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Implement something better (such as an FFT blur operator) to eliminate this bottleneck.
where Φ 1 x) denotes the regularizer on the latent sharp image and Φ 2(K) denotes the regularizer on the blur operator.
For non-uniform blur, (boldsymbol {K} boldsymbol {x} = {sum nolimits }_{j} {{w_{j}}} {{boldsymbol {K}}_{j}}{boldsymbol {x}}phantom {dot {i}!}), where the blur operator is parameterized by the weights w j.
To speed up the blur estimation step, Gupta et al. [30] pre-computed a sparse matrix for each homography transform, and thus, the forward non-uniform blur operator can be equivalently defined as the weighted sum of the homography transform matrices, and Hu and Yang [33] further restricted the possible camera pose in a low dimensional subspace.
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Some works introduced noise or blur operators to further distort the LR image [20 22].
In this article, we just consider the spatial down-sampling and blurring operator.
where η ∈ R n is an additive noise and A ∈ R m × n is a linear blurring operator.
Then, the degraded version of u proceeds to the next stage, where it is blurred by the blurring operator, B k.
The blurring operator H (j), which is a Toeplitz matrix, satisfies the following equation: H ( j ) x ( j ) = vec K ( j ) ⊗ X ( j ), (6).
Restoring an image x is usually an ill-posed or ill-conditioned problem since either the blurring operator H does not admit inverse or is nearly singular.
In Equation (4), the motion blur kernel of j th (j=i-M,…,i+M) frame, which corresponds to the blurring operator H (j), is denoted in a vector form by k ( j ) = k 1 ( j ), k 2 ( j ), …, k L 1 L 2 ( j ) T ∈ R L 1 L 2, where L 1×L 2 is the size of the motion blur kernel.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com