Image coding method on basis of secondary transform and device therefor

A encoding apparatus for image encoding, the encoding apparatus comprising:

• a memory;
• and
• at least one processor connected to the memory, the at least one processor configured to:
• derive residual samples for a target block;
• generate a non-separable secondary transform (NSST) index;
• generate transform coefficients for the target block by based on a reduced transform using the NSST index and the residual samples;
• generate information about the transform coefficients for the target block;
• and
• encode the information about the transform coefficients and the NSST index,
• wherein based on a case that the NSST index is greater than 0, the reduced transform is applied to a target region included in the target block and the transform coefficients for the target block in a range of an R+1th to Nth transform coefficients are equal to 0,
• wherein the reduced transform is performed based on a transform matrix of which size is R×N, the N is equal to a number of transform coefficients in the target region to which the reduced transform is applied, and the R is smaller than the N,
• wherein the information about the transform coefficients for the target block includes information about a location of a last non-zero transform coefficient, and
• wherein based on the case that the NSST index is greater than 0, the last non-zero transform coefficient is derived from transform coefficients other than the transform coefficients for the target block in the range of the R+1th to Nth transform coefficients.

A transmission apparatus of data for image, the transmission apparatus comprising:

• at least one processor configured to obtain bitstream generated based on:
• deriving residual samples for a target block;
• generating a non-separable secondary transform (NSST) index;
• generating transform coefficients for the target block by based on a reduced transform using the NSST index and the residual samples;
• generating information about the transform coefficients for the target block;
• and
• encoding the information about the transform coefficients and the NSST index, and
• a transmitter configured to transmit the data comprising the bitstream,
• wherein based on a case that the NSST index is greater than 0, the reduced transform is applied to a target region included in the target block and the transform coefficients for the target block in a range of an R+1th to Nth transform coefficients are equal to 0,
• wherein the reduced transform is performed based on a transform matrix of which size is R×N, the N is equal to a number of transform coefficients in the target region to which the reduced transform is applied, and the R is smaller than the N,
• wherein the information about the transform coefficients for the target block includes information about a location of a last non-zero transform coefficient, and
• wherein based on the case that the NSST index is greater than 0, the last non-zero transform coefficient is derived from transform coefficients other than the transform coefficients for the target block in the range of the R+1th to Nth transform coefficients.