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Not all natural signals are sparse but a wide range of natural signals can be represented sparsely in terms of a dictionary and this makes it possible to use sparsity prior on a wide range of inverse problems.
Here we have assumed each non-overlapping patch of the images can be represented sparsely in the domain of Ψ.
The proposed regularization is based on the assumption that the underlying image can be represented sparsely in TIHP tight frame.
Here we train a dictionary, Ψ, for which the original image can be represented sparsely in its domain.
Assume x ∈ ℝ N × 1, which can be represented sparsely in a known transform domain (e.g., Fourier, or wavelet).
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Thus, given a class S ⊂ R n, an important problem is to find a basis or a frame in which all signals in S can be represented sparsely.
Given these two dictionaries, each corresponding patch of low resolution image, y, and high resolution image, x, can be represented sparsely with the same coefficient vector, α in Algorithm 2. y = Ψ l α (38) x = Ψ h α (39).
In (17), the noise cannot be represented sparsely by either wavelet or hyperanalytic hearlet, and then it can be related with the residual f j - W j - S j.
In holistic representation, the candidates are represented sparsely to obtain the total reconstruction error.
S. abyssinica is represented by few large and sparsely scattered trees in the forest (Abiyu et al. 2013).
A compressible signal means that it can sparsely be represented in some basis, and can exactly be reconstructed only with a small set of random projections on an incoherent basis[8 10].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com