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Reconstruction of Binary Functions and Shapes from Incomplete Frequency Information

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Yu Mao

Information Theory · Submitted 4 Apr 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization problem.

how it is stated · asserted 0.87 read the record →

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arXiv ID1104.0446 (version 3)
Pith IDFKGL7HSX, Pith's permanent record of this paper and its review
CitationYu Mao. "Reconstruction of Binary Functions and Shapes from Incomplete Frequency Information." arXiv:1104.0446 (2011). https://pith.science/paper/FKGL7HSX
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,207 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.05 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization problem. We further prove that if a binary function is spatially structured (e.g. a general black-white image or an indicator function of a shape), then it can be recovered from very few low frequency measurements in general. These results would lead to efficient methods of sensing, characterizing and recovering a binary signal or a shape as well as other applications like deconvolution of binary functions blurred by a low-pass filter. Numerical results are provided to demonstrate the theoretical arguments.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The characterization of a binary function by partial frequency information is considered. background 0.97 0.25 0.03 asserted 0.55
s1 We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization problem. result 0.46 0.94 0.63 asserted 0.87
s2 We further prove that if a binary function is spatially structured (e.g. a general black-white image or an indicator function of a shape), then it can be recovered from very few low frequency measurements in general. result 0.93 0.90 0.45 asserted 1.00
s3 These results would lead to efficient methods of sensing, characterizing and recovering a binary signal or a shape as well as other applications like deconvolution of binary functions blurred by a low-pass filter. interpretation 0.99 0.38 0.14 hedged possibility 0.93
s4 Numerical results are provided to demonstrate the theoretical arguments. contribution 0.39 0.91 0.03 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.94 · evidence from proof or derivation 0.97.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization problem. We further prove that if a binary function is spatially structured (e.g. a general black-white image or an indicator function of a shape), then it can be recovered from very few low frequency measurements in general. These results would lead to efficient methods of sensing, characterizing and recovering a binary signal or a shape as well as other applications like deconvolution of binary functions blurred by a low-pass filter. Numerical results are provided to demonstrate the theoretical arguments.

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