title: Can we use PCA to detect small signals in noisy data?
abstract: Principal component analysis (PCA) is among the most commonly applied dimension reduction techniques suitable to denoise data. Focusing on its limitations to detect low variance signals in noisy data, we discuss how statistical and systematical errors occur in PCA reconstructed data as a function of the size of the data set, which extends the work of Lichtert and Verbeeck, (2013) [16]. Particular attention is directed towards the estimation of bias introduced by PCA and its influence on experiment design. Aiming at the denoising of large matrices, nullspace based denoising (NBD) is introduced.
authors: Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden.
authors: Jakob
authors: J
authors: Spiegelberg
authors: Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden.
authors: Ján
authors: J
authors: Rusz
keywords: Bias estimation; Blind source separation; Nullspace based denoising; PCA; Spectrum imaging