A Spatially Adaptive Edge-Preserving Denoising Method Based on Fractional-Order Variational PDEs

Image denoising is a basic problem in image processing. An important task of image denoising is to preserve the significant geometric features such as edges and textures while filtering out noise. So far, this is still a problem to be further studied. In this paper, we firstly introduce an edge detection function based on the Gaussian filtering operator and then analyze the filtering characteristic of the fractional derivative operator. On the basis, we establish the spatially adaptive fractional edge-preserving denoising model in the variational framework, discuss the existence and uniqueness of our proposed model solution and derive the nonlinear fractional Euler-Lagrange equation for solving our proposed model. This forms a fractional order extension of the first and second order variational approaches. Finally, we apply the proposed method to the synthetic images and real seismic data denoising to verify the effectiveness of our method and compare the experimental results of our method with the related state-of-the-art methods. Experimental results illustrate that our proposed method can not only improve the signal to noise ratio (SNR) but also adaptively preserve the structural information of an image compared with other contrastive methods. Our proposed method can also be applied to remote sensing imaging, medical imaging and so onThe work of Dehua Wang was supported in part by the Science and Technology Planning Project of Shaanxi Province under Grant 2020JM-561, in part by the Postdoctoral Foundation of China under Grant 2019M663462, in part by the Innovative Talents Cultivate Program of Shaanxi Province under Grant 2019KJXX-032, in part by the President Fund of Xi’an Technological University under Grant XAGDXJJ17026, and in part by the Teaching Reform Project of Xi’an Technological University under Grant 18JGY08. The work of Juan J. Nieto was supported in part by the Agencia Estatal de Investigacion (AEI) of Spain under Grant MTM2016-75140-P, and in part by the European Community Fund FEDER. The work of Xiaoping Li was supported in part by the NSFC under Grant 61701086, and in part by the Fundamental Research Funds for the Central Universities under Grant ZYGX2016KYQD143S

Research Status and Prospect for CT Imaging

Computed tomography (CT) is a very valuable imaging method and plays an important role in clinical diagnosis. As people pay more and more attention to radiation doses these years, decreasing CT radiation dose without affecting image quality is a hot direction for research of medical imaging in recent years. This chapter introduces the research status of low-dose technology from following aspects: low-dose scan implementation, reconstruction methods and image processing methods. Furthermore, other technologies related to the development tendency of CT, such as automatic tube current modulation technology, rapid peak kilovoltage (kVp) switching technology, dual-source CT technology and Nano-CT, are also summarized. Finally, the future research prospect are discussed and analyzed

Deep Anisotropic Structure under the Central Volcanic Region, New Zealand

Seismic anisotropy across the Hikurangi subduction zone measured from shear-wave splitting exhibits strong lateral changes over distances of about 250 km. Teleseismic S-phases show trench-parallel fast polarisations with increasing delay times across the forearc and arc region. In the arc region, delay times reach up to 4.5 s, one of the largest delay times measured in the world. Such large delay times suggest strong anisotropy or long travel paths through the anisotropic regions. Delay times decrease systematically in the backarc region. In contrast, local S-phases exhibit a distinct change from trench-parallel fast orientations in the forearc to rench-perpendicular in the backarc, with average delay times of 0.35 s. In the far backarc, no apparent anisotropy is observed for teleseismic S-phases. The three different anisotropic regions across the subduction zone are interpreted by distinct anisotropic domains at depth: 1) In the forearc region, the observed "average" anisotropy (about 4%) is attributed to trench-parallel mantle flow below the slab with possible contributions fromanisotropy in the slab. 2) In the arc region, high (up to 10%) frequency dependent anisotropy in the mantle wedge, ascribed to melt, together with the sub-slab anisotropy add up to cause the observed high delay times. 3) In the far backarc region, the mantle wedge dynamic ends. The apparent isotropy must be caused by different dynamics, e.g. vertical mantle flow or small-scale convection, possibly induced by convective removal of thickened lithosphere. The proposed hypothesis is tested using anisotropicwave propagation in two-dimensional finite difference models. Large-scale models of the subduction zone (hundreds of kilometres) incorporating the proposed anisotropic domains of the initial interpretation result in synthetic shear-wave splittingmeasurements that closely resemble all large-scale features of real data observations across the central North Island. The preferred model constrains the high (10%) anisotropy to the mantle wedge down to about 100 kmunder the CVR, bound to the west by an isotropic region under the western North Island; the slab is isotropic and the subslab region has average (3.5%) anisotropy, down to 300 km. This model succeeds in reproducing the constant splitting parameters in the forearc region, the strong lateral changes across the CVR and the apparent isotropy in the far backarc region, as well as the backazimuthal variations. The influence of melt on seismic anisotropy is examined with different small-scale (tens of kilometres) analytical modelling approaches calculating anisotropy due to melt occurring in inclusions, cracks or bands. Conclusions are kept conservative with the intention not to over-interpret the data due to model complexities. The models show that seismic anisotropy strongly depends on the scale of inclusions and wavelengths. Frequency dependent anisotropy for local and teleseismic shear-waves, e.g. for frequency ranges of 0.01-1Hz can be observed for aligned inclusions on the order of tens of meters. To test the proposed frequency dependence in the recorded data, two different approaches are introduced. Delay times exhibit a general trend of -3 s/Hz. A more detailed analysis is difficult due to the restricted frequency content of the data. Future studies with intermediate frequency waves (such as regional S-phases) are needed to further investigate the cause of the discrepancy between local and teleseismic shear-wave splitting. An additional preliminary study of travel time residuals identifies a characteristic pattern across central North Island. Interpretation highlights the method as a valuable extension of the shear-wave splitting study and suggests a more detailed examination to be conducted in future

Ultrasound tomography using pyroelectric and piezoelectric sensors

Acoustic absorption is one of several quantities which can differentiate healthy breast tissue from cancerous tissue. In order to accurately quantify the acoustic absorption, the sensor system must be able to accurately distinguish acoustic power loss due to absorption from other modes of attenuation. Traditional piezoelectric sensors are susceptible to phase-cancellation artifacts due to their directional signal response, and thus pyroelectric ultrasound sensors, which have a much flatter directional response, have been suggested as an alternate measurement device for improved absorption reconstructions in ultrasound tomography (UST). In this thesis we investigate the use of pyroelectric phase-insensitive sensors in UST — the thesis is divided into two parts. In the first part we present a model for a pyroelectric ultrasound sensor and investigate its directional response and sensitivity properties. The model’s time-series response and directional response are compared to real-world measurements to confirm accuracy. The second part focuses on the inverse problem aspect of ultrasound tomography, where we consider various reconstruction methods and sensor geometries to determine which situations can benefit from phase-insensitive data for acoustic absorption reconstruction. Reconstructions for both phase-insensitive as well as phase-sensitive sensors are analysed, with future work considerations for combined sensor systems

Seismic Waves

The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This has led to some novel applications such as using artificially-induced shocks for exploration of the Earth's subsurface and seismic stimulation for increasing the productivity of oil wells. This book demonstrates the latest techniques and advances in seismic wave analysis from theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. A review process was conducted in cooperation with sincere support by Drs. Hiroshi Takenaka, Yoshio Murai, Jun Matsushima, and Genti Toyokuni