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Record W2727279498 · doi:10.1017/9781316084267.006

Linear Inversion in Fourier Space

2017· book-chapter· en· W2727279498 on OpenAlexaff
Natalia K. Nikolova

Bibliographic record

VenueCambridge University Press eBooks · 2017
Typebook-chapter
Languageen
FieldEarth and Planetary Sciences
TopicGeophysics and Gravity Measurements
Canadian institutionsMcMaster University
Fundersnot available
KeywordsFourier transformSynthetic aperture radarDiscrete-time Fourier transformFrequency domaink-spaceDiffraction tomographyInverse synthetic aperture radarIterative reconstructionMathematicsShort-time Fourier transformFourier analysisComputer scienceComputer visionMathematical analysisRadar imagingRadar

Abstract

fetched live from OpenAlex

In this chapter, methods for image reconstruction, both qualitative and quantitative, are described that solve a linearized model of scattering in Fourier space. They are referred to as spectral-domain reconstruction methods. In all of these methods, the data sets, which are originally functions of the observation position in real space (e.g., x and y ), are subjected to Fourier transformation. The reconstruction of the object's contrast function is then performed in Fourier space, e.g., with respect to k x and k y (the Fourier variables corresponding to x and y ). This necessitates a final step of an inverse Fourier transform to return the result in real space. This category of reconstruction methods includes MW holography, diffraction tomography, and a great variety of techniques used to produce imagery from synthetic aperture radar (SAR) measurements. The spectral-domain reconstruction methods are well studied. Their greatest advantage is that they are fast, allowing for image generation in real time. Their disadvantage is that, like other linear inversion methods, they are limited to problems where multiplescattering and mutual-coupling effects in the object under test (OUT) can be neglected. They are the workhorse of the real-time MW and millimeter-wave imaging systems with various applications in concealed weapon detection [62, 63, 164, 165, 166], nondestructive testing [167–173], medical-imaging research [174–179], antenna measurements [180, 181], and many other areas. The subject of reconstruction in Fourier space is extensive, and it would be impossible to present it in its entirety here. The goal here is to introduce its basic principles and to give the reader an appreciation for the mathematical beauty of the methodology and its power in real-life applications. MW holography is chosen as the method through which the reader is introduced to the subject. There are several reasons for this choice. First, modern MW holography is akin to SAR reconstruction; in fact, it was developed as an extension of SAR to 3D imaging with data acquired on planes. Thus, it can serve as a sound basis for further studies of the various SAR imaging methods. Second, when applied in a cylindrical coordinate system, MW holography can also be viewed as an extension of diffraction tomography to 3D imaging. Third, MW holography is arguably the most widely used real-time reconstruction method applied to data in the MW and millimeter-wave frequency ranges.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.001
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.020
Threshold uncertainty score0.066

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0010.001
Science and technology studies0.0000.001
Scholarly communication0.0020.002
Open science0.0010.001
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0200.013

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.034
GPT teacher head0.193
Teacher spread0.158 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designNot applicable
Domainnot available
GenreMethods

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

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Citations0
Published2017
Admission routes1
Has abstractyes

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