Inpainting via High-dimensional Universal Shearlet Systems

Amiri, Zahra; Gol, Rajab Ali Kamyabi

doi:10.1007/s10440-018-0159-0

Cited by 3 publications

(3 citation statements)

References 20 publications

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“…In theory, recoveries are accurate when the gap size is (at most) asymptotically smaller [37,50] than the length of the shearlet elements. This can be understood geometrically by looking at Fig.…”

Section: Gap Size Vs Randomnessmentioning

confidence: 99%

Compressed sensing of impulse responses in rooms of unknown properties and contents

Zea

2019

Journal of Sound and Vibration

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Section: Gap Size Vs Randomnessmentioning

confidence: 99%

Compressed sensing of impulse responses in rooms of unknown properties and contents

Zea

2019

Journal of Sound and Vibration

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“…and the orthogonal projection associated with this missing part is Note that this models a local and axis aligned missing part, corresponding to the local model of texture ( 8) and the local and axis aligned cartoon model (14). When combining and re-orienting the local patches, we can obtain many missing stripes at various orientations.…”

Section: 2mentioning

confidence: 99%

“…Without loss of generality, we can prove only for j = j. We first note that in supp ψ αj ,(v) j,l,k we have wS 0 ≡ wS, where wS is defined in (14). We now consider the line distribution wL introduced in [25] by…”

Section: Relative Sparsity Of Texture and Cartoonmentioning

confidence: 99%

Analysis of simultaneous inpainting and geometric separation based on sparse decomposition

Do¹,

Levie²,

Kutyniok³

2020

Preprint

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Natural images are often the superposition of various parts of different geometric characteristics. For instance, an image might be a mixture of cartoon and texture structures. In addition, images are often given with missing data. In this paper we develop a method for simultaneously decomposing an image to its two underlying parts and inpainting the missing data. Our separation-inpainting method is based on an l 1 minimization approach, using two dictionaries, each sparsifying one of the image parts but not the other. We introduce a comprehensive convergence analysis of our method, in a general setting, utilizing the concepts of joint concentration, clustered sparsity, and cluster coherence. As the main application of our theory, we consider the problem of separating and inpainting an image to a cartoon and texture parts.

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Analysis of simultaneous inpainting and geometric separation based on sparse decomposition

2021

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Natural images are often the superposition of various parts of different geometric characteristics. For instance, an image might be a mixture of cartoon and texture structures. In addition, images are often given with missing data. In this paper, we develop a method for simultaneously decomposing an image to its two underlying parts and inpainting the missing data. Our separation–inpainting method is based on an [Formula: see text] minimization approach, using two dictionaries, each sparsifying one of the image parts but not the other. We introduce a comprehensive convergence analysis of our method, in a general setting, utilizing the concepts of joint concentration, clustered sparsity, and cluster coherence. As the main application of our theory, we consider the problem of separating and inpainting an image to a cartoon and texture parts.

show abstract

Inpainting via High-dimensional Universal Shearlet Systems

Cited by 3 publications

References 20 publications

Compressed sensing of impulse responses in rooms of unknown properties and contents

Compressed sensing of impulse responses in rooms of unknown properties and contents

Analysis of simultaneous inpainting and geometric separation based on sparse decomposition

Analysis of simultaneous inpainting and geometric separation based on sparse decomposition

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