Method and apparatus for performing graph-based prediction using optimization function
Performing a graph-based prediction using a graph signal can be performed using a method that includes obtaining a context signal; generating a graph signal based on a graph parameter set; obtaining a graph-based transform matrix based on the graph signal, wherein the graph-based transform matrix includes an eigenvector; obtaining a prediction vector using an optimal transform vector calculated through an optimization function; and generating a prediction signal using the prediction vector, where the optimization function has the context signal, an eigenvalue of a graph Laplacian matrix and the eigenvector as a variable. Accordingly, a prediction value may be obtained with reduced complexity and the prediction performance may be improved.
1. A method for performing a graph-based prediction using a graph parameter set, comprising:
obtaining the graph parameter set corresponding a target unit of a residual signal, wherein the graph parameter set includes a vertex parameter and an edge parameter, the vertex parameter includes position information and number information of a vertex, and the edge parameter includes a weight value and number information of an edge;
obtaining a graph-based transform matrix based on the graph parameter set, wherein the graph-based transform matrix includes an eigenvector and is obtained by a spectral decomposition of a graph laplacian matrix L, wherein the graph laplacian matrix L is obtained by an equation L=D−A, where D is a degree matrix that represents a diagonal matrix including degree information of each vertex and A is an adjacency matrix that represents interconnection with an adjacent pixel by a weighting value;
obtaining a prediction vector using an optimal transform vector calculated through an optimization function, wherein the optimization function has a context signal, an eigenvalue of the graph laplacian matrix L and the eigenvector as variables, wherein the context signal means a signal reconstructed according to an encoding loop, and wherein the prediction vector is obtained based on a linear combination of the optimal transform vector and the eigenvector; and
generating a prediction signal using the prediction vector.
2. The method of claim 1 , wherein the optimization function is represented as an unconstrained optimization function based on a Lagrange multiplier, and the unconstrained optimization function is represented by a pre-determined M-dimensional vector.
3. A method for decoding a video signal based on a graph-based prediction, comprising:
receiving the video signal including a graph parameter set and a residual signal, wherein the graph parameter set includes a vertex parameter and an edge parameter, the vertex parameter includes position information and number information of a vertex, and the edge parameter includes a weight value and number information of an edge;
obtaining a graph-based transform matrix including an eigenvector based on the graph parameter set, wherein the graph-based transform matrix is obtained by a spectral decomposition of a graph laplacian matrix L, wherein the graph laplacian matrix L is obtained by an equation L=D−A, where D is a degree matrix that represents a diagonal matrix including degree information of each vertex and A is an adjacency matrix that represents interconnection with an adjacent pixel by a weighting value;
obtaining a prediction vector using an optimal transform vector calculated through an optimization function, wherein the optimization function has a context signal, an eigenvalue of the graph laplacian matrix L and the eigenvector as variables, wherein the context signal means a signal reconstructed according to a decoding loop, and wherein the prediction vector is obtained based on a linear combination of the optimal transform vector and the eigenvector;
generating a prediction signal using the prediction vector; and
reconstructing the video signal by adding up the prediction signal and the residual signal.
4. The method of claim 3 , wherein the optimization function is a convex function of the optimal transform vector, and the convex function includes a weighted P-norm of transform vector components.
5. The method of claim 4 , wherein the optimization function is represented as an unconstrained optimization function based on a Lagrange multiplier, and the unconstrained optimization function is represented by a pre-determined M-dimensional vector.
6. An apparatus for performing a graph-based prediction using a graph parameter set, comprising:
a processor configured to:
obtain the graph parameter set corresponding a target unit of a residual signal, wherein the graph parameter set includes a vertex parameter and an edge parameter, the vertex parameter includes position information and number information of a vertex, and the edge parameter includes a weight value and number information of an edge;
obtain a graph-based transform matrix based on the graph parameter set, wherein the graph-based transform matrix includes an eigenvector and is obtained by a spectral decomposition of a graph laplacian matrix L, wherein the graph laplacian matrix L is obtained by an equation L=D−A, where D is a degree matrix that represents a diagonal matrix including degree information of each vertex and A is an adjacency matrix that represents interconnection with an adjacent pixel by a weighting value;
obtain a prediction vector using an optimal transform vector calculated through an optimization function, wherein the optimization function has a context signal, an eigenvalue of the graph laplacian matrix L and the eigenvector as variables, wherein the context signal means a signal reconstructed according to an encoding loop, and wherein the prediction vector is obtained based on a linear combination of the optimal transform vector and the eigenvector; and
generate a prediction signal using the prediction vector.
7. The apparatus of claim 6 , wherein the optimization function is represented as an unconstrained optimization function based on a Lagrange multiplier, and the unconstrained optimization function is represented by a pre-determined M-dimensional vector.
8. An apparatus for decoding a video signal based on a graph-based prediction, comprising:
a processor configured to:
receive the video signal including a graph parameter set and a residual signal, wherein the graph parameter set includes a vertex parameter and an edge parameter, the vertex parameter includes position information and number information of a vertex, and the edge parameter includes a weight value and number information of an edge;
obtain a graph-based transform matrix including an eigenvector based on the graph parameter set, wherein the graph-based transform matrix is obtained by a spectral decomposition of a graph laplacian matrix L, wherein the graph laplacian matrix L is obtained by an equation L=D−A, where D is a degree matrix that represents a diagonal matrix including degree information of each vertex and A is an adjacency matrix that represents interconnection with an adjacent pixel by a weighting value;
obtain a prediction vector using an optimal transform vector calculated through an optimization function, wherein the optimization function has a context signal, an eigenvalue of the graph laplacian matrix L and the eigenvector as variables, wherein the context signal means a signal reconstructed according to a decoding loop, and wherein the prediction vector is obtained based on a linear combination of the optimal transform vector and the eigenvector;
generate a prediction signal using the prediction vector; and
reconstruct the video signal by adding up the prediction signal and the residual signal.
9. The apparatus of claim 8 , wherein the optimization function is a convex function of the optimal transform vector, and the convex function includes a weighted P-norm of transform vector components.
10. The apparatus of claim 9 , wherein the optimization function is represented as an unconstrained optimization function based on a Lagrange multiplier, and the unconstrained optimization function is represented by a pre-determined M-dimensional vector.