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

A decoding method, comprising:

• receiving an encoded bit stream that includes coded data and a plurality of tap coefficients;
• decoding the coded data based on a first filter image, to generate a decoded image;
• and
• executing filter processing on the decoded image for generating a second filter image, wherein the filter processing includes:
• applying a prediction equation including at least one of a second-order term or a higher-order term, wherein
• the second-order term includes a product of two prediction taps of a plurality of prediction taps,
• an order of the higher-order term is higher than an order of the second-order term, and
• the plurality of prediction taps corresponds to a plurality of pixels of the decoded image, and
• executing product-sum calculation of the plurality of tap coefficients and the plurality of prediction taps.

An encoding device, comprising:

• circuitry configured to:
• acquire a locally decoded image;
• execute filter processing on the locally decoded image to generate a filter image, wherein the filter processing includes:
• application of a prediction equation including at least one of a second-order term or a higher-order term, wherein
• the second-order term includes a product of two prediction taps of a plurality of prediction taps,
• an order of the higher-order term is higher than an order of the second-order term, and
• the plurality of prediction taps corresponds to a plurality of pixels of the locally decoded image, and
• product-sum calculation of a plurality of tap coefficients and the plurality of prediction taps;
• and
• encode an original image based on the filter image to obtain coded data.

An encoding method, comprising:

• obtaining a locally decoded image;
• executing filter processing on the locally decoded image for generating a filter image, wherein the filter processing includes:
• applying a prediction equation including at least one of a second-order term or a higher-order term, wherein
• the second-order term includes a product of two prediction taps of a plurality of prediction taps,
• an order of the higher-order term is higher than an order of the second-order term, and
• the plurality of prediction taps corresponds to a plurality of pixels of the locally decoded image, and
• executing product-sum calculation of a plurality of tap coefficients and the plurality of prediction taps;
• and
• encoding an original image based on by using the filter image.