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Article Dans Une Revue Mathematical Problems in Engineering Année : 2018

Error in the Reconstruction of Nonsparse Images

Miloš Daković
Cornel Ioana
Ljubiša Stanković

Résumé

Sparse signals, assuming a small number of nonzero coefficients in a transformation domain, can be reconstructed from a reduced set of measurements. In practical applications, signals are only approximately sparse. Images are a representative example of such approximately sparse signals in the two-dimensional (2D) discrete cosine transform (DCT) domain. Although a significant amount of image energy is well concentrated in a small number of transform coefficients, other nonzero coefficients appearing in the 2D-DCT domain make the images be only approximately sparse or nonsparse. In the compressive sensing theory, strict sparsity should be assumed. It means that the reconstruction algorithms will not be able to recover small valued coefficients (above the assumed sparsity) of nonsparse signals. In the literature, this kind of reconstruction error is described by appropriate error bound relations. In this paper, an exact relation for the expected reconstruction error is derived and presented in the form of a theorem. In addition to the theoretical proof, the presented theory is validated through numerical simulations.

Dates et versions

hal-01970006 , version 1 (04-01-2019)

Identifiants

Citer

Miloš Brajović, Isidora Stankovic, Miloš Daković, Cornel Ioana, Ljubiša Stanković. Error in the Reconstruction of Nonsparse Images. Mathematical Problems in Engineering, 2018, 2018, pp.ID 4314527. ⟨10.1155/2018/4314527⟩. ⟨hal-01970006⟩
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