A sparse modeling for small data: Case studies in controlled syntheses of 2D materials

Data-scientific approaches have permeated in chemistry and materials science. In general, these approaches are not easily applied to small data, such as experimental data in laboratories. Our group has focused...

Finding an optimal dictionary of different wavelet types using sparse modeling to denoise ECG signal

Sparse signal modeling often reconstructs a signal with few atoms from a pre-defined dictionary. Hence the choice of wavelet dictionary that represents the sparsity of the target signal is crucial in sparse modeling approach. The challenge of finding an optimal dictionary of different wavelet types using sparse denoising model (SDM) to denoise ECG signal is investigated in this work. A method of finding an optimal wavelet dictionary from a set of orthogonal wavelet sub-dictionaries by the means of the best correlation with ECG signal, is developed. The highly correlated sub-dictionaries from three wavelet dictionaries, namely daubechies, symlets, coiflets and discrete cosine transform are combined to construct an overcomplete dictionary. The weight of Akaike’s information criterion and the signal-to-noise ratio improvement are considered as a criterion to evaluate the performance of the proposed SDM. The results indicate that multi-wavelet dictionary of different types is highly sparse and efficient in denoising the target signal, e.g., ECG.

Improved Mitigation Method for the Multipath Delays of BDS-3 Code Observations with the Aid of a Sparse Modeling Algorithm

Global navigation satellite systems are essential for positioning, navigation, and timing services. The quality and reliability of satellite observations determine the system performance, especially in the case of the newly launched global BDS-3 service. However, analyses of multipath delays in BDS-3 satellite observations suggest that there are appreciable errors at different frequencies. Improvement of the accuracy and precision of positioning, navigation, and timing services provided by BDS-3 requires the mitigation of multipath delays of the satellite observations. This paper models the multipath delays of BDS-3 observations using a least-squares combined autoregressive method. Furthermore, a sparse modeling algorithm is proposed to obtain a multipath delay series using total variation and elastic net terms for denoising and eliminating the effect of limited original observations. The estimated coefficients of multipath delays are then set as prior information to correct the next-arc code observations, where the square-root information filter is used in the coefficient estimation. Moreover, four groups of experiments are conducted to analyze the results of modeling the BDS-3 multipath delay using the proposed methods, with single-frequency precise point positioning (PPP) and real-time PPP solutions being selected to test the correction of multipath delays in BDS-3 code observations. The residuals of iGMAS and MGEX station coordinates indicate improvements in eastward, northward, and upward directions of at least 4.1%, 9.6%, and 1.2%, respectively, for the frequency B1I; 6.6%, 5.3%, and 0.2%, respectively, for B3I, 12.5%, 14.3%, and 3.8%, respectively, for B1C; and 5.9%, 7.4%, and 18.1%, respectively, for B2a relative to the use of the traditional method in BDS-3 single-frequency PPP. Furthermore, the real-time double-frequency PPP is optimized by at least 10% for B 1 I + B 3 I and B 1 C + B 2 a . An improved result was obtained with the proposed strategy in a standard point positioning experiment. The proposed multipath delay mitigation method is therefore effective in improving BDS-3 satellite code observations.