Publication

Iterative Demosaicking Accelerated: Theory and Fast Noniterative Implementations

Martin Vetterli
2009
Conference Papers

Abstract

Color image demosaicking is a key process in the digital imaging pipeline. In this paper, we present a rigorous treatment of a classical demosaicking algorithm based on alternating projections (AP). Since its publication, the AP algorithm has been widely cited and served as a benchmark in a flurry of papers in the demosaicking literature. Despite its impressive performances, a relative weakness of the AP algorithm is its high computational complexity. In our work, we provide a rigorous analysis of the convergence of the AP algorithm based on the concept of contraction mapping. Furthermore, we propose an efficient noniterative implementation of the AP algorithm in the polyphase domain. Numerical experiments show that the proposed noniterative implementation achieves the same results obtained by the original AP algorithm at convergence, but is about an order of magnitude faster than the latter.

Official source

https://infoscience.epfl.ch/entities/publication/9698af06-404e-46a2-9866-cf0df3974c4d

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Martin Vetterli
2009
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/9698af06-404e-46a2-9866-cf0df3974c4d

About this result

Related concepts (29)

Algorithmic information theory

Algorithmic information theory (AIT) is a branch of theoretical computer science that concerns itself with the relationship between computation and information of computably generated objects (as opposed to stochastically generated), such as strings or any other data structure. In other words, it is shown within algorithmic information theory that computational incompressibility "mimics" (except for a constant that only depends on the chosen universal programming language) the relations or inequalities found in information theory.

Numerical linear algebra

Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.

Contraction mapping

In mathematics, a contraction mapping, or contraction or contractor, on a metric space (M, d) is a function f from M to itself, with the property that there is some real number such that for all x and y in M, The smallest such value of k is called the Lipschitz constant of f. Contractive maps are sometimes called Lipschitzian maps. If the above condition is instead satisfied for k ≤ 1, then the mapping is said to be a non-expansive map. More generally, the idea of a contractive mapping can be defined for maps between metric spaces.