Method and apparatus for encoding/decoding video signal by using graph-based separable transform
The present invention provides a method for encoding a video signal on the basis of a graph-based separable transform (GBST), the method comprising the steps of: generating an incidence matrix representing a line graph; training a sample covariance matrix for rows and columns from the rows and columns of a residual signal; calculating a graph Laplacian matrix for rows and columns on the basis of the incidence matrix and the sample covariance matrix for rows and columns; and obtaining a GBST by performing eigen decomposition of the graph Laplacian matrix for rows and columns.
1. A method for encoding a video signal based on a graph-based separable transform(GBST) by an apparatus, the method comprising:
generating prediction data for a current block;
generating residual data by subtracting the prediction data from an original data of the current block;
performing a transform on the residual data to obtain transform coefficients; and
performing a quantization and an entropy encoding on the transform coefficients,
wherein a step of performing the transform on the residual data includes
generating an incidence matrix corresponding to a line graph;
training a sample covariance matrix for a row and a column from a row and a column of the residual data;
calculating a graph Laplacian matrix for a row and a column based on the incidence matrix and the sample covariance matrix for the row and the column; and
obtaining the GBST by performing an eigen decomposition to the graph Laplacian matrix for the row and the column.
2. The method of claim 1 , wherein the graph Laplacian matrix for the row and the column is defined by a link weighting parameter and a recursive loop parameter.
3. The method of claim 1 , wherein two different Gaussian Markov Random fields (GMRFs) are used for modeling of inter residual data and intra residual data.
4. The method of claim 3 , wherein, in the case of the intra residual data, a one-dimensional GMRF comprises at least one of a distortion component of a reference sample, a Gaussian noise component of a current sample, or a spatial correlation coefficient.
5. The method of claim 3 , wherein, in the case of the inter residual data, a one-dimensional GMRF comprises at least one of a distortion component of a reference sample, a Gaussian noise component of a current sample, a temporal correlation coefficient, or a spatial correlation coefficient.
6. A method for decoding a video signal based on a graph-based separable transform (GBST) by an apparatus, the method comprising:
obtaining residual data from the video signal;
performing an inverse-transform on the residual data based on the GBST; and
generating a reconstruction signal based on the residual signalresidual data and prediction data,
wherein the GBST represents a graph-based transform generated based on two separable line graphs, which are obtained by a Gaussian Markov Random Field (GMRF) modelling of a row and a column of the residual data,
wherein the two separable line graphs have been generated based on row-wise and column-wise statistical properties of residual data in each prediction mode, and
wherein the GBST has been generated by performing an eigen decomposition to a graph Laplacian matrix based on an incidence matrix and a sample covariance matrix for the row and the column.
7. An apparatus for decoding a video signal based on a graph-based separable transform (GBST), the apparatus comprising:
a processor configured to
obtain residual data from the video signal;
perform an inverse transform on the residual data based on the GBST; and
generate a reconstruction signal based on the residual data and prediction data,
wherein the GBST corresponds to a graph-based transform generated based on two separable line graphs, which are obtained by GMRF modeling of a row and a column of the residual data,
wherein the two separable line graphs have been generated based on row-wise and column-wise statistical properties of residual data in each prediction mode, and
wherein the GBST has been generated by performing an eigen decomposition to a graph Laplacian matrix based on an incidence matrix and a sample covariance matrix for the row and the column.
8. A non-transitory computer-readable medium storing video information generated by performing the steps of:
generating prediction data for a current block;
generating residual data by subtracting the prediction data from an original data of the current block;
performing a transform on the residual data to obtain transform coefficients; and
performing a quantization and an entropy encoding on the transform coefficients,
wherein a step of performing the transform on the residual data includes generating an incidence matrix corresponding to a line graph;
training a sample covariance matrix for a row and a column from a row and a column of the residual data;
calculating a graph Laplacian matrix for a row and a column based on the incidence matrix and the sample covariance matrix for the row and the column; and
obtaining a graph-based separable transform(GBST) by performing an eigen decomposition to the graph Laplacian matrix for the row and the column.