Decomposition of residual data during signal encoding, decoding and reconstruction in a tiered hierarchy

1. A method comprising:

via computer processing hardware:

receiving an image signal at a first level of quality;

producing a rendition of the image signal at a second level of quality, the second level of quality being of lower resolution than the first level of quality;

producing residual data, said residual data corresponding to a difference between the image signal at the first level of quality and a predicted rendition of the signal at the first level of quality as constructed using the rendition of the image signal at the second level of quality;

transforming the residual data to generate transformed residual components; and

processing the transformed residual components to generate encoded data for transmission to a target device,

wherein the transforming is applied to groupings of M×N blocks of residuals,

wherein the transforming comprises:

generating vectors of length M*N from the groupings of M×N blocks of residuals; and

applying a (M*N)×(M*N) matrix multiplication to the vectors of length M*N, wherein M=2 and N=2 and a 4×4 matrix used in the matrix multiplication comprises:

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2. The method as in claim 1 , wherein transforming the residual data comprises performing a directional decomposition transform to generate transformed residual components.

3. The method as in claim 1 , wherein producing residual data comprises:

simulating a set of decoding operations upon data derived from the rendition of the image signal at the second level of quality; and

upsampling the output of the simulating to generate the predicted rendition of the signal at the first level of quality.

4. The method as in claim 1 , comprising:

producing multiple sets of residual data, each set of residual data representing a difference between two renditions of the image signal, one of the two renditions being a reconstructed signal, each set of residual data being generated at a different level of quality;

transforming each set of residual data to generate multiple sets of transformed residual components corresponding to the multiple sets of residual data; and

processing the multiple sets of transformed residual components to generate encoded data for transmission to a target device.

5. The method as in claim 1 , wherein processing the transformed residual components to generate encoded data for transmission to a target device comprises quantizing the transformed residual components.

6. The method as in claim 1 , comprising:

predicting a value for a transformed residual component at the first level of quality using a corresponding value of a predicted rendition of the image signal at the second level of quality;

determining a difference between the predicted value and an actual value of the transformed residual component computed using a predicted rendition of the image signal at the first level of quality; and

using the difference in place of the actual value for the transformed residual component to generate encoded data for transmission to a target device.

7. A method comprising:

via computer processing hardware:

receiving encoded data associated with a rendition of an image signal at a second level of quality;

receiving encoded data associated with a set of transformed residual components;

performing an inverse transform to generate residual data from the set of transformed residual components;

producing a preliminary rendition of the image signal at a first level of quality based on the encoded data associated with the rendition of the image signal at the second level of quality, the first level of quality being of a higher resolution than the second level of quality; and

producing a secondary rendition of the image signal at the first level of quality based on the residual data and the preliminary rendition of the image signal at the first level of quality,

wherein the inverse transform is applied to generate M×N blocks of residuals,

wherein performing the inverse transform comprises:

decoding a vector of length L representing a set of transformed residual components, wherein L=M*N; and

applying a L×L matrix multiplication to the vectors of length L to generate the residual data,

wherein M=2 and N=2 and a 4×4 matrix used in the matrix multiplication comprises an inverse of the following:

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8. The method as in claim 7 , wherein performing the inverse transform comprises performing an inverse directional decomposition to generate transformed residual components.

9. The method as in claim 7 , comprising:

receiving encoded data associated with multiple sets of transformed residual components, each set of transformed residual components being associated with a different level of quality;

performing the inverse transform on each set of transformed residual components to generate residual data for each level of quality; and

reconstructing an initial image signal at an initial level of quality using the residual data for multiple levels of quality.

10. The method as in claim 7 , comprising:

dequantizing the set of transformed residual components.

11. The method as in claim 7 , comprising:

determining a predicted value for a transformed residual component at the first level of quality using a corresponding value of a predicted rendition of the image signal at the second level of quality;

decoding a difference between the predicted value and an actual value of the transformed residual component computed using a predicted rendition of the image signal at the first level of quality; and

using the difference and the predicted value to reconstruct the actual value of the transformed residual component.

12. An encoder for an image signal comprising:

a downsampler to receive an image signal at a first level of quality and to produce a rendition of the image signal at a second level of quality, the second level of quality being of lower resolution than the first level of quality;

a residual calculator to produce residual data, said residual data corresponding to a difference between the image signal at the first level of quality and a predicted rendition of the image signal at the first level of quality as constructed using the rendition of the image signal at the second level of quality; and

a transformer to generate transformed residual components from the residual data,

wherein the encoder is configured to process the transformed residual components to generate encoded data for transmission to a target device,

wherein the transforming is applied to groupings of M×N blocks of residuals,

wherein the transforming comprises:

generating vectors of length M*N from the groupings of M×N blocks of residuals; and

applying a (M*N)×(M*N) matrix multiplication to the vectors of length M*N, wherein M=2 and N=2 and a 4×4 matrix used in the matrix multiplication comprises:

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13. The encoder of claim 12 , further comprising:

a quantizer to quantize a rendition of the image signal at a second level of quality; and

an upsampler to upsample data derived from the quantizer to generate the predicted rendition of the signal at the first level of quality.

14. A decoder comprising:

an inverse directional decomposer to receive encoded data associated with a set of transformed residual components and to perform an inverse directional decomposition to generate residual data from the set of transformed residual components,

wherein the decoder is configured to receive encoded data associated with a rendition of an image signal at a second level of quality and to produce a secondary rendition of the image signal at the first level of quality, the first level of quality being of a higher resolution than the second level of quality, the secondary rendition of the image signal being produced based on the residual data and a preliminary rendition of the signal at the first level of quality, the preliminary rendition of the signal at the first level of quality being produced from the received encoded data associated with the rendition of the image signal at the second level of quality,

wherein the inverse directional decomposition is applied to generate M×N blocks of residuals,

wherein performing the inverse directional decomposition comprises:

decoding a vector of length L representing a set of transformed residual components, wherein L=M*N; and

applying a L×L matrix multiplication to the vectors of length L to generate the residual data,

wherein M=2 and N=2 and a 4×4 matrix used in the matrix multiplication comprises an inverse of the following:

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15. The decoder of claim 14 , comprising:

a dequantizer to dequantize the set of transformed residual components prior to production of the secondary rendition of the image signal at the first level of quality.