Iterative Deconvolution Research Articles

Multi-scale CLEAN for Fourier-based hard x-ray solar imaging

Abstract Multi-scale deconvolution is an ill-posed inverse problem in imaging, with applications ranging from microscopy, through medical imaging, to astronomical remote sensing. In the case of high-energy space telescopes, multi-scale deconvolution algorithms need to account for the peculiar property of native measurements, which are sparse samples of the Fourier transform of the incoming radiation. The present paper proposes a multi-scale version of CLEAN, which is the most popular iterative deconvolution method in Fourier-based astronomical imaging. Using synthetic data generated according to a simulated but realistic source configuration, we show that this multi-scale version of CLEAN performs better than the original one in terms of accuracy, photometry, and regularization. Further, the application to a data set measured by the NASA Reuven Ramaty High Energy Solar Spectroscopic Imager shows the ability of multi-scale CLEAN to reconstruct rather complex flaring topographies.

A Fast iterative shrinkage and threshold algorithm-based least-squares deconvolution technique with application to bearing fault signals

Bearings are commonly subjected to load, transmission, and impact during operation, resulting in bearing failure that ultimately leads to mechanical breakdown. The low energy level of fault-induced impulsive signals, however, renders it vulnerable to being masked by environmental noise and other disturbances present in the vibration signal. To cope with this issue, this paper investigates the application of the finite impulse response (FIR) filter for bearing fault detection. In this work, the estimation of the FIR is formulated as a least squares optimization problem, aiming to minimize the l 2 norm of the FIR and effectively suppress noise and interference sources. The solutions of the least squares optimization problem are obtained using the fast iterative shrinkage–thresholding (FISTA) algorithm. Furthermore, to better select the regularization parameter in our method, an improved gray wolf optimizer (I–GWO) is employed to conduct the parameter selection. Based on these improvements, the proposed FISTA–LSD technique enables rapid and precise detection of fault characteristics upon their occurrence, thereby mitigating the propagation of faults and preventing accidents from happening. Furthermore, with this automated selection process, engineers can save valuable time that would otherwise be spent on trial-and-error approaches. Through its rapid response capabilities and precise fault detection abilities enabled by the FISTA–LSD technique along with I–GWO integration for automatic parameter selection; this FISTA–LSD technique greatly enhances its practical value. The proposed technique is validated through the utilization of both numerical and experimental data.

Assessment of image-derived input functions from small vessels for patlak parametric imaging using total-body PET/CT.

The image-derived input function (IDIF) from the descending aorta has demonstrated performance comparable to arterial blood sampling while avoiding its invasive nature in parametric imaging. However, in conventional PET, large vessels may not always be within the imaging field of view (FOV). This study aims to evaluate the efficacy of dynamic parametric Ki imaging using image-derived input functions (IDIFs) extracted from various arteries, facilitated by total-body PET/CT. Twenty-three participants underwent a 60-minute total-body [18F]FDG PET scan. Data from each subject were used to reconstruct both total-body PET images and short-axis field-of-view PET images at different bed positions, each with a 25cm axial field-of-view (AFOV). Partial volume correction (PVC) was performed using the blurred Van Cittert iterative deconvolution. IDIFs extracted from the descending aorta, carotid artery, abdominal aorta, and iliac artery were employed for Patlak analysis. The resulting Ki images were compared using quantification indicators and subjective assessment. Linear regression analysis was conducted to examine the correlation of Ki values among IDIFs in normal organ and lesion regions of interest (ROIs). High similarities were observed in Ki images derived from the IDIFs from the descending aorta and other arteries, with a median structural similarity index measure (SSIM) above 0.98 and a median peak signal-to-noise ratio (PSNR) above 37dB. Linear regression analysis revealed strong correlations in Ki values (r² > 0.88) between the descending aorta and the three alternative vessels, with slopes of the linear fits close to 1. No significant difference in lesion detectability among IDIFs was found, as assessed visually and using metrics such as tumor-to-background ratio (TBR) and contrast-to-noise ratio (CNR) (P < 0.05). IDIFs from smaller vessels can reliably reconstruct parametric Ki images without compromising lesion detectability, providing clinically relevant information.

Iterative decoupling deconvolution network for image restoration

The iterative decoupled deblurring BM3D (IDDBM3D) (Danielyan et al., 2011) combines the analysis representation and the synthesis representation, where deblurring and denoising operations are decoupled, so that both problems can be easily solved. However, the IDDBM3D has some limitations. First, the analysis transformation and the synthesis transformation are analytical, thus have limited representation ability. Second, it is difficult to effectively remove image noise from threshold transformation. Third, there exists hyper-parameters to be tuned manually, which is difficult and time consuming. In this work, we propose an iterative decoupling deconvolution network(IDDNet), by unrolling the iterative decoupling algorithm of the IDDBM3D. In the proposed IDDNet, the analysis/synthesis transformation are implemented by encoder/decoder modules; the denoising is implemented by convolutional neural network based denoiser; the hyper-parameters are estimated by hyper-parameter module. We apply our models for image deblurring and super-resolution. Experimental results show that the IDDNet significantly outperforms the state-of-the-art unfolding networks.

The rupture process of the Hualien M7.3 sequence on April 3, 2024

The Hualien M7.3 earthquake on April 3, 2024, was a significant and strong earthquake in Taiwan, China in the past two decades. The rupture process of the main shock and strong aftershocks is of great significance to the subsequent seismic activity and seismogenic tectonic research. Based on local strong-motion data, we used the IDS (Iterative Deconvolution and Stacking) method to obtain the rupture process of the mainshock and two strong aftershocks on the 23rd. The rupture of the mainshock was mainly unilateral, lasting 31 s, with a maximum slip of 2 m, and the depth of the large slip zone is about 41-49 km. There is a clear difference between the rupture depth of the main shock and the two strong aftershocks. The depths of the large slip zones of the latter two are 3-9 km and 8-10 km, respectively. There is also a significant difference in the seismogenic fault between the mainshock and the aftershocks, and we believe that there are two seismogenic fault zones in the study area, the deep and the shallow fault zone. The slip of the deep faults activates the shallow faults.

Scatter estimation and correction using time-of-flight and deconvolution in x-ray medical imaging.

Objective Time-of-flight (TOF) scatter rejection requires a total timing jitter,&#xD;including the detector timing jitter and the X-ray source's pulses width, of 50 ps or less&#xD;to mitigate most of the effects of scattered photons in radiography and CT imaging.&#xD;However, since the total contribution of the source and detector to the timing jitter&#xD;can be retrieved during an acquisition with nothing between the source and detector,&#xD;it can be demonstrated that this contribution may be partially removed to improve&#xD;the image quality.&#xD;Approach A scatter correction method using iterative deconvolution of the measured&#xD;time point-spread function estimates the number of scattered photons detected in each&#xD;pixel. To evaluate the quality of the estimation, GATE was used to simulate the&#xD;radiography of a water cylinder with bone inserts, and a head and torso in a system&#xD;with total timing jitters from 100 ps up to 500 ps full-width-at-half-maximum.&#xD;Main results With a total timing jitter of 200 ps, 89% of the contrast degradation&#xD;caused by scattered photons was recovered in a head and torso radiography, compared&#xD;to 28% with a simple time threshold method. Corrected images using the estimation&#xD;have a percent root-mean square error between 2 and 14% in both phantoms with&#xD;timing jitters from 100 to 500 ps which is lower than the error achieved with scatter&#xD;rejection alone at 100 ps.&#xD;Significance TOF X-ray imaging has the potential to mitigate the effects of the&#xD;scattering contribution and offers an alternative to anti-scatter grids that avoids loss&#xD;of primary photons. Compare to simple TOF scatter rejection using only a threshold,&#xD;the deconvolution estimation approach has lower requirements on both the source and&#xD;detector. These requirements are now within reach of state-of-the-art systems.

Artifacts-free lensless on-chip tomography empowered by three-dimensional deconvolution

A lensless holographic microscope based on in-line holograms and optical diffraction tomography is an ideal imaging system for label-free 3D biological samples and can achieve large-volume imaging with single-cell resolution in a convenient way. However, due to the phase information loss and the missing cone problem, the imaging quality is significantly degraded by the reconstructed artifacts of twin images and out-of-focus images, which severely hinders the identification and interpretation of the objects. We propose an artifacts-free lensless on-chip tomography certified by three-dimensional deconvolution, which facilitates the extraction of real object morphology through straightforward yet effective computation. Initially, a globally valid systemic point spread function (PSF) is generated by simulating the imaging output of an ideal point light source positioned at the origin of the object space coordinate. Subsequently, an iterative three-dimensional deconvolution process is applied to the primitive imaging outcome of the lensless on-chip tomography using this PSF. Through rapid iterations, the optimized imaging result is swiftly obtained. Both the simulated and experimental results indicate that the artifacts-free lensless on-chip tomography can effectively circumvent the reconstructed artifacts and retrieve the real object morphology, which is critical for detailed observation and further quantitative analysis. In addition, we anticipate that the proposed approach has the potential to be transferred to other 3D imaging systems in systemic artifacts removal after corresponding modifications.

The Basic Iterative Deconvolution: A Fast Instrumental Point-Spread Function Deconvolution Method That Corrects for Light That Is Scattered Out of the Field of View of a Detector

The Basic Iterative Deconvolution: A Fast Instrumental Point-Spread Function Deconvolution Method That Corrects for Light That Is Scattered Out of the Field of View of a Detector

High-resolution cell imaging using white light phase shifting interferometry and iterative phase deconvolution.

An optimization algorithm is presented for the deconvolution of a complex field to improve the resolution and accuracy of quantitative phase imaging (QPI). A high-resolution phase map can be recovered by solving a constrained optimization problem of deconvolution using a complex gradient operator. The method is demonstrated on phase measurements of samples using a white light based phase shifting interferometry (WLPSI) method. The application of the algorithm on real and simulated objects shows a significant resolution and contrast improvement. Experiments performed on Escherichia coli bacterium have revealed its sub-cellular structures that were not visible in the raw WLPSI images obtained using a five phase shifting method. These features can give valuable insights into the structures and functioning of biological cells. The algorithm is simple in implementation and can be incorporated into other QPI modalities .

Evaluation of partial volume correction and analysis of longitudinal [18F]GTP1 tau PET imaging in Alzheimer's disease using linear mixed-effects models.

We evaluated the impact of partial volume correction (PVC) methods on the quantification of longitudinal [18F]GTP1 tau positron-emission tomography (PET) in Alzheimer's disease and the suitability of describing the tau pathology burden temporal trajectories using linear mixed-effects models (LMEM). We applied van Cittert iterative deconvolution (VC), 2-compartment, and 3-compartment, and the geometric transfer matrix plus region-based voxelwise methods to data acquired in an Alzheimer's disease natural history study over 18 months at a single imaging site. We determined the optimal PVC method by comparing the standardized uptake value ratio change (%ΔSUVR) between diagnostic and tau burden-level groups and the longitudinal repeatability derived from the LMEM. The performance of LMEM analysis for calculating %ΔSUVR was evaluated in a natural history study and in a multisite clinical trial of semorinemab in prodromal to mild Alzheimer's disease by comparing results to traditional per-visit estimates. The VC, 2-compartment, and 3-compartment PVC methods had similar performance, whereas region-based voxelwise overcorrected regions with a higher tau burden. The lowest within-subject variability and acceptable group separation scores were observed without PVC. The LMEM-derived %ΔSUVR values were similar to the per-visit estimates with lower variability. The results indicate that the tested PVC methods do not offer a clear advantage or improvement over non-PVC images for the quantification of longitudinal [18F]GTP1 PET data. LMEM offers a robust framework for the longitudinal tau PET quantification with low longitudinal test-retest variability. NCT02640092 and NCT03289143.

Enhancing the spatial resolution of time-of-flight based non-line-of-sight imaging via instrument response function deconvolution.

Non-line-of-sight (NLOS) imaging retrieves the hidden scenes by utilizing the signals indirectly reflected by the relay wall. Benefiting from the picosecond-level timing accuracy, time-correlated single photon counting (TCSPC) based NLOS imaging can achieve theoretical spatial resolutions up to millimeter level. However, in practical applications, the total temporal resolution (also known as total time jitter, TTJ) of most current TCSPC systems exceeds hundreds of picoseconds due to the combined effects of multiple electronic devices, which restricts the underlying spatial resolution of NLOS imaging. In this paper, an instrument response function deconvolution (IRF-DC) method is proposed to overcome the constraints of a TCSPC system's TTJ on the spatial resolution of NLOS imaging. Specifically, we model the transient measurements as Poisson convolution process with the normalized IRF as convolution kernel, and solve the inverse problem with iterative deconvolution algorithm, which significantly improves the spatial resolution of NLOS imaging after reconstruction. Numerical simulations show that the IRF-DC facilitates light-cone transform and frequency-wavenumber migration solver to achieve successful reconstruction even when the system's TTJ reaches 1200 ps, which is equivalent to what was previously possible when TTJ was about 200ps. In addition, the IRF-DC produces satisfactory reconstruction outcomes when the signal-to-noise ratio (SNR) is low. Furthermore, the effectiveness of the proposed method has also been experimentally verified. The proposed IRF-DC method is highly applicable and efficient, which may promote the development of high-resolution NLOS imaging.

Partial volume correction of PET image data using geometric transfer matrices based on uniform B-splines

Objective. Most methods for partial volume correction (PVC) of positron emission tomography (PET) data employ anatomical segmentation of images into regions of interest. This approach is not optimal for exploratory functional imaging beyond regional hypotheses. Here, we describe a novel method for unbiased voxel-wise PVC. Approach. B-spline basis functions were combined with geometric transfer matrices to enable a method (bsGTM) that provides PVC or alternatively provides smoothing with minimal regional crosstalk. The efficacy of the proposed method was evaluated using Monte Carlo simulations, human PET data, and murine functional PET data. Main results. In simulations, bsGTM provided recovery of partial volume signal loss comparable to iterative deconvolution, while demonstrating superior resilience to noise. In a real murine PET dataset, bsGTM yielded much higher sensitivity for detecting amphetamine-induced reduction of [11C]raclopride binding potential. In human PET data, bsGTM smoothing enabled increased signal-to-noise ratios with less degradation of binding potentials relative to Gaussian convolution or non-local means. Significance. bsGTM offers improved performance for PVC relative to iterative deconvolution, the current method of choice for voxel-wise PVC, especially in the common PET regime of low signal-to-noise ratio. The new method provides an anatomically unbiased way to compensate partial volume errors in cases where anatomical segmentation is unavailable or of questionable relevance or accuracy.

A Centroiding Method for Targets in Star Images Based on Local PSF Estimation and Iterative Deconvolution

A Centroiding Method for Targets in Star Images Based on Local PSF Estimation and Iterative Deconvolution

Moho Depth Estimation and The Presence of Subducting Slab in West Sumatra, Jambi, and Riau Islands Regions Using Teleseismic Receiver Function Method: A Preliminary Result

The teleseismic receiver function method was used to investigate the crustal structure in West Sumatra, Jambi, and Riau Islands regions. These regions have a high level of seismicity because it is in an active tectonic zone where the oblique subduction between the Indo-Australian and Eurasian plates occurs. This study aims to determine the depth of Moho discontinuity and the presence of subducting slab beneath 6 BMKG seismic stations that form a line perpendicular to the trench and cover 3 different geological zones. PPSI and RASM are in the forearc zone, SKSM is in the volcanic arc zone, and MBBI, JMBI, and DSRI are in the back-arc zone. This study used teleseismic earthquake record data with epicentral distance between 30°-90° from the receiver and magnitude 6 or more. The iterative time-domain deconvolution and receiver function migration techniques were applied to estimate the depth of Moho discontinuity and the presence of subducting slab. The depth of Moho discontinuity in West Sumatra, Jambi, and Riau Islands regions ranges from 21-39 km and generally deeper in the volcanic arc zone possibly due to the isostatic effect. Moho is at a depth of 21-29 km in the forearc zone, 36-39 km in the volcanic arc zone, and 30-36 km in the back-arc zone. Then the subducting slab was observed at a depth of 20 km under PPSI station to 200 km under MBBI station.

Depth Estimation of Moho Discontinuity Layer at 5 BMKG Seismic Stations in East Java Using Receiver Function Method

East Java is one of the areas with a high level of seismicity due to the existence of a subduction zone in the south of Java Island. In addition, there are also active faults and active volcanos in East Java. This study aims to determine the depth of the Moho Discontinuity layer and subduction slab using receiver function method based on the iterative time domain deconvolution. This study was conducted using teleseismic earthquake data with an epicenter distance of 30°–90° from the receiver station and magnitude more than 6 (M≥6). 5 BMKG seismic stations that form a straight line are used, including those in the Bawean Arc (BWJI), Rembang Zone (BAJI), Kendeng Zone (SIJM), Modern Mountain Arc (PPJI), Southern Mountain Zone (GEJI). The depth of the Moho Discontinuity layer at BWJI Station was observed in ranges from 36–38 km, at BAJI Station it ranges from 39–40 km, at SIJM Station it ranges from 39–40 km, at PPJI Station it ranges from 46–48 km, and at GEJI Station it ranges from 33–36 km. In general, the Moho Discontinuity layer in the mountainous region is deeper due to the isostasy effect.

Identification of Moho Discontinuity Depth and Subduction Slab in Bengkulu and South Sumatra Region using Receiver Function Method: A Preliminary Result

Bengkulu and South Sumatra regions are areas with high seismic activity due to faults and subduction zones. This study aims to analyze the depth of the Moho discontinuity layer and subduction slab under 4 BMKG seismic stations that form a perpendicular line of trench in the Bengkulu and South Sumatra areas. The distribution of stations used are Enggano Station (EGSI) in the front arc islands, Manna Station (MNAI) in the front arc basin, Pagar Alam Station (PKSI) in the volcanic-arc zone, and Lahat Station (LHSI) in the proto-volcanic zone. We selected teleseismic earthquake data with a distance of 30°-90° from the stations and magnitudes above 6 (M>6). For the identification of Moho and slab depths, we used analysis of receiver functions with iterative time domain deconvolution and migration of receiver functions with the AK-135 velocity model. The Oceanic Moho layer and the subduction slab under the EGSI Station were identified at depths of 34 km and 23 km respectively, under the MNAI Station the Moho layer and the subduction slab were identified at a depth of 18 km and 87 km respectively, under the PKSI Station the Moho layer and the subduction slab were identified at a depth of 34 km and 129 km respectively, and under the LHSI Station the Moho layer and subduction slab were identified at depths of 35 km and 175 km respectively.

Anisotropic Velocity Structure Beneath Shikoku, Japan: Insights From Receiver Function and Shear Wave Splitting Analyses

AbstractA combination of receiver function (RF) analysis and shear wave splitting can reveal the anisotropic properties of the Earth's velocity structure. The RF profile exhibits harmonic patterns partially generated from the discontinuities of anisotropic media near the receiver. The anisotropic properties are determined using splitting parameters, which include the fast polarization direction (FPD) and split time. We utilized the seismograms recorded by stations on Shikoku Island, Japan. Also, we applied the Bayesian information criterion to control the spike count of each RF, which consists of a series of spikes generated by time‐domain iterative deconvolution. Anisotropic differences arose between northern and southern regions along the 30‐km iso‐depth line of the top surface of the Philippine Sea Plate. In the southern part of Shikoku Island, the FPDs are sub‐perpendicular to the plunge of the subducting slab, while in the northern part, they are sub‐parallel to the plunge of the slab. Our results indicate that anisotropic strengths are weaker in the tectonic‐tremor band in northwestern Shikoku and stronger in the northern part of central and eastern Shikoku around the no tectonic‐tremor area. These anisotropic variations may characterize Shikoku Island’s geological structure.

Computational aspects of the equivalent-layer technique: review

Equivalent-layer technique is a powerful tool for processing potential-field data in the space domain. However, the greatest hindrance for using the equivalent-layer technique is its high computational cost for processing massive data sets. The large amount of computer memory usage to store the full sensitivity matrix combined with the computational time required for matrix-vector multiplications and to solve the resulting linear system, are the main drawbacks that made unfeasible the use of the equivalent-layer technique for a long time. More recently, the advances in computational power propelled the development of methods to overcome the heavy computational cost associated with the equivalent-layer technique. We present a comprehensive review of the computation aspects concerning the equivalent-layer technique addressing how previous works have been dealt with the computational cost of this technique. Historically, the high computational cost of the equivalent-layer technique has been overcome by using a variety of strategies such as: moving data-window scheme, column- and row-action updates of the sensitivity matrix, reparametrization, sparsity induction of the sensitivity matrix, iterative methods using the full sensitivity matrix, iterative deconvolution by using the concept of block-Toeplitz Toeplitz-block (BTTB) matrices and direct deconvolution. We compute the number of floating-point operations of some of these strategies adopted in the equivalent-layer technique to show their effectiveness in reducing the computational demand. Numerically, we also address the stability of some of these strategies used in the equivalent-layer technique by comparing with the stability via the classic equivalent-layer technique with the zeroth-order Tikhonov regularization. We show that even for the most computationally efficient methods, which can save up to 109 flops, the stability of the linear system is maintained. The two most efficient strategies, iterative and direct deconvolutions, can process large datasets quickly and yield good results. However, direct deconvolution has some drawbacks. Real data from Carajás Mineral Province, Brazil, is also used to validate the results showing a potential field transformation.

CRUSTAL THICKNESS BENEATH UTAKO ABUJA USING RECEIVER FUNCTION ANALYSIS

Understanding the Mohorovicc discontinuity (Moho depth) is crucial in unraveling the Earth’s subsurface structure. In this research, we present the report of the crustal thickness and the ratio of the primary wave to the shear wave velocities (p-to-s) beneath the seismic station located at the Nigerian Geological Survey Agency (NGSA) Abuja using Receiver Function Analysis (RFA). The primary objective of this study is to determine the depth of the Moho boundary and gain insights into the geological properties of the Earth’s crust and upper mantle beneath the receiver station. This analysis focused on teleseismic earthquakes that were recorded at the station between 2020 and 2021, with epicentere distances between 30o and 90o and magnitudes 5.5 or greater. The P wave Receiver Function (PRF) was modeled from iterative time domain deconvolution using the converted phases (Ps) at the Moho interface.

Unbiased CLEAN for STIX in Solar Orbiter

CLEAN is an iterative deconvolution method for radio and hard-X-ray solar imaging. In a specific step of its pipeline, CLEAN requires the convolution between an idealized version of the instrumental point-spread function (PSF), and a map collecting point sources located at positions from where most of the flaring radiation is emitted. This step has highly heuristic motivations and the shape of the idealized PSF, which depends on the user’s choice, impacts the shape of the reconstruction. This study introduces a user-independent release of CLEAN for image reconstruction from observations recorded by the Spectrometer/Telescope for Imaging X-rays (STIX) on board Solar Orbiter. Specifically, we show here that this unbiased release of CLEAN outperforms the standard version of the algorithm, with reconstructions in line with the ones offered by other imaging methods developed in the STIX framework.