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Deterministic sensing matrices in compressive sensing: a survey.

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  • 1School of Electronic Engineering, Soongsil University, Seoul 156-743, Republic of Korea.

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Deterministic sensing matrices offer efficient signal compression and recovery in compressive sensing (CS). This survey highlights their structural advantages over random matrices for faster, storage-efficient CS applications.

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Area of Science:

  • Signal Processing
  • Information Theory
  • Applied Mathematics

Background:

  • Compressive sensing (CS) enables signal reconstruction from fewer measurements than traditional methods.
  • The efficiency of CS relies heavily on the properties of sensing matrices used for data acquisition.
  • Random sensing matrices are well-studied but often lack structural efficiency.

Purpose of the Study:

  • To survey deterministic sensing matrices for compressive sensing.
  • To discuss the limitations of random sensing matrices in CS.
  • To present recent advancements in constructing deterministic sensing matrices.

Main Methods:

  • Literature review of deterministic sensing matrices in CS.
  • Analysis of the structural properties and advantages of deterministic matrices.
  • Discussion of construction methods for deterministic sensing matrices.

Main Results:

  • Deterministic sensing matrices offer inherent structure for efficient implementation.
  • These matrices can reduce storage requirements and increase processing speed in CS systems.
  • Recent research focuses on novel constructions for improved deterministic sensing matrices.

Conclusions:

  • Deterministic sensing matrices are crucial for practical and efficient compressive sensing.
  • Their structured nature provides significant advantages over random matrices.
  • Further research into their construction will enhance CS performance.