Image coding method on basis of transformation and device therefor

An 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;
• perform a transform based on the residual samples, wherein the transform is performed based on a transform matrix;
• derive transform coefficients for the target block based on a result of the transform;
• derive quantized transform coefficients by performing quantization based on the transform coefficients for the target block;
• generate information on the quantized transform coefficients;
• and
• encode the information on the quantized transform coefficients to output a bitstream,
• wherein based on a number of output elements of the transform being R, a size of the transform matrix is R×N, where each of N and R is a positive integer, and R is less than N.

An apparatus for transmitting data for an image, the apparatus comprising:

• at least one processor configured to obtain a bitstream for the image, wherein the bitstream is generated based on deriving residual samples for a target block, performing a transform based on the residual samples, wherein the transform is performed based on a transform matrix, deriving transform coefficients for the target block based on a result of the transform, deriving quantized transform coefficients by performing quantization based on the transform coefficients for the target block, generating information on the quantized transform coefficients, and encoding the information on the quantized transform coefficients;
• and
• a transmitter configured to transmit the data comprising the bitstream,
• wherein based on a number of output elements of the transform being R, a size of the transform matrix is R×N, where each of N and R is a positive integer, and R is less than N.