Image Reconstruction from Fan-Beam Projections without Back-Projection Weight in a 2-D Dynamic CT: Compensation of Time-Dependent Rotational, Uniform Scaling and Translational Deformations

In a dynamic CT, the acquired projections are corrupted due to strong dynamic nature of the object, for example: lungs, heart etc. In this paper, we present fan-beam reconstruction algorithm without position-dependent backprojection weight which compensates for the time-dependent translational, uniform scaling and rotational deformations occurring in the object of interest during the data acquisition process. We shall also compare the computational cost of the proposed reconstruction algorithm with the existing one which has position-dependent weight. To accomplish the objective listed above, we first formulate admissibility conditions on deformations that is required to exactly reconstruct the object from acquired sequential deformed projections and then derive the reconstruction algorithm to compensate the above listed deformations satisfying the admissibility conditions. For this, 2-D time-dependent deformation model is incorporated in the fan-beam FBP reconstruction algorithm with no backprojection weight, assuming the motion parameters being known. Finally the proposed reconstruction algorithm is evaluated with the motion corrupted projection data simulated on the computer.

Rupture imaging of the 25 April 2015 M_W7.9 Nepal earthquake from back-projection of teleseismic P waves

The M7.9 Nepal earthquake of 25 April2015 had over 8, 500 fatalities and was the most destructive earthquake in Nepal since the Bihar-Nepal earthquake in 1934.In this study, we imaged the rupture process of this Nepal event by back-projecting the teleseismic P-wave energy recorded at the three regional networks in Alaska, Australia and Europe. The back-projection images of the three subarrays revealed that the Nepal earthquake propagated along the strike in a southeast direction over a distance of ～ 160–170 km with the duration of ～ 50–55 s. The rupture process was found to be a simple, unilateral event with a near constant velocity of 3.3 km/s.The beam power was mainly distributed in the geographic region just north of Kathmandu and the peak intensity for the source time function curve occurred at about 30 s. The earthquake was destructive due to its occurrence at shallow depth(～ 12–15 km) and the fact that the capital lies in a basin of soft sediment. Additionally, the resonance effect for the longer period waves that occurred in the Kathmandu valley led to destructive aggravation, impacting mainly the taller buildings.

Multi-example feature-constrained back-projection method for image super-resolution

Example-based super-resolution algorithms,which predict unknown high-resolution image information using a relationship model learnt from known high- and low-resolution image pairs, have attracted considerable interest in the field of image processing. In this paper, we propose a multi-example feature-constrained back-projection method for image super-resolution. Firstly, we take advantage of a feature-constrained polynomial interpolation method to enlarge the low-resolution image. Next, we consider low-frequency images of different resolutions to provide an example pair. Then, we use adaptive k NN search to find similar patches in the low-resolution image for every image patch in the high-resolution low-frequency image, leading to a regression model between similar patches to be learnt. The learnt model is applied to the low-resolution high-frequency image to produce high-resolution high-frequency information. An iterative back-projection algorithm is used as the final step to determine the final high-resolution image.Experimental results demonstrate that our method improves the visual quality of the high-resolution image.

Rapid rupture characterization for the 2023 M_(S)6.2 Jishishan earthquake

On December 18, 2023, the M_(S)6.2 Jishishan earthquake occurred in the northeastern region of the QinghaiXizang Plateau, causing heavy casualties and property damage in Gansu and Qinghai Provinces. In this study,we integrate space imaging geodesy, finite fault inversion, and back-projection methods to decipher its rupture property, including fault geometry, coseismic slip distribution, rupture direction, and propagation speed. The results reveal that the seismogenic fault dips to the southwest at an angle of 29°. The major slip asperity is dominated by reverse slip and is concentrated within a depth range of 7–16 km, which explains the significant uplift near the epicenter observed by both the Sentinel-1 ascending and descending In SAR data. Moreover, the teleseismic array waveforms indicate a northwest propagating rupture with an overall slow rupture velocity of~1.91 km/s(AK array) or 1.01 km/s(AU array).

Source complexity of the 2016 M_W7.8 Kaikoura (New Zealand) earthquake revealed from teleseismic and InSAR data

On November 13, 2016, an MW7.8 earthquake struck Kaikoura in South Island of New Zealand. By means of back-projection of array recordings, ASTFs-analysis of global seismic recordings, and joint inversion of global seismic data and co-seismic In SAR data, we investigated complexity of the earthquake source. The result shows that the 2016 MW7.8 Kaikoura earthquake ruptured about 100 s unilaterally from south to northeast(~N28°–33°E), producing a rupture area about 160 km long and about 50 km wide and releasing scalar moment 1.01×1021 Nm. In particular, the rupture area consisted of two slip asperities, with one close to the initial rupture point having a maximal slip value ~6.9 m while the other far away in the northeast having a maximal slip value ~9.3 m. The first asperity slipped for about 65 s and the second one started 40 s after the first one had initiated. The two slipped simultaneously for about 25 s.Furthermore, the first had a nearly thrust slip while the second had both thrust and strike slip. It is interesting that the rupture velocity was not constant, and the whole process may be divided into 5 stages in which the velocities were estimated to be 1.4 km/s, 0 km/s, 2.1 km/s, 0 km/s and 1.1 km/s, respectively. The high-frequency sources distributed nearly along the lower edge of the rupture area, the highfrequency radiating mainly occurred at launching of the asperities, and it seemed that no high-frequency energy was radiated when the rupturing was going to stop.

Rapid assessment of the September 5,2022 M_(S)6.8 Luding earthquake in Sichuan,China

At 12:52,September 5,2022,an M_(S)6.8 earthquake occurred in Luding,Sichuan.The earthquake caused serious casualties and property loss,and was determined to have an epicenter intensity of Ⅸ degree.In this study,we used three earthquake intensity rapid assessment methods(i.e.WFM,BPM and ASM) to evaluate the intensity of this earthquake.Then,we comparatively analyzed the three methods based on strong ground motion observation data and actual intensity maps.The results show that:(1) The earthquake is associated with a southeast-oriented single-sided rupture.The WFM method can only evaluate earthquakes with two-sided ruptures,which has some limitations;(2) The intensity of BPM and ASM was overestimated on the southwest and north sides of the epicenter,but other high-intensity zones were similar to the intensities measured by actual surveys;(3) The residuals of the three intensity assessment methods were all between-0.5 and 1.Although a small number of stations were underestimated,the overall residuals were good,and the residuals gradually approached 0 with the increase of distance;(4) The number of towns and villages evaluated by the three methods in the earthquake area was almost all lower than the field survey results.One exception is the area of Ⅷ degree,where the BPM and ASM were higher than the survey results;(5) The area of the earthquake area evaluated by the three methods was low in Ⅵ and Ⅶ degree,moderate in Ⅷ degree,and low in Ⅸ degree(the area from ASM is similar to the area measured by actual survey).Overall,ASM is applicable to this earthquake intensity assessment.

Influence of limited-view scanning on depth imaging of photoacoustic tomography

We study the influence of limited-view scanning on the depth imaging of photoacoustic tomography. The situation, in which absorbers are located at different depths with respect to the limited-view scanning trajectory, is called depth imaging and is investigated in this paper. The results show that limited-view scanning causes the reconstructed intensity of deep absorbers to be weaker than that of shallow ones and that deep absorbers will be invisible if the scanning range is too small. The concept of effective scanning angle is proposed to analyse that phenomenon. We find that an effective scanning angle can well predict the relationship between scanning angle and the intensity ratio of absorbers. In addition, limited-view scanning is employed to improve image quality.

Imaging the rupture process of the 10 January 2018 Mw7.5 Swan island, Honduras earthquake

The 10 January 2018 Mw7.5 Swan island,Honduras earthquake occurred on the Swan island fault,which is a transform plate boundary between the North American and Caribbean plates.Here we back-project the rupture process of the earthquake using dense seismic stations in Alaska,and find that the earthquake ruptured at least three faults(three stages)for a duration of~40 s.The rupture speed for the longest fault(stage 3)is as fast as 5 km/s,which is much faster than the local shear wave velocity of~4 km/s.Supershear rupture was incidentally observed on long and straight strike-slip faults.This study shows a supershear rupture that occured on a strike-slip fault with moderate length,implying that supershear rupture might commonly occur on large strike-slip earthquakes.The common occurrence of supershear rupture on strike-slip earthquakes will challenge present understanding of crack physics,as well as strong ground motion evaluation in earthquake engineering.

Approach for ISAR imaging of near-field targets based on coordinate conversion and image interpolation

Inverse synthetic aperture radar(ISAR)imaging of near-field targets is potentially useful in some specific applications,which makes it very important to efficiently produce highquality image of the near-field target.In this paper,the simplified target model with uniform linear motion is applied to the near-field target imaging,which overcomes the complexity of the traditional near-field imaging algorithm.According to this signal model,the method based on coordinate conversion and image interpolation combined with the range-Doppler(R-D)algorithm is proposed to correct the near-field distortion problem.Compared with the back-projection(BP)algorithm,the proposed method produces better focused ISAR images of the near-field target,and decreases the computation complexity significantly.Experimental results of the simulated data have demonstrated the effectiveness and robustness of the proposed method.

Distribution of Lg coda Q in Xinjiang and its adjacent regions

In this study, we collected 1156 broadband vertical components records at 22 digital seismic stations in Xinjiang region, Urumqi station, and 7 stations in the adjacent regions during the period of 1999-2003. The records were firstly processed by the stacked spectral ratio method to obtain Q0 (Q at 1 Hz) and the frequency correlation factor η corresponding to each path. Based on the results, the distribution images of Q0 and η in 1°×1° grids for Xinjiang region were gained by the back-projection technique. The results indicate that Q0 is high (300-450) in the Tarim platform and marginal Siberian platform, while Q0 is low (150-250) in the southern regions as west Kunlun fold system and Songpan-Ganzi fold system. In the northern regions as Junggar fold system and Tianshan fold system, Q0 is also low (250-300) and η varies between 0.5 and 0.9.

Novel Channel Attention Residual Network for Single Image Super-Resolution

A novel channel attention residual network(CAN)for SISR has been proposed to rescale pixel-wise features by explicitly modeling interdependencies between channels and encoding where the visual attention is located.The backbone of CAN is channel attention block(CAB).The proposed CAB combines cosine similarity block(CSB)and back-projection gating block(BG).CSB fully considers global spatial information of each channel and computes the cosine similarity between each channel to obtain finer channel statistics than the first-order statistics.For further exploration of channel attention,we introduce effective back-projection to the gating mechanism and propose BG.Meanwhile,we adopt local and global residual connections in SISR which directly convey most low-frequency information to the final SR outputs and valuable high-frequency components are allocated more computational resources through channel attention mechanism.Extensive experiments show the superiority of the proposed CAN over the state-of-the-art methods on benchmark datasets in both accuracy and visual quality.

Rupture pattern of the Oct 23,2011 Van-Merkez,Eastern Turkey earthquake

High-frequency rupture process of the Oct 23, 2011 Van-Merkez earthquake is imaged by back-projection method using high-quality teleseismic P wave data from the US Array, and prestack Kirchhoff migration using P wave data from a subarray of global seismic networks. The rupture model with two asperities is confirmed by previous two methods. In low-frequency imaging, a large asperity derived from the migration method corresponds to the second one from the high-frequency P waves. The con- sistency of the locations of asperities from datasets with different frequency bands indicates that there is possible insignificance of the frequency-dependent feature for the earthquake. The resultant images illustrate the spatial and temporal evolution of the rupture, which mainly propa- gated WSW over a length of 33 km during the first 18 s, accompanying with bursts of two asperities at 3 and 11-13 s. The rupture direction is confirmed by the S wave comer frequency variations of strong ground accelerations. The rupture fronts are mainly located at the updip of the causative fault. Based on polarities of the P waveforms and focal mechanisms of the mainshock and aftershocks, the failure of these two asperities is determined to have occurred on a reverse fault with a dip angle of 47°. Hence, the rupture pattern of the 2011 Van-Merkez earthquakewas dominated by a unilateral rupture toward the west- southwest direction.

Analytical image reconstruction methods in emission tomography

Data collected in two-dimensional projections give planar images of object at each projection angle. To obtain information along the depth of the object, tomographic images are reconstructed using these projections. There are basically two approaches to solve the problem of reconstruction: analytical and iterative, each one presenting its own advantages and limitations. This paper provides a detailed introduction and comparison to four analytical image reconstruction methods including Fourier transformation, simple back-projection, back-projection filtering and filtered back-projection.

Estimating Seismic Intensity Maps of the 2021 Mw 7.3 Madoi,Qinghai and Mw 6.1 Yangbi,Yunnan,China Earthquakes

This study focuses on rapidly determining seismic intensity maps of earthquakes because it offers fundamental information for effective emergency rescue and subsequent scientific research,and remains challenging to accurately determine seismic intensity map in regions with sparse instrumental observations.Here we applied a novel method that consisted of array technology(backprojection),ground-motion prediction equations,and site corrections,to estimate the seismic intensity maps of the 2021 Mw 7.3 Madoi,Qinghai and the Mw 6.1 Yangbi,Yunnan,China earthquakes.We used seismic data recorded at European stations to back-project the source processes of the 2021 Mw7.3 Madoi,Qinghai and the Mw 6.1 Yangbi,Yunnan,China earthquakes.The back-projected energy radiations were then used as subevents or used to define the fault geometry.Summing the contributions of each subevent or estimating the shortest distances from each site to the rupture fault,we obtained the ground motion(PGA and PGV)for each site under rock site conditions.The estimated ground motions were corrected at each site for local site amplification according to the Vs30 database.Our estimated seismic intensity maps and field reports showed high similarity,which further validated the effectiveness of the novel approach,and pushed the limit of earthquake size down to~M 6.Such efforts would substantially help in the fast and accurate evaluation of earthquake damage,and precise rescue efforts.

Magnitude of the 23 January 2018 M7.9 Alaska Earthquake Estimated from Local Dense Seismic Records in Alaska

We apply a novel method to estimate the magnitude of the 23 January 2018 M7.9 Alaska earthquake using seismic stations recorded at local to regional distances in Alaska, US. We determine the source duration from back-projection results derived from the Alaska stations in a relatively compact azimuth range. Then we calculate the maximum P-wave displacements recorded on a wide azimuth range at distances of 8 to 15 degrees. Combining the source duration and the maximum P-wave displacements, we obtain magnitudes of 7.86–8.03 for the 23 January 2018 earthquake in 3–5 min, very close to the Mw 7.9 determined by the USGS and GCMT. This example validates the new approach for determining magnitude of large earthquakes using local to regional stations, and its time efficiency that magnitudes of large earthquakes can be accurately estimated within in 3–5 min after origin time. Therefore, further application of this new method would help accurate estimation of size of earthquakes that occur offshore and might cause tsunami hazards.

ISAR imaging of high-speed moving targets in short-range using impulse radar

In order to improve the measurement accuracy of weapons, ultra-wideband(UWB) inverse synthetic aperture radar(ISAR) imaging of high-speed moving targets in short-range is studied. In the scheme, because the positions of scatters vary with the radar line-of-sight(LOS) angle when the high-speed target is passing through the closest point of the approach, the concept of equivalent scattering point(ESP) is proposed. The Hough transform is employed to implement ESP motion parameter estimation,while the target translational motion is compensated by using the ESP time delay, and the angle spanned by the target is estimated by utilizing geometric relationship of ESP motion. Finally, the twodimensional image of the target is restructured by using the near field time-domain back-projection algorithm. Simulation results confirm that the proposed method is efficient.

Distribution of L_g coda Q in the Chinese continent and its adjacent regions

785 traces of vertical components from shallow earthquakes recorded by 10 CDSN (Chinese Digital Seismographic Network) stations and 5 GSN (Global Seismographic Network) stations were collected to study the attenuation characteristics ofL g coda in the Chinese continent and its adjacent regions. The records were processed first using the stack spectral ratio method to obtain the average values ofQ 0 (Q at 1Hz) and η, the frequency dependence, ofL g coda in the ellipses corresponding to the paths. The back-projection technique was then employed to obtain the tomographic maps ofQ 0 and η values, and the distribution of their errors. Results indicate that in the studied areaQ 0 varies between 200 and 500. The lowest value ofQ 0 exists in the Yun-nan-Tibetan region, while the highest value ofQ 0 occurs in the southern edge of Siberian platform. η varies between 0.3 and 0.8. For most part of the studied area η varies inversely withQ 0.

A nonparametric estimation of the infection curve

Predicting the future course of an epidemic depends on being able to estimate the current numbers of infected individuals.However,while back-projection techniques allow reliable estimation of the numbers of infected individuals in the more distant past,they are less reliable in the recent past.We propose two new nonparametric methods to estimate the unobserved numbers of infected individuals in the recent past in an epidemic.The proposed methods are noniterative,easily computed and asymptotically normal with simple variance formulas.Simulations show that the proposed methods are much more robust and accurate than the existing back projection method,especially for the recent past,which is our primary interest.We apply the proposed methods to the 2003 Severe Acute Respiratory Syndorme(SARS) epidemic in Hong Kong.

INVERSE RADON TRANSFORM WITH ONE-DIMENSIONAL WAVELET TRANSFORM

In this paper, the wavelet inverse formula of Radon transform is obtained with onedimensional wavelet. The convolution back-projection method of Radon transform is derived from this inverse formula. An asymptotic relation between wavelet inverse formula of Radon transform and convolution-back projection algorithm of Radon transform in 2 dimensions is established.