Sentence examples for matrix convolution operation from inspiring English sources

A novel post-processing strategy based on the matrix convolution operation and a priori knowledge of the shape of the particles is developed that makes it possible to accurately identify the phase interfaces in an unbiased way.

where k i is the i-th basis convolution kernel, α i denotes the i-th weight matrix, ⊗ denotes the convolution operation, ∘ denotes the pixel-wise multiplication operator, and C is the number of basis convolution kernels.

Formulated by Equation (5), coefficient matrix K is guaranteed to accomplish the convolution operation without approximation.

Filtering structure is basically similar to the Hopfield neural network structure except for the adjustable filter mask and 2D convolution operation instead of weight matrix operations.

where " " denotes convolution operation, the superscript symbol " " denotes matrix transposition, and " " denotes conjugation.

Comparing Equations (1) and (2), product of matrix K and vector F is equivalent to convolution operation A ⊗ F. This means that the convolution should be expressed as the product.

where is a sequence of matrices containing the unmixing filters, and the operator "*" denotes matrix convolution.

where is a sequence of matrices containing the impulse responses of the mixing channels, and the operator "*" denotes matrix convolution.

Then, considering the effect of convolution operation of the channels on users' signals, we can model the channel matrix for user k as mathbf{H}_{k} = left[ begin{array}{cccccc} h_{1,k} & & & & & h_{2,k} & h_{1,k} & & & & vdots & h_{2,k} & ddots & & & h_{L,k} & vdots & & ddots & & & h_{L,k} & & & h_{1,k} & & & & & h_{2,k} & h_{1,k} end{array} right]_{N times N}, (1).

The matrix of wavelet coefficients C s,p) is formed by changing the values of s and repeating the convolution operation.

where ⋆ denotes convolution operation.