Wavelet thresholding for symmetric positive-definite matrix-valued curves in a log-Euclidean manifold

von Sachs, RainerWachel, YannicYannicWachel2025-05-142025-05-142025-05-142022https://hdl.handle.net/2078.2/41831In this work, we perform nonparametric estimation of symmetric and positive-definite (SPD) matrix-valued curves living in a Riemannian manifold equipped with the log-Euclidean metric. Using wavelet thresholding methods, together with a simple signal-plus-noise data model, we find several thresholding rules in the wavelet domain, such as a generic non-scalar signal-plus-noise expression. We implement a sum-thresholding (ST) rule that we compare with an existing trace-thresholding (TT) rule, derived in the context of Hermitian positive-definite matrices in the awaveletsstatisticsnon-EuclideancovariancethresholdingWavelet thresholding for symmetric positive-definite matrix-valued curves in a log-Euclidean manifoldtext::thesis::master thesisthesis:38341