This paper presents a new type of interpolation of Bα spaces,with which a new characterization of Bα spaces by the Jackson means of entire exponential type is given.
Objective To investigate the microstructure characteristics in human kidney with the WD cepstrum of ultrasonic backscattering. Methods By using this method, an analysis of the backscattering signals of normal and path...Objective To investigate the microstructure characteristics in human kidney with the WD cepstrum of ultrasonic backscattering. Methods By using this method, an analysis of the backscattering signals of normal and pathological human kidney in vitro was made and the mean spacing of the scatterers of biological soft tissues was estimated, then compared the means of this new approach with the means of the AR cepstrum. Results The results show that the mean spacings of the scatterers of the two different kidney tissues are noticeably different, which reveals the fact that the WD cepstrum works more effective than the AR cepstrum in showing the features of the microstructure of soft tissues. Conclusion The WD cepstrum is an effective mean to analyze the ultrasonic scattering signals and determine the features of the mean spacing of the scatterers of soft tissues. This method provides more available clinical diagnosis and improves the results of mean spacing of the scatterers of soft tissues.展开更多
Ultrasonic backscatter signals from cancellous bone are sensitive to the microstructure of trabecular bone,and thus enable the feasibility to extract microstructural information of trabecular bone.The mean trabecular ...Ultrasonic backscatter signals from cancellous bone are sensitive to the microstructure of trabecular bone,and thus enable the feasibility to extract microstructural information of trabecular bone.The mean trabecular bone spacing(MTBS)is an important parameter for characterizing bone microstructure.This paper proposes an MTBS estimation method based on the combination of Hilbert transform and fundamental frequency estimation(CHF). The CHF was verified with ultrasonic backscatter signals from simulations and in vitro measurements at a central frequency of 5MHz.The CHF method was compared with the simplified inverse filter tracking(SIFT)method,Simons' Quadratic Transformation(QT)method,Singular Spectrum Analysis(SSA)method,and Spectral Autocorrelation(SAC)method.Monte-Carlo simulations were performed by varying the MTBS,signal-to-noise ratio(SNR),standard deviation of regular spacing(SDRS),amplitude ratio of diffuse scattering to regular scattering(Ad)and frequency dependent attenuation(nBUA).The simulation results showed that the CHF method had a better performance in MTBS estimation under almost all the examination conditions except for SNR.The estimation percentage correct(EPC)was greater than 90% when the MTBS was in the range of 0.4to 1.4mm.In the in vitro measurements,the estimated EPC by the CHF method was91.25±7.81%(mean±standard deviation).A significant correlation was observed for the CHF-estimated MTBS and micro-computed tomography(μ-CT)-measured values(R^2=0.75,p<0.01).These results demonstrate that the CHF method is anti-interference for MTBS estimation and can be used to estimate trabecular bone spacing.展开更多
In this paper,we first introduce the weak Lipschitz spaces WLip_(q,α),1<q<∞,0<α<1 which are the analog of weak Lebesgue spaces L^(q,∞)in the setting of Lipschitz space.We obtain the equivalence between...In this paper,we first introduce the weak Lipschitz spaces WLip_(q,α),1<q<∞,0<α<1 which are the analog of weak Lebesgue spaces L^(q,∞)in the setting of Lipschitz space.We obtain the equivalence between the norm ||·||_(Lipα)and ||·||_(()WLip_(q,α)).As an application,we show that the commutator M_(β)~b is bounded from L~p to L^(q,∞) for some p ∈(1,∞) and 1/p-1/q=(α+β)/n if and only if b is in Lip_(α).We also introduce the weak central bounded mean oscillation space WCBMO_(q,α) and give a characterization of WCBMO_(q,α) via the boundedness of the commutators of Hardy type operators.展开更多
文摘This paper presents a new type of interpolation of Bα spaces,with which a new characterization of Bα spaces by the Jackson means of entire exponential type is given.
文摘Objective To investigate the microstructure characteristics in human kidney with the WD cepstrum of ultrasonic backscattering. Methods By using this method, an analysis of the backscattering signals of normal and pathological human kidney in vitro was made and the mean spacing of the scatterers of biological soft tissues was estimated, then compared the means of this new approach with the means of the AR cepstrum. Results The results show that the mean spacings of the scatterers of the two different kidney tissues are noticeably different, which reveals the fact that the WD cepstrum works more effective than the AR cepstrum in showing the features of the microstructure of soft tissues. Conclusion The WD cepstrum is an effective mean to analyze the ultrasonic scattering signals and determine the features of the mean spacing of the scatterers of soft tissues. This method provides more available clinical diagnosis and improves the results of mean spacing of the scatterers of soft tissues.
基金supported by the NSFC(11327405,11504057&11525416)
文摘Ultrasonic backscatter signals from cancellous bone are sensitive to the microstructure of trabecular bone,and thus enable the feasibility to extract microstructural information of trabecular bone.The mean trabecular bone spacing(MTBS)is an important parameter for characterizing bone microstructure.This paper proposes an MTBS estimation method based on the combination of Hilbert transform and fundamental frequency estimation(CHF). The CHF was verified with ultrasonic backscatter signals from simulations and in vitro measurements at a central frequency of 5MHz.The CHF method was compared with the simplified inverse filter tracking(SIFT)method,Simons' Quadratic Transformation(QT)method,Singular Spectrum Analysis(SSA)method,and Spectral Autocorrelation(SAC)method.Monte-Carlo simulations were performed by varying the MTBS,signal-to-noise ratio(SNR),standard deviation of regular spacing(SDRS),amplitude ratio of diffuse scattering to regular scattering(Ad)and frequency dependent attenuation(nBUA).The simulation results showed that the CHF method had a better performance in MTBS estimation under almost all the examination conditions except for SNR.The estimation percentage correct(EPC)was greater than 90% when the MTBS was in the range of 0.4to 1.4mm.In the in vitro measurements,the estimated EPC by the CHF method was91.25±7.81%(mean±standard deviation).A significant correlation was observed for the CHF-estimated MTBS and micro-computed tomography(μ-CT)-measured values(R^2=0.75,p<0.01).These results demonstrate that the CHF method is anti-interference for MTBS estimation and can be used to estimate trabecular bone spacing.
基金Supported by the National Natural Science Foundation of China (Grant No.11871452)the Natural Science Foundation of Henan Province (Grant No.202300410338)the Nanhu Scholar Program for Young Scholars of Xinyang Normal University。
文摘In this paper,we first introduce the weak Lipschitz spaces WLip_(q,α),1<q<∞,0<α<1 which are the analog of weak Lebesgue spaces L^(q,∞)in the setting of Lipschitz space.We obtain the equivalence between the norm ||·||_(Lipα)and ||·||_(()WLip_(q,α)).As an application,we show that the commutator M_(β)~b is bounded from L~p to L^(q,∞) for some p ∈(1,∞) and 1/p-1/q=(α+β)/n if and only if b is in Lip_(α).We also introduce the weak central bounded mean oscillation space WCBMO_(q,α) and give a characterization of WCBMO_(q,α) via the boundedness of the commutators of Hardy type operators.
