| CPC H04N 19/61 (2014.11) [H04N 19/124 (2014.11); H04N 19/136 (2014.11); H04N 19/176 (2014.11); H04N 19/184 (2014.11)] | 11 Claims |

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1. An image decoding apparatus capable of decoding an image from a bitstream by using a plurality of blocks including a first block of a P×Q array of pixels, where P and Q are integers, and a second block of an N×M array of pixels, where N is an integer satisfying N<P, and M is an integer satisfying M<Q, the image decoding apparatus comprising:
a decoding unit configured to decode, from the bitstream, data corresponding to a first array of quantized transform coefficients corresponding to the first block and data corresponding to a second array of quantized transform coefficients corresponding to the second block;
an inverse quantization unit configured to derive a first array of transform coefficients representing frequency components from the first array of quantized transform coefficients by using a first quantization matrix of an N×M array of elements, and configured to derive a second array of transform coefficients representing frequency components from the second array of quantized transform coefficients by using a second quantization matrix of an N×M array of elements; and;
an inverse transform unit configured to derive a first array of prediction residuals corresponding to the first block by performing inverse transform processing on the first array of transform coefficients, and configured to derive a second array of prediction residuals corresponding to the second block by performing inverse transform processing on the second array of transform coefficients,
wherein, in a case where a target block to be decoded is the first block, the inverse transform unit is configured to derive an N×Q array of intermediate values by performing multiplication of the first array of transform coefficients, which is an N×M array, and a matrix of an M×Q array, and to derive a P×Q array of prediction residuals for the first block by performing multiplication of a matrix of a P×N array and the N×Q array of intermediate values,
wherein the first quantization matrix of an N×M array of elements includes a part of elements of a third quantization matrix of an R×S array of elements and does not include the other elements of the third quantization matrix, where R is an integer satisfying R≤N, and S is an integer satisfying S≤M,
wherein the second quantization matrix of an N×M array of elements includes all elements of a fourth quantization matrix of an R×S array of elements,
wherein the third quantization matrix is different from the fourth quantization matrix,
wherein the first quantization matrix, except for an element corresponding to a DC component, consists of the part of elements of the third quantization matrix and
wherein the second quantization matrix, except for an element corresponding to a DC component, consists of all elements of the fourth quantization matrix.
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