1D sampling using ideal measurements, the maximum bandwidth of regular and irregular sampling is well known using Nyquist and Gröchenig sampling theorems and lemmas, respectively. However, determining the appropriate reconstruction bandwidth becomes difficult when considering 2D sampling geometries, samples with variable apertures, or signal to noise ratio limitations. Instead of determining the maximum bandwidth a priori, we derive an inverse method to simultaneously reconstruct a signal and determine its effective bandwidth. This inverse method is equivalent to incrementally computing a band-limited inverse using a frequency-constrained QR decomposition (FQR). Comparisons between reconstruction results using FQR and QR decompositions illustrate how FQR is less sensitive to noisy measurement errors, but it is more sensitive to high-frequency components. These methods are particularly useful in the reconstruction of remote sensing images from such as microwave radiometers and scatterometers. [ABSTRACT FROM AUTHOR]
Copyright of Remote Sensing is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Frequency-Constrained QR: Signal and Image Reconstruction.
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  Data: <searchLink fieldCode="AR" term="%22Garrett%2C+Harrison%22">Garrett, Harrison</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hcgarret@byu.edu</i><br /><searchLink fieldCode="AR" term="%22Long%2C+David+G%2E%22">Long, David G.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> long@ee.byu.edu</i>
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  Data: Because a finite set of measurements is limited in the amount of spectral content it can represent, the reconstruction process from discrete samples is inherently band-limited. In the case of 1D sampling using ideal measurements, the maximum bandwidth of regular and irregular sampling is well known using Nyquist and Gröchenig sampling theorems and lemmas, respectively. However, determining the appropriate reconstruction bandwidth becomes difficult when considering 2D sampling geometries, samples with variable apertures, or signal to noise ratio limitations. Instead of determining the maximum bandwidth a priori, we derive an inverse method to simultaneously reconstruct a signal and determine its effective bandwidth. This inverse method is equivalent to incrementally computing a band-limited inverse using a frequency-constrained QR decomposition (FQR). Comparisons between reconstruction results using FQR and QR decompositions illustrate how FQR is less sensitive to noisy measurement errors, but it is more sensitive to high-frequency components. These methods are particularly useful in the reconstruction of remote sensing images from such as microwave radiometers and scatterometers. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Remote Sensing is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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      – SubjectFull: Sampling theorem
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      – SubjectFull: Signal-to-noise ratio
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      – SubjectFull: Microwave imaging
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      – SubjectFull: Signal reconstruction
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      – SubjectFull: Image reconstruction
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              Text: Feb2025
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