Convolutional Multidimensional Amplitude Spectrum Nuclear Norm for Frequency-domain Robust Principal Component Analysis

In this paper, we propose convolutional multidimensional amplitude spectrum nuclear norm (CMASNN) for the task of frequency-domain robust principal component analysis (FRPCA). Principal component extraction (PCE) from observed signals, particularly in the presence of outliers, has long been recognized as a fundamental challenge in the field of signal processing. Although RPCA has demonstrated its efficacy as a technique, it suffers significant limitations when confronted with misaligned principal components due to its reliance on the low-rankness assumption. To address this issue, we initially introduced ASNN, which leverages the invariant property of amplitude spectra under (circular) shifts, enabling the robust extraction of principal components from observed signals by incorporating the ASNN into RPCA. Building upon this foundation, the CMASNN further enhances the ASNN by unifying multiple signals into a higher dimensional representation. This enhancement enables us to discriminate between true principal components and outliers more effectively. By substituting the CMASNN for the ASNN in FRPCA, our experimental results show that the proposed CMASNN-based FRPCA outperforms the performance of its conventional counterpart.