  This paper explores a new version of the Levenberg-Marquardt algorithm used
for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image
compression and reconstruction. Tensor computation, especially CP
decomposition, holds significant applications in data compression and analysis.
In this study, we formulate CP as a nonlinear least squares optimization
problem. Then, we present an iterative Levenberg-Marquardt (LM) based algorithm
for computing the CP decomposition. Ultimately, we test the algorithm on
various datasets, including randomly generated tensors and RGB images. The
proposed method proves to be both efficient and effective, offering a reduced
computational burden when compared to the traditional Levenberg-Marquardt
technique.
