Yes, the techniques developed for threshold-constrained indirect quantization can indeed be extended to other distortion measures beyond mean-squared error (MSE). While MSE is a common metric due to its mathematical tractability and ease of optimization, many applications require more nuanced approaches to quantization that consider perceptual or task-specific distortion metrics.
For instance, in audio and video compression, perceptual distortion measures, such as the Perceptual Evaluation of Speech Quality (PESQ) or Structural Similarity Index (SSIM), can be integrated into the quantization framework. These measures account for human perception, allowing for quantization that prioritizes perceptually significant features while minimizing the impact of distortion on perceived quality.
In machine learning, task-specific distortion metrics can be employed, particularly in applications like object detection or image classification. Here, the quantization process can be tailored to minimize the error in specific tasks rather than overall signal fidelity. For example, one could optimize quantization to reduce classification error rates instead of focusing solely on MSE.
To implement these extensions, the necessary conditions for optimality and the algorithms would need to be adapted to accommodate the new distortion metrics. This may involve redefining the cost functions and potentially modifying the iterative or dynamic programming algorithms to ensure they align with the new objectives. Overall, the flexibility of the proposed techniques allows for their application across a wide range of distortion measures, enhancing their utility in diverse fields.