Haiwen Zhang

Bo Zhang, Haiwen Zhang

This paper is concerned with a nonlinear imaging problem, which aims to reconstruct a locally perturbed, perfectly reflecting, infinite plane from intensity-only (or phaseless) far-field or near-field data. A recursive Newton iteration algorithm in frequencies is developed to reconstruct the locally rough surface from multi-frequency intensity-only far-field or near-field data, where the fast integral equation solver developed in [39] is used to solve the direct scattering problem in each iteration. For the case with far-field data, a main feature of our work is that the incident field is taken as a superposition of two plane waves with different directions rather than one plane wave, so the location and shape of the local perturbation of the infinite plane can be reconstructed simultaneously from intensity-only far-field data with multiple wave numbers. This is different from previous work on inverse scattering from phaseless far-field data, where only the shape reconstruction was considered due to the translation invariance property of the phaseless far-field pattern corresponding to one plane wave as the incident field. Finally, numerical examples are carried out to demonstrate that our reconstruction algorithm is stable and accurate even for the case of multiple-scale profiles.

Bo Zhang, Haiwen Zhang

This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field pattern or the phaseless far-field pattern generated by one plane wave as the incident field, which means that the location of the obstacle can not be recovered from such phaseless far-field data at a fixed frequency. It was recently proved in our previous work \cite{XZZ18} that the obstacle can be uniquely determined by the phaseless far-field patterns generated by infinitely many sets of superpositions of two plane waves with different directions at a fixed frequency if the obstacle is a priori known to be a sound-soft or an impedance obstacle with real-valued impedance function. The purpose of this paper is to develop a direct imaging algorithm to reconstruct the location and shape of the obstacle from the phaseless far-field data corresponding to infinitely many sets of superpositions of two plane waves with a fixed frequency as the incident fields. Our imaging algorithm only involves the calculation of the products of the measurement data with two exponential functions at each sampling point and is thus fast and easy to implement. Further, the proposed imaging algorithm does not need to know the type of boundary conditions on the obstacle in advance and is capable to reconstruct multiple obstacles with different boundary conditions. Numerical experiments are also carried out to illustrate that our imaging method is stable, accurate and robust to noise.

Haiwen Zhang, Bo Zhang

This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel integral equation formulation for the direct scattering problem which is defined on a bounded curve (consisting of a bounded part of the infinite plane containing the local perturbation and the lower part of a circle) with two corners. This novel integral equation can be solved efficiently by using the Nystrom method with a graded mesh introduced previously by Kress and is capable of dealing with large wavenumber cases. For the inverse problem, we propose a Newton iteration method to reconstruct the local perturbation of the plane from multiple frequency far-field data, based on the novel integral equation formulation. Numerical examples are carried out to demonstrate that our reconstruction method is stable and accurate even for the case of multiple-scale profiles.

Haiwen Zhang, Bo Zhang

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves from a penetrable and buried obstacles. By introducing a related transmission scattering problem, a Newton iteration method is proposed to simultaneously reconstruct both the penetrable interface and the buried obstacle inside from far-field data. A main feature of our method is that we do not need to know the type of boundary conditions on the buried obstacle. In particular, the boundary condition on the buried obstacle can also be determined simultaneously by the method. Finally, numerical examples using multi-frequency data are carried out to illustrate the effectiveness of our method.

Xiaoli Liu, Bo Zhang, Haiwen Zhang

This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and measured on a horizontal straight line segment at a finite distance above the rough surface. Theoretical analysis of the imaging algorithm is given for the case of a penetrable rough surface, but the imaging algorithm also works for impenetrable surfaces with Dirichlet or impedance boundary conditions. Numerical experiments are presented to show that the direct imaging algorithm is fast, accurate and very robust with respect to noise in the data.

Xiaoxu Xu, Bo Zhang, Haiwen Zhang

This paper is concerned with inverse scattering of plane waves by a locally perturbed infinite plane (which is called a locally rough surface) with the modulus of the total-field data (also called the phaseless near-field data) at a fixed frequency in two dimensions. We consider the case where a Dirichlet boundary condition is imposed on the locally rough surface. This problem models inverse scattering of plane acoustic waves by a one-dimensional sound-soft, locally rough surface; it also models inverse scattering of plane electromagnetic waves by a locally perturbed, perfectly reflecting, infinite plane in the TE polarization case. We prove that the locally rough surface is uniquely determined by the phaseless near-field data generated by a countably infinite number of plane waves and measured on an open domain above the locally rough surface. Further, a direct imaging method is proposed to reconstruct the locally rough surface from the phaseless near-field data generated by plane waves and measured on the upper part of the circle with a sufficiently large radius. Theoretical analysis of the imaging algorithm is derived by making use of properties of the scattering solution and results from the theory of oscillatory integrals (especially the method of stationary phase). Moreover, as a by-product of the theoretical analysis, a similar direct imaging method with full far-field data is also proposed to reconstruct the locally rough surface. Finally, numerical experiments are carried out to demonstrate that the imaging algorithm with phaseless near-field data and full far-field data are fast, accurate and very robust with respect to noise in the data.

Fenglong Qu, Haiwen Zhang

Consider the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with complex refractive index. We show that an approximate factorization method can be applied to reconstruct the support of the complex inhomogeneous medium from the far-field data. Numerical examples are also provided to illustrate the practicability of the inversion algorithm.

Xiaoli Liu, Bo Zhang, Haiwen Zhang

This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered near-field Cauchy data generated by point sources. A Helmholtz-Kirchhoff-type identity is derived and then used to provide a theoretical analysis of the direct imaging algorithm. Numerical experiments are presented to show that the direct imaging algorithm is fast, accurate and robust with respect to noise in the data.

Guanghui Hu, Xiaoli Liu, Bo Zhang et al.

This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface in a half plane. The elastic scattered field is measured on a horizontal straight line segment within a finite distance above the rough surface. A direct imaging algorithm is proposed to recover the unbounded rough surface from the scattered near-field data, which involves only inner products between the data. Numerical experiments are presented to show that the inversion scheme is not only efficient but also accurate and robust with respect to noise.

Haiwen Zhang, Zixi Yang, Yuanzhi Liu et al.

Currently, large vision-language models have gained promising progress on many downstream tasks. However, they still suffer many challenges in fine-grained visual understanding tasks, such as object attribute comprehension. Besides, there have been growing efforts on the evaluations of large vision-language models, but lack of in-depth study of attribute comprehension and the visual language fine-tuning process. In this paper, we propose to evaluate the attribute comprehension ability of large vision-language models from two perspectives: attribute recognition and attribute hierarchy understanding. We evaluate three vision-language interactions, including visual question answering, image-text matching, and image-text cosine similarity. Furthermore, we explore the factors affecting attribute comprehension during fine-tuning. Through a series of quantitative and qualitative experiments, we introduce three main findings: (1) Large vision-language models possess good attribute recognition ability, but their hierarchical understanding ability is relatively limited. (2) Compared to ITC, ITM exhibits superior capability in capturing finer details, making it more suitable for attribute understanding tasks. (3) The attribute information in the captions used for fine-tuning plays a crucial role in attribute understanding. We hope this work can help guide future progress in fine-grained visual understanding of large vision-language models.

Qiao Hu, Bo Zhang, Haiwen Zhang

The contrast source inversion (CSI) method and the subspace-based optimization method (SOM) are first proposed in 1997 and 2009, respectively, and subsequently modified. The two methods and their variants share several properties and thus are called the CSI-type methods. The CSI-type methods are efficient and popular methods for solving inverse medium scattering problems, but their rigorous convergence remains an open problem. In this paper, we propose two iteratively regularized CSI-type (IRCSI-type) methods with a novel $\ell_1$ proximal term as the iteratively regularized term: the iteratively regularized CSI (IRCSI) method and the iteratively regularized SOM (IRSOM) method, which have a similar computation complexity to the original CSI and SOM methods, respectively, and prove their global convergence under natural and weak conditions on the original objective function. To the best of our knowledge, this is the first convergence result for iterative methods of solving nonlinear inverse scattering problems with a fixed frequency. The convergence and performance of the two IRCSI-type algorithms are illustrated by numerical experiments.

Xinran Wang, Haiwen Zhang, Baoteng Li et al.

Object description plays an important role for visually impaired individuals to understand and compare the differences between objects. Recent multimodal large language models(MLLMs) exhibit powerful perceptual abilities and demonstrate impressive potential for generating object-centric descriptions. However, the descriptions generated by such models may still usually contain a lot of content that is not relevant to the user intent or miss some important object dimension details. Under special scenarios, users may only need the details of certain dimensions of an object. In this paper, we propose a training-free object description refinement pipeline, Dimension Tailor, designed to enhance user-specified details in object descriptions. This pipeline includes three steps: dimension extracting, erasing, and supplementing, which decompose the description into user-specified dimensions. Dimension Tailor can not only improve the quality of object details but also offer flexibility in including or excluding specific dimensions based on user preferences. We conducted extensive experiments to demonstrate the effectiveness of Dimension Tailor on controllable object descriptions. Notably, the proposed pipeline can consistently improve the performance of the recent MLLMs. The code is currently accessible at https://github.com/xin-ran-w/ControllableObjectDescription.

Xinran Wang, Muxi Diao, Baoteng Li et al.

The Controllable Image Captioning Agent (CapAgent) is an innovative system designed to bridge the gap between user simplicity and professional-level outputs in image captioning tasks. CapAgent automatically transforms user-provided simple instructions into detailed, professional instructions, enabling precise and context-aware caption generation. By leveraging multimodal large language models (MLLMs) and external tools such as object detection tool and search engines, the system ensures that captions adhere to specified guidelines, including sentiment, keywords, focus, and formatting. CapAgent transparently controls each step of the captioning process, and showcases its reasoning and tool usage at every step, fostering user trust and engagement. The project code is available at https://github.com/xin-ran-w/CapAgent.

Bo Zhang, Haiwen Zhang

It is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so the shape but not the location of the obstacle can be recovered from the phaseless far-field data. In this paper, it is proved that the translation invariance property of the phaseless far-field pattern can be broken if superpositions of two plane waves are used as the incident fields for all wave numbers in a finite interval. Based on this, a recursive Newton-type iteration algorithm in frequencies is then developed to recover both the location and the shape of the obstacle simultaneously from multi-frequency phaseless far-field data. Numerical examples are also carried out to illustrate the validity of the approach and the effectiveness of the inversion algorithm.