Image decoding apparatus, image decoding method, and storage medium

An image decoding method capable of decoding an image from a bitstream using a plurality of blocks including a first block of a P×Q (P and Q are integers) array of pixels and a second block of an N×M (N is an integer satisfying N<P, and M is an integer satisfying M<Q) array of pixels, the image decoding method comprising:

• decoding data corresponding to a first array of quantized transform coefficients and data corresponding to a second array of quantized transform coefficients from the bitstream, the first array of quantized transform coefficients corresponding to the first block, the second array of quantized transform coefficients corresponding to the second block;
• deriving a first array of transform coefficients from the first array of quantized transform coefficients by using a first quantization matrix of an N×M array of elements, and deriving a second array of transform coefficients from the second array of quantized transform coefficients by using a second quantization matrix of an N×M array of elements, wherein the first array of transform coefficients represents frequency components, and wherein the second array of transform coefficients represents frequency components;
• deriving a first array of prediction residuals corresponding to the first block by performing inverse transform processing on the first array of transform coefficients, and deriving a second array of prediction residuals corresponding to the second block by performing inverse transform processing on the second array of transform coefficients;
• and
• reconstructing at least picture data based on the second array of prediction residuals and predicted image data, the predicted image data being capable of being derived by using inter prediction,
• wherein the first quantization matrix of the N×M array of elements is a quantization matrix including a part of elements of a third quantization matrix of an R×S array (R is an integer satisfying R≤N, and S is an integer satisfying S≤M) of elements, and not including the other elements of the third quantization matrix,
• wherein the second quantization matrix of the N×M array of elements is a quantization matrix including all elements of a fourth quantization matrix of the R×S array of elements, and
• wherein the third quantization matrix is different from the fourth quantization matrix.

An image encoding apparatus capable of encoding an image using a plurality of blocks including a first block of a P×Q (P and Q are integers) array of pixels and a second block of an N×M (N is an integer satisfying N<P, and M is an integer satisfying M<Q) array of pixels, the image encoding apparatus comprising:

• a transform unit configured to derive a first array of transform coefficients by performing transform processing on a first array of prediction residuals corresponding to the first block, and derive a second array of transform coefficients by performing transform processing on a second array of prediction residuals corresponding to the second block, at least the second array of prediction residuals being capable of being derived by using inter prediction;
• a quantization unit configured to derive a first array of quantized transform coefficients by quantizing the first array of transform coefficients using a first quantization matrix of an N×M array of elements, and derive a second array of quantized transform coefficients by quantizing the second array of transform coefficients using a second quantization matrix of an N×M array of elements;
• and
• an encoding unit configured to encode data corresponding to the first array of quantized transform coefficients corresponding to the first block and data corresponding to the second array of quantized transform coefficients corresponding to the second block,
• wherein the first quantization matrix of the N×M array of elements is a quantization matrix including a part of elements of a third quantization matrix of an R×S array (R is an integer satisfying R≤N, and S is an integer satisfying S≤M) of elements, and not including the other elements of the third quantization matrix,
• wherein the second quantization matrix of the N×M array of elements is a quantization matrix including all elements of a fourth quantization matrix of the R×S array of elements, and
• wherein the third quantization matrix is different from the fourth quantization matrix.

An image encoding method capable of encoding an image using a plurality of blocks including a first block of a P×Q (P and Q are integers) array of pixels and a second block of an N×M (N is an integer satisfying N<P, and M is an integer satisfying M<Q) array of pixels, the image encoding method comprising:

• deriving a first array of transform coefficients by performing transform processing on a first array of prediction residuals corresponding to the first block, and deriving a second array of transform coefficients by performing transform processing on a second array of prediction residuals corresponding to the second block, at least the second array of prediction residuals being capable of being derived by using inter prediction;
• deriving a first array of quantized transform coefficients by quantizing the first array of transform coefficients using a first quantization matrix of an N×M array of elements, and deriving a second array of quantized transform coefficients by quantizing the second array of transform coefficients using a second quantization matrix of an N×M array of elements;
• and
• encoding data corresponding to the first array of quantized transform coefficients corresponding to the first block and data corresponding to the second array of quantized transform coefficients corresponding to the second block,
• wherein the first quantization matrix of the N×M array of elements is a quantization matrix including a part of elements of a third quantization matrix of an R×S array (R is an integer satisfying R≤N, and S is an integer satisfying S≤M) of elements, and not including the other elements of the third quantization matrix,
• wherein the second quantization matrix of the N×M array of elements is a quantization matrix including all elements of a fourth quantization matrix of the R×S array of elements, and
• wherein the third quantization matrix is different from the fourth quantization matrix.