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Zilong Li

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Published work

15 published item(s)

preprint2026arXiv

GraphMAR: Geometry-Aware Graph Learning Framework for Spatially Adaptive CT Metal Artifact Reduction

Computed tomography (CT) metal artifact reduction (MAR) aims to reduce the severe streaking artifacts induced by metallic implants and other high-density objects. Effective MAR generally requires both accurate artifact localization and artifact removal. Sinogram-domain methods can exploit explicit geometric cues, such as metal traces, to identify metal-corrupted measurements, while requiring raw projection data, which is often unavailable in clinical and practical scenarios. Image-domain methods are more flexible and widely applicable, yet they usually lack comparable geometric guidance, limiting their ability to localize artifacts and leading to suboptimal results. To address this limitation, we propose GraphMAR, a geometry-aware learning framework for explicit artifact identification and spatially adaptive MAR in the image domain. The key idea is to introduce graph-based geometric modeling as an image-domain analogue of sinogram metal traces. Specifically, we first construct a geometric graph from the metal mask and derive a geometric density graph that coarsely localizes artifact-prone regions according to inter-implant geometry. We then design GraphMoE, a graph-routed mixture-of-experts module that builds a polar-coordinate artifact graph in feature space and adaptively routes different experts to different spatial regions for MAR. By aligning the learned routing maps with the geometric density graph, GraphMAR provides explicit and interpretable artifact localization while enabling region-adaptive artifact reduction. Experiments on both simulated and real-world datasets demonstrate that GraphMAR achieves superior MAR performance compared with existing methods. To the best of our knowledge, this is the first work to introduce graph-based modeling for CT MAR and to enable explicit artifact identification in the image domain, improving both restoration quality and interpretability.

preprint2023arXiv

CORE: Learning Consistent Ordinal REpresentations for Image Ordinal Estimation

The goal of image ordinal estimation is to estimate the ordinal label of a given image with a convolutional neural network. Existing methods are mainly based on ordinal regression and particularly focus on modeling the ordinal mapping from the feature representation of the input to the ordinal label space. However, the manifold of the resultant feature representations does not maintain the intrinsic ordinal relations of interest, which hinders the effectiveness of the image ordinal estimation. Therefore, this paper proposes learning intrinsic Consistent Ordinal REpresentations (CORE) from ordinal relations residing in groundtruth labels while encouraging the feature representations to embody the ordinal low-dimensional manifold. First, we develop an ordinal totally ordered set (toset) distribution (OTD), which can (i) model the label embeddings to inherit ordinal information and measure distances between ordered labels of samples in a neighborhood, and (ii) model the feature embeddings to infer numerical magnitude with unknown ordinal information among the features of different samples. Second, through OTD, we convert the feature representations and labels into the same embedding space for better alignment, and then compute the Kullback Leibler (KL) divergence between the ordinal labels and feature representations to endow the latent space with consistent ordinal relations. Third, we optimize the KL divergence through ordinal prototype-constrained convex programming with dual decomposition; our theoretical analysis shows that we can obtain the optimal solutions via gradient backpropagation. Extensive experimental results demonstrate that the proposed CORE can accurately construct an ordinal latent space and significantly enhance existing deep ordinal regression methods to achieve better results.

preprint2022arXiv

Estimation of the covariance structure from SNP allele frequencies

We propose two new statistics, V and S, to disentangle the population history of related populations from SNP frequency data. If the populations are related by a tree, we show by theoretical means as well as by simulation that the new statistics are able to identify the root of a tree correctly, in contrast to standard statistics, such as the observed matrix of F2-statistics (distances between pairs of populations). The statistic V is obtained by averaging over all SNPs (similar to standard statistics). Its expectation is the true covariance matrix of the observed population SNP frequencies, offset by a matrix with identical entries. In contrast, the statistic S is put in a Bayesian context and is obtained by averaging over pairs of SNPs, such that each SNP is only used once. It thus makes use of the joint distribution of pairs of SNPs. In addition, we provide a number of novel mathematical results about old and new statistics, and their mutual relationship.

preprint2015arXiv

Shadow of a dressed black hole and determination of spin and viewing angle

Shadows of black holes surrounded by an optically thin emitting medium have been extensively discussed in the literature. The Hioki-Maeda algorithm is a simple recipe to characterize the shape of these shadows and determine the parameters of the system. Here we extend their idea to the case of a dressed black hole, namely a black hole surrounded by a geometrically thin and optically thick accretion disk. While the boundary of the shadow of black holes surrounded by an optically thin emitting medium corresponds to the apparent photon capture sphere, that of dressed black holes corresponds to the apparent image of the innermost stable circular orbit. Even in this case, we can characterize the shape of the shadow and infer the black hole spin and viewing angle. The shape and the size of the shadow of a dressed black hole are strongly affected by the black hole spin and inclination angle. Despite that, it seems that we cannot extract any additional information from it. Here we study the possibility of testing the Kerr metric. Even with the full knowledge of the boundary of the shadow, those of Kerr and non-Kerr black holes are very similar and it is eventually very difficult to distinguish the two cases.

preprint2015arXiv

Shadows of CPR black holes and tests of the Kerr metric

We study the shadow of the Cardoso-Pani-Rico (CPR) black hole for different values of the black hole spin $a_*$, the deformation parameters $ε_3^t$ and $ε_3^r$, and the viewing angle $i$. We find that the main impact of the deformation parameter $ε_3^t$ is the change of the size of the shadow, while the deformation parameter $ε_3^r$ affects the shape of its boundary. In general, it is impossible to test the Kerr metric, because the shadow of a Kerr black hole can be reproduced quite well by a black hole with non-vanishing $ε_3^t$ or $ε_3^r$. Deviations from the Kerr geometry could be constrained in the presence of high quality data and in the favorable case of a black hole with high values of $a_*$ and $i$. However, the shadows of some black holes with non-vanishing $ε_3^r$ present peculiar features and the possible detection of these shadows could unambiguously distinguish these objects from the standard Kerr black holes of general relativity.

preprint2015arXiv

Testing SgrA$^*$ with the spectrum of its accretion structure

SgrA$^*$ is the supermassive black hole candidate at the center of the Galaxy and an ideal laboratory to test general relativity. Following previous work by other authors, we use the Polish doughnut model to describe an optically thin and constant angular momentum ion torus in hydrodynamical equilibrium and model the accretion structure around SgrA$^*$. The radiation mechanisms are bremsstrahlung, synchrotron emission, and inverse Compton scattering. We compute the spectrum as seen by a distant observer in Kerr and non-Kerr spacetimes and we study how an accurate measurement can constrain possible deviations form the Kerr solution. As in the case of emission from a thin accretion disk, we find a substantial degeneracy between the determination of the spin and of possible deviations from the Kerr geometry, even when the parameters of the ion torus are fixed. This means that this technique cannot independently test the nature of SgrA$^*$ even in the presence of good data and with the systematics under control. However, it might do it in combination with other measurements (black hole shadow, radio pulsar, etc.).

preprint2015arXiv

X-ray spectropolarimetric measurements of the Kerr metric

It is thought that the spacetime geometry around black hole candidates is described by the Kerr solution, but an observational confirmation is still missing. Today, the continuum-fitting method and the analysis of the iron K$α$ line cannot unambiguously test the Kerr paradigm because of the degeneracy among the parameters of the system, in the sense that it is impossible with current X-ray data to distinguish a Kerr black hole from a non-Kerr object with different values of the model parameters. In this paper, we study the possibility of testing the Kerr nature of black hole candidates with X-ray spectropolarimetric measurements. Within our simplified model that does not include the effect of returning radiation, we find that it is impossible to test the Kerr metric and the problem is still the strong correlation between the spin and possible deviations from the Kerr geometry. Moreover, the correlation is very similar to that of other two techniques, which makes the combination of different measurements not very helpful. Nevertheless, our results cannot be taken as conclusive and, in order to arrive at a final answer, the effect of returning radiation should be properly taken into account.

preprint2014arXiv

Constraining the spin and the deformation parameters from the black hole shadow

Within 5-10 years, very-long baseline interferometry (VLBI) facilities will be able to directly image the accretion flow around SgrA$^*$, the super-massive black hole candidate at the center of the Galaxy, and observe the black hole "shadow". In 4-dimensional general relativity, the no-hair theorem asserts that uncharged black holes are described by the Kerr solution and are completely specified by their mass $M$ and by their spin parameter $a$. In this paper, we explore the possibility of distinguishing Kerr and Bardeen black holes from their shadow. In Hioki & Maeda (2009), under the assumption that the background geometry is described by the Kerr solution, the authors proposed an algorithm to estimate the value of $a/M$ by measuring the distortion parameter $δ$, an observable quantity that characterizes the shape of the shadow. Here, we try to extend their approach. Since the Hioki-Maeda distortion parameter is degenerate with respect to the spin and possible deviations from the Kerr solution, one has to measure another quantity to test the Kerr black hole hypothesis. We study a few possibilities. We find that it is extremely difficult to distinguish Kerr and Bardeen black holes from the sole observation of the shadow, and out of reach for the near future. The combination of the measurement of the shadow with possible accurate radio observations of a pulsar in a compact orbit around SgrA$^*$ could be a more promising strategy to verify the Kerr black hole paradigm.

preprint2014arXiv

Constraints on the spacetime geometry around 10 stellar-mass black hole candidates from the disk's thermal spectrum

In a previous paper, one of us has described a code to compute the thermal spectrum of geometrically thin and optically thick accretion disks around generic stationary and axisymmetric black holes, which are not necessarily of the Kerr type. As the structure of the accretion disk and the propagation of electromagnetic radiation from the disk to the distant observer depend on the background metric, the analysis of the thermal spectrum of thin disks can be used to test the actual nature of black hole candidates. In this paper, we consider the 10 stellar-mass black hole candidates for which the spin parameter has been already estimated from the analysis of the disk's thermal spectrum and under the assumption of the Kerr background, and we translate the measurements reported in the literature into constraints on the spin parameter--deformation parameter plane. The analysis of the disk's thermal spectrum can be used to estimate only one parameter of the geometry close to the compact object, and therefore it is not possible to get independent measurements of both the spin and the deformation parameters. The constraints obtained here will be used in combination with other measurements in future work, with the final goal to break the degeneracy between the spin and possible deviations from the Kerr solution and thus test the Kerr black hole hypothesis.

preprint2014arXiv

Distinguishing black holes and wormholes with orbiting hot spots

The supermassive black hole candidates at the center of every normal galaxy might be wormholes created in the early Universe and connecting either two different regions of our Universe or two different universes in a Multiverse model. Indeed, the origin of these supermassive objects is not well understood, topological non-trivial structures like wormholes are allowed both in general relativity and in alternative theories of gravity, and current observations cannot rule out such a possibility. In a few years, the VLTI instrument GRAVITY will have the capability to image blobs of plasma orbiting near the innermost stable circular orbit of SgrA$^*$, the supermassive black hole candidate in the Milky Way. The secondary image of a hot spot orbiting around a wormhole is substantially different from that of a hot spot around a black hole, because the photon capture sphere of the wormhole is much smaller. The radius of the photon capture sphere is independent of the hot spot model, and therefore its possible detection, which is observationally challenging but not out of reach, can unambiguously test if the center of our Galaxy harbors a wormhole rather than a black hole.

preprint2014arXiv

Measuring the Kerr spin parameter of regular black holes from their shadow

In a previous paper, one of us has showed that, at least in some cases, the Kerr-nature of astrophysical black hole candidates is extremely difficult to test and current techniques, even in presence of excellent data not available today, cannot distinguish a Kerr black hole from a Bardeen one, despite the substantial difference of the two backgrounds. In this paper, we investigate if the detection of the "shadow" of nearby super-massive black hole candidates by near future mm/sub-mm very long baseline interferometry experiments can do the job. More specifically, we consider the measurement of the Kerr spin parameter of the Bardeen and Hayward regular black holes from their shadow, and we then compare the result with the estimate inferred from the K$α$ iron line and from the frequency of the innermost stable circular orbit. For non-rotating black holes, the shadow approach provides different values, and therefore the Kerr black hole hypothesis can potentially be tested. For near extremal objects, all the approaches give quite similar results, and therefore it is not possible to constrain deviations from the Kerr solution. The present work confirms that it is definitively challenging to test this kind of metrics, even with future facilities. However, the detection of a source that looks like a fast-rotating Kerr black hole can put meaningful constraints on the nature of the compact object.

preprint2014arXiv

Testing a class of non-Kerr metrics with hot spots orbiting SgrA$^*$

SgrA$^*$, the supermassive black hole candidate at the Galactic Center, exhibits flares in the X-ray, NIR, and sub-mm bands that may be interpreted within a hot spot model. Light curves and images of hot spots orbiting a black hole are affected by a number of special and general relativistic effects, and they can be potentially used to check whether the object is a Kerr black hole of general relativity. However, in a previous study we have shown that the relativistic features are usually subdominant with respect to the background noise and the model-dependent properties of the hot spot, and eventually it is at most possible to estimate the frequency of the innermost stable circular orbit. In this case, tests of the Kerr metric are only possible in combination with other measurements. In the present work, we consider a class of non-Kerr spacetimes in which the hot spot orbit may be outside the equatorial plane. These metrics are difficult to constrain from the study of accretion disks and indeed current X-ray observations of stellar-mass and supermassive black hole candidates cannot put interesting bounds. Here we show that near future observations of SgrA$^*$ may do it. If the hot spot is sufficiently close to the massive object, the image affected by Doppler blueshift is brighter than the other one and this provides a specific observational signature in the hot spot's centroid track. We conclude that accurate astrometric observations of SgrA$^*$ with an instrument like GRAVITY should be able to test this class of metrics, except in the more unlikely case of a small viewing angle.

preprint2014arXiv

Testing the nature of the supermassive black hole candidate in SgrA* with light curves and images of hot spots

General relativity makes clear predictions about the spacetime geometry around black holes. In the near future, new facilities will have the capability to explore the metric around SgrA$^*$, the supermassive black hole candidate at the Center of our Galaxy, and open a new window to test the Kerr black hole hypothesis. In this paper, we compute light curves and images associated with compact emission regions (hot spots) orbiting around Kerr and non-Kerr black holes. We study how the analysis of the properties of the radiation emitted by a hot spot can be used to test the Kerr nature of SgrA$^*$. We find that the sole observation of the hot spot light curve can at most constrain a combination of the black hole spin and of possible deviations from the Kerr solution. This happens because the same orbital frequency around a Kerr black hole can be found for a non-Kerr object with a different spin parameter. Second order corrections in the light curve due to the background geometry are typically too small to be identified. While the observation of the hot spot centroid track can potentially bound possible deviations from the Kerr solution, that is out of reach for the near future VLTI instrument GRAVITY. The Kerr black hole hypothesis could really be tested in the case of the discovery of a radio pulsar in a compact orbit around SgrA$^*$. Radio observations of such a pulsar would provide precise estimates of the mass and the spin of SgrA$^*$, and the combination of these measurements (probing the weak field) with the hot spot light curve information (probing the strong field) may constrain/find possible deviations from the Kerr solution with quite good precision.

preprint2013arXiv

Destroying the event horizon of regular black holes

Recently, several authors have studied the possibility of overspinning or overcharging an existing black hole to destroy its event horizon and make the central singularity naked. When all the effects are properly taken into account, any attempt to destroy the black hole seems to be doomed to fail, in agreement with the weak cosmic censorship conjecture. In this letter, we study the possibility of destroying the event horizon of regular black holes. These objects have no central singularity and therefore they are not protected by the cosmic censorship hypothesis. Our results strongly support the conclusion that regular black holes can be destroyed. If we believe that the central singularity in astrophysical black holes is solved by quantum gravity effects, we might have a chance to see the black hole's internal region and observe quantum gravity phenomena. As our finding implies the violation of the black hole's area theorem, the collision of two black holes may release an amount of energy exceeding the Hawking bound, which can be experimentally tested by gravitational wave detectors.

preprint2013arXiv

Super-spinning compact objects generated by thick accretion disks

If astrophysical black hole candidates are the Kerr black holes predicted by General Relativity, the value of their spin parameter must be subject to the theoretical bound $|a_*| \le 1$. In this work, we consider the possibility that these objects are either non-Kerr black holes in an alternative theory of gravity or exotic compact objects in General Relativity. We study the accretion process when their accretion disk is geometrically thick with a simple version of the Polish doughnut model. The picture of the accretion process may be qualitatively different from the one around a Kerr black hole. The inner edge of the disk may not have the typical cusp on the equatorial plane any more, but there may be two cusps, respectively above and below the equatorial plane. We extend previous work on the evolution of the spin parameter and we estimate the maximum value of $a_*$ for the super-massive black hole candidates in galactic nuclei. Since measurements of the mean radiative efficiency of AGNs require $η> 0.15$, we infer the "observational" bound $|a_*| \lesssim 1.3$, which seems to be quite independent of the exact nature of these objects. Such a bound is only slightly weaker than $|a_*| \lesssim 1.2$ found in previous work for thin disks.