Encoding device, encoding method, decoding device, and decoding method

An encoding method performed by an encoding device, the encoding method comprising the steps of:

• performing a second orthogonal transform of which a calculation amount is smaller than a calculation amount of a first orthogonal transform for an image;
• performing the first orthogonal transform for a low-frequency component of the image that is acquired as a result of the second orthogonal transform;
• and
• encoding the low-frequency component after the first orthogonal transform and a high-frequency component of the image that is acquired as a result of the second orthogonal transform.

A decoding device comprising:

• a decoding unit that acquires a coefficient of a low-frequency component of an image after a first orthogonal transform that is acquired as a result of performing a second orthogonal transform of which a calculation amount is smaller than a calculation amount of the first orthogonal transform as a result of encoding the image and a result of encoding a high-frequency component of the image that is acquired as a result of performing the second orthogonal transform and decodes a result of encoding of the image;
• a prior inverse orthogonal transformation unit that performs a first inverse orthogonal transform that corresponds to the first orthogonal transform for the coefficient of the low-frequency component after the first orthogonal transform that is acquired as a result of the decoding;
• and
• a posterior inverse orthogonal transformation unit that acquires the image by performing a second inverse orthogonal transform that corresponds to the second orthogonal transform for the low-frequency component that is acquired as a result of the first inverse orthogonal transform and the high-frequency component that is acquired as a result of the decoding.

A decoding method performed by a decoding device, the decoding method comprising the steps of:

• acquiring a coefficient of a low-frequency component of an image after a first orthogonal transform that is acquired as a result of performing a second orthogonal transform of which a calculation amount is smaller than a calculation amount of the first orthogonal transform as a result of encoding the image and a result of encoding a high-frequency component of the image that is acquired as a result of performing the second orthogonal transform and decoding a result of encoding of the image;
• performing a first inverse orthogonal transform that corresponds to the first orthogonal transform for the coefficient of the low-frequency component after the first orthogonal transform that is acquired as a result of the decoding;
• and
• acquiring the image by performing a second inverse orthogonal transform that corresponds to the second orthogonal transform for the low-frequency component that is acquired as a result of the first inverse orthogonal transform and the high-frequency component that is acquired as a result of the decoding.