Coding and decoding of source signals using constrained relative entropy quantization
Methods and devices for encoding and decoding are provided. A source signal value is encoded by a quantization index determined using a partition into quantization cells. Decoding of the quantization index takes place by sampling a reconstruction probability distribution, thereby obtaining a reconstructed signal value, such that the reconstructed signal value lies in the same quantization cell as the source signal value. In one embodiment, encoding and decoding are such that their succession preserves the source signal distribution. In another embodiment, the partition and the reconstruction probability distribution are determined in such manner that the quantization error is minimized subject to a constraint on the relative entropy between the source signal and the reconstructed signal.
1. A method for decoding an audio or video source signal encoded as a sequence of quantization indices, each quantization index referring to a quantization cell containing a corresponding source signal value and belonging to a partition into quantization cells, the method including one of the following steps:
a) receiving an estimated probability distribution of the source signal and determining a reconstruction probability distribution based on the estimated probability distribution of the source signal by an optimization process tending to minimize a quantization error; and
b) receiving the reconstruction probability distribution obtainable by an optimization process tending to minimize a weighted sum of at least a first term and a second term, wherein the first term is a quantization error and the second term is the difference between the source signal probability distribution and the reconstruction probability distribution,
wherein the method further includes the step of
generating, for each quantization index, a reconstructed signal value by sampling the reconstruction probability distribution wherein said reconstructed signal value lies in the quantization cell indicated by the quantization index.
2. A method according to claim 1 , wherein the quantization error is measured in the mean-squared sense.
3. A method according to claim 1 , wherein said quantization cells are delimited by values b 0 , b 1 , b 2 , . . . , b M and the reconstruction probability distribution is proportional to
[θ i (x−E i ) 2 −1] −1 in the ith cell, where E i denotes a conditional expectation of the source signal in the ith cell, and b 0 , b 1 , b 2 , . . . , b M , θ 1 , θ 2 , . . . θ M are solutions of
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4. A method according to claim 1 , wherein said quantization cells are delimited by values b 0 , b 1 , b 2 , . . . , b M and the reconstruction probability distribution is proportional to [θ i (x−E i ) 2 +1] −1 in the ith cell, where E i denotes a conditional expectation of the source signal in the ith cell, and b 0 , b 1 , b 2 , . . . , b M , θ 1 , θ 2 , . . . θ M are solutions of
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5. A non-transitory computer-readable medium having stored thereon computer-readable instructions which, when executed on a general-purpose computer, perform the method of claim 1 .
6. A method according to claim 1 , wherein source signal values and quantization indices are n-dimensional vectors, n being an integer greater than 1.
7. A decoder for decoding an audio or video source signal encoded as a sequence of quantization indices, each quantization index referring to a cell containing a corresponding source signal value and belonging to a partition into quantization cells, which decoder comprises:
a first receiving section for receiving a quantization index;
a second receiving section for receiving a probability distribution, which is either:
a) an estimated probability distribution of the source signal, or
b) a reconstruction probability distribution;
optional means for determining a reconstruction probability distribution, based on the estimated probability distribution of the source signal received by the second receiving section, by minimizing a sum of at least at first term and a second term, wherein the first term is a quantization error and the second term is the difference between the source signal probability distribution and the reconstruction probability distribution; and
a random number generator for generating a reconstructed signal value by sampling the reconstruction probability distribution, said random number generator being adapted to generate the reconstructed signal value lying in the quantization cell indicated by the quantization index.
8. A decoder according to claim 7 , wherein the quantization error is measured in the mean-squared sense.
9. A decoder according to claim 7 , wherein said quantization cells are delimited by values b 0 , b 1 , b 2 , . . . , b M and the reconstruction probability distribution is proportional to [θ i (x−E i ) 2 −1] −1 in the ith cell, where E i denotes a conditional expectation of the source signal in the ith cell, and b 0 , b 1 , b 2 , . . . , b M , θ 1 , θ 2 , . . . θ M are solutions of
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10. A decoder according to claim 7 , wherein said quantization cells are delimited by values b 0 , b 1 , b 2 , . . . , b M and the reconstruction probability distribution is proportional to [θ i (x−E i ) 2 +1] −1 in the ith cell, where E i denotes a conditional expectation of the source signal in the ith cell, and b 0 , b 1 , b 2 , . . . , b M , θ 1 , θ 2 , . . . θ M are solutions of
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11. A decoder according to claim 7 , wherein source signal values, quantization indices and reconstructed signal values are n-dimensional vectors, n being an integer greater than 1.