Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In quantization theory, one typically works with a unique distortion function (e.g. the squared-error distortion function) that quantifies the cost of quantizing a given source sample to any given reproduction point of the quantizer. Many applications, hover, induce quantization problems where different distortion functions should be associated with different reproduction points. ,  consider the case where the distortion of a given reproduction point is the squared distance to the source sample ighted by a factor that varies from one reproduction point to another. For a uniform distribution of source samples,  determine the corresponding optimal scalar quantizers and their distortions.  also find upper and lor bounds on the distortion of optimal vector quantizers. For non-uniform distributions,  provide a high resolution analysis of the minimum possible distortion. As a byproduct of our analysis,  show that for certain distributions of ights, a tessellation of non-congruent quantization cells can outperform tessellations of congruent polytopes. This suggests that Gersho's conjecture cannot be extended to the case of squared-error distortion functions with ighted reproduction points.
['Erdem Koyuncu', 'Hamid Jafarkhani']
I am writing a research paper on a idea On the Minimum Distortion of Quantizers with Heterogeneous Reproduction Points
[{"from": "human", "value": "I am writing a research paper on a idea On the Minimum Distortion of Quantizers with Heterogeneous Reproduction Points"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In quantization theory, one typically works with a unique distortion function (e.g. the squared-error distortion function) that quantifies the cost of quantizing a given source sample to any given reproduction point of the quantizer. Many applications, hover, induce quantization problems where different distortion functions should be associated with different reproduction points. ,  consider the case where the distortion of a given reproduction point is the squared distance to the source sample ighted by a factor that varies from one reproduction point to another. For a uniform distribution of source samples,  determine the corresponding optimal scalar quantizers and their distortions.  also find upper and lor bounds on the distortion of optimal vector quantizers. For non-uniform distributions,  provide a high resolution analysis of the minimum possible distortion. As a byproduct of our analysis,  show that for certain distributions of ights, a tessellation of non-congruent quantization cells can outperform tessellations of congruent polytopes. This suggests that Gersho's conjecture cannot be extended to the case of squared-error distortion functions with ighted reproduction points."}]