Video coding method on basis of secondary transform, and device for same

An image encoding method performed by an image encoding apparatus, the method comprising:

• deriving residual samples for the target block based on the prediction samples for a target block;
• deriving transform coefficients for the target block based on a primary transform for the residual samples;
• and
• deriving modified transform coefficients based on a reduced secondary transform (RST) using a predetermined matrix kernel matrix for the transform coefficients,
• wherein the deriving the modified transform coefficients derive the modified transform coefficients in the top-left 4×4 region of the 8×8 region by applying the transform kernel matrix to the transform coefficients of the top-left 4×4 region, the top-right 4×4 region and the bottom-left 4×4 region of the 8×8 region of the target block,
• wherein the transform kernel matrix is a 16×48 matrix, and
• wherein a matrix operation between the transform kernel matrix and the transform coefficients of the top-left 4×4 region, the top-right 4×4 region and the bottom-left 4×4 region of the 8×8 region is (16×48 matrix)*(48×1 transform coefficient vector).

A non-transitory computer readable storage medium storing encoded information causing a decoding apparatus to perform an image decoding method, the method comprising:

• deriving modified transform coefficients based on an inverse reduced secondary transform (RST) using a preset transform kernel matrix for transform coefficients for a target block;
• deriving residual samples for the target block based on an inverse primary transform for the modified transform coefficients;
• and
• generating a reconstructed picture based on the residual samples for the target block,
• wherein the deriving the modified transform coefficients derive the modified transform coefficients of the top-left 4×4 region, the top-right 4×4 region and the bottom-left 4×4 region of the 8×8 region by applying the transform kernel matrix to the transform coefficients of the top-left 4×4 region of the 8×8 region of the target block,
• wherein the transform kernel matrix is a 48×16 matrix, and
• wherein a matrix operation between the transform kernel matrix and the transform coefficients of the top-left 4×4 region is (48×16 matrix)*(16×1 transform coefficient vector.