Denoising of sparse images in impulsive disturbance environment

Stanković, Isidora; Orović, Irena; Daković, Miloš; Stanković, Srdjan

doi:10.1007/s11042-017-4502-7

Cited by 23 publications

(13 citation statements)

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“…Signal sparsity in a transformation domain can be observed in a number of important applications. For example, ISAR images are commonly sparse in the two-dimensional Fourier transform domain, whereas digital images are well known for their good concentration in the domain of two-dimensional (2D) discrete cosine transform (DCT) [8,[21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

“…In many applications, strong disturbances (noise) can significantly corrupt the signal samples. Such signals are processed by detecting and intentionally neglecting the corrupted measurements [7,9,23]. Regardless of their unavailability reasons, under certain reasonable conditions, missing samples can be reconstructed using well developed CS methods and algorithms [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…The DCT is an important and frequently used tool in signal processing [21][22][23][24][25][26][27]. Many signal classes can be more compactly represented in the DCT domain than in the Fourier domain.…”

Section: Introductionmentioning

confidence: 99%

“…Due to its superior compressibility, the 2D-DCT is one of the most exploited transforms in the compression of digital images [24]. Moreover, this transform domain has been convenient for the reconstruction of digital images with missing pixels and/or noise corruption using the sparsity assumption [21][22][23]. Measuring the 2 Mathematical Problems in Engineering 2D-DCT coefficients concentration (using the ℓ 1 -norm based measure) and varying missing samples values to obtain the sparsest possible solution leads to the prominent compressive sensing reconstruction results [20,23].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, this transform domain has been convenient for the reconstruction of digital images with missing pixels and/or noise corruption using the sparsity assumption [21][22][23]. Measuring the 2 Mathematical Problems in Engineering 2D-DCT coefficients concentration (using the ℓ 1 -norm based measure) and varying missing samples values to obtain the sparsest possible solution leads to the prominent compressive sensing reconstruction results [20,23]. In the orthogonal matching pursuit (OMP) framework, successful reconstruction is easily obtained if the coefficients corresponding to signal component positions are successfully identified [12,[28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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Error in the Reconstruction of Nonsparse Images

Brajović

Stanković

Daković

et al. 2018

Mathematical Problems in Engineering

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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.

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Section: Introductionmentioning

confidence: 99%