Circular-shift transformation for image and video coding

A method comprising:

• obtaining a current block from a current input frame;
• generating a prediction block for the current block;
• obtaining a residual block by subtracting the prediction block from the current block;
• obtaining optimal circular-shift offsets by performing circular-shift optimization for the residual block, wherein circular-shift optimization includes:
• obtaining a circular-shifted residual block by circular shifting the residual block in accordance with the optimal circular-shift offsets;
• obtaining a transform block by Discrete Cosine Transforming the circular-shifted residual block;
• and
• obtaining a quantized block by quantizing the transform block;
• obtaining entropy coded data by entropy coding the quantized block;
• including the entropy coded data in an output bitstream;
• and
• outputting the output bitstream.

An apparatus, comprising:

• a non-transitory computer-readable medium;
• and
• a processor configured to execute instructions stored on the non-transitory computer-readable medium to:
• generate a reconstructed image, wherein, to generate the reconstructed image, the processor is configured to execute the instructions to:
• obtain a circular-shift indicator indicating that circular-shift transformation is enabled for a current block by decoding the circular-shift indicator from an encoded bitstream;
• obtain quantized transform coefficients for the current block, wherein, to obtain the quantized transform coefficients for the current block, the processor is configured to execute the instructions to entropy decode the quantized transform coefficients from the encoded bitstream;
• obtain circular-shift offsets for the current block, wherein, to obtain the circular-shift offsets for the current block, the processor is configured to execute the instructions to decode the circular-shift offsets from the encoded bitstream;
• obtain dequantized transform coefficients for the current block, wherein, to obtain the dequantized transform coefficients for the current block, the processor is configured to execute the instructions to dequantize the quantized transform coefficients;
• obtain reconstruction circular-shifted residual values for the current block, wherein, to obtain the reconstruction circular-shifted residual values for the current block, the processor is configured to execute the instructions to inverse transform the dequantized transform coefficients;
• obtain reconstruction residual values for the current block, wherein, to obtain the reconstruction residual values for the current block, the processor is configured to execute the instructions to inverse circular shift the reconstruction circular-shifted residual values;
• generate prediction values for the current block;
• obtain reconstructed pixels for the current block, wherein, to obtain the reconstructed pixels for the current block, the processor is configured to execute the instructions to combine the reconstruction residual values and the prediction values;
• and
• use the reconstructed pixels to form the reconstructed image;
• and output the reconstructed image.