Moving sum procedure for change point detection under piecewise linearity

We propose a computationally and statistically efficient procedure for segmenting univariate data under piecewise linearity. The proposed moving sum (MOSUM) methodology detects multiple change points where the underlying signal undergoes discontinuous jumps and/or slope changes. Theoretically, it controls the family-wise error rate at a given significance level asymptotically and achieves consistency in multiple change point detection, as well as matching the minimax optimal rate of estimation when the signal is piecewise linear and continuous, all under weak assumptions permitting serial dependence and heavy-tailedness. Computationally, the complexity of the MOSUM procedure is $O(n)$ which, combined with its good performance on simulated datasets, making it highly attractive in comparison with the existing methods. We further demonstrate its good performance on a real data example on rolling element-bearing prognostics

Moving sum procedure for change point detection under piecewise linearity

We propose a computationally and statistically efficient procedure for segmenting univariate data under piecewise linearity. The proposed moving sum (MOSUM) methodology detects multiple change points where the underlying signal undergoes discontinuous jumps and/or slope changes. Theoretically, it controls the family-wise error rate at a given significance level asymptotically and achieves consistency in multiple change point detection, as well as matching the minimax optimal rate of estimation when the signal is piecewise linear and continuous, all under weak assumptions permitting serial dependence and heavy-tailedness. Computationally, the complexity of the MOSUM procedure is $O(n)$ which, combined with its good performance on simulated datasets, making it highly attractive in comparison with the existing methods. We further demonstrate its good performance on a real data example on rolling element-bearing prognostics

Wyner-Ziv side information generation using a higher order piecewise trajectory temporal interpolation algorithm

Distributed video coding (DVC) reverses the traditional coding paradigm of complex encoders allied with basic decoding, to one where the computational cost is largely incurred by the decoder. This enables low-cost, resource-poor sensors to be used at the transmitter in various applications including multi-sensor surveillance. A key constraint governing DVC performance is the quality of side information (SI), a coarse representation of original video frames which are not available at the decoder. Techniques to generate SI have generally been based on linear temporal interpolation, though these do not always produce satisfactory SI quality especially in sequences exhibiting asymmetric (non-linear) motion. This paper presents a higher-order piecewise trajectory temporal interpolation (HOPTTI) algorithm for SI generation that quantitatively and perceptually affords better SI quality in comparison to existing temporal interpolation-based approaches