Error in the Reconstruction of Nonsparse Images
Joint Authors
Stanković, Ljubiša
Daković, Miloš
Ioana, Cornel
Brajović, Miloš
Stanković, Isidora
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-02-12
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Brajović, Miloš& Stanković, Isidora& Daković, Miloš& Ioana, Cornel& Stanković, Ljubiša. 2018. Error in the Reconstruction of Nonsparse Images. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1207421
Modern Language Association (MLA)
Brajović, Miloš…[et al.]. Error in the Reconstruction of Nonsparse Images. Mathematical Problems in Engineering No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1207421
American Medical Association (AMA)
Brajović, Miloš& Stanković, Isidora& Daković, Miloš& Ioana, Cornel& Stanković, Ljubiša. Error in the Reconstruction of Nonsparse Images. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1207421
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1207421