Noise-Robust Processing of Phase Dislocations using Combined Unwrapping and Sparse Inpainting with Dictionary Learning

Pineda, Jesús; Meza, Jhacson; Barrios, Erik; Romero, Lenny A.; Marrugo, Andrés G.

doi:10.1109/stsiva.2019.8730228

Cited by 1 publication

(1 citation statement)

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“…However, in practice, a system of linear equations with matching unknowns are very rare and often ends up being sparse. The sparse solution of the equations also find numerous applications, especially in image processing [25], [9], [4], [17]. The field of sparse representation elicits its structure from the conventional transforms which ensures simplicity of processing, efficiency of representation, speed etc.…”

Section: Introductionmentioning

confidence: 99%

Analytics of Unconstrained Convex Problems in Sparse and Redundant Representations: A Case Study on Image Processing Applications

Patil¹,

Kulkarni²

2019

IJCA

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The key objective of sparse and redundant representations is all about the introduction of a highly elegant data model with well-defined mathematical foundations. The structure of this model has been emerged from the conventional transforms represented in redundant unitary form. This draws out a new flavor of treatment to data. The appeal of this model is attributed to compact representation it facilitates. A lot of freedom persists in model adaptation to fit the data depending on the application.Many models are available aiming to serve the data of interest. Models can be given as mathematical descriptions or the conditions that the underlying signal of interest are believed to obey. Models that are available in image processing are Discrete Cosine Transform (DCT), Principal Component Analysis (PCA), wiener filtering, anisotropic diffusion, etc. Posing a new model requires a delicate attention to attain the simplest possible and reliable model while justifying the actual content of the data. To this Sparseland model emerges out as a new universal data model serving many applications in image processing.A class of applications in image processing demand the recovery of clean image from the naturally available perturbed images, which are treated as inverse problems. Some examples of such problems are image deblurring, image inpainting, etc. This paper discusses sparse approach to an inverse problem with image deblurring as a case study. The comparison of various shrinkage algorithms supporting sparse approach, used to serve this application is discussed along with the key constraints involved in these algorithms.

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