Quantization Effects on Dynamic Mode Decomposition for Koopman Operator Estimation

The core message of this work is that the estimation of the Koopman operator using Dynamic Mode Decomposition (DMD) with quantized data can be interpreted as a regularized DMD problem with unquantized data, where the regularization parameter depends on the quantization resolution. This connection provides a framework to potentially recover the unquantized Koopman operator estimate from the quantized data.