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The aim of electrical impedance tomography is to reconstruct the admittivity distribution inside a physical body from boundary measurements of current and voltage. Due to the severe ill-posedness of the underlying inverse problem, the…
We consider the imaging of cosmic strings by using Cosmic Microwave Background (CMB) data. Mathematically, we study the inversion of an X-ray transform in Lorentzian geometry, called the light ray transform. The inverse problem is highly…
We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced…
The paper studies an imaging problem in the diffusive ultrasound-modulated bioluminescence tomography with partial boundary measurement in an anisotropic medium. Assuming plane-wave modulation, we transform the imaging problem to an inverse…
Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the…
Increasingly in medical imaging has emerged an issue surrounding the reconstruction of noisy images from raw measurement data. Where the forward problem is the generation of raw measurement data from a ground truth image, the inverse…
This paper proposes a novel approach to reconstruct changes in a target conductivity from electrical impedance tomography measurements. As in the conventional difference imaging, the reconstruction of the conductivity change is based on…
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed…
This paper presents an iterative inversion algorithm for computed tomography image reconstruction that performs well in terms of accuracy and speed using limited data. The computational method combines an image domain technique and…
Magneto-acousto-electrical tomography (MAET), a combination of ultrasound imaging and electrical impedance tomography (EIT), offers both high resolution (in comparison to EIT) and high contrast (in comparison to ultrasound imaging). It is…
In this paper we consider the mathematical model of thermo- and photo-acoustic tomography for the recovery of the initial condition of a wave field from knowledge of its boundary values. Unlike the free-space setting, we consider the wave…
The article deals with a classical inverse problem: the computation of the refractive index of a medium from ultrasound time-of-flight (TOF) measurements. This problem is very popular in seismics but also for tomographic problems in…
Over the years, the Invariant Scattering Transform (IST) technique has become popular for medical image analysis, including using wavelet transform computation using Convolutional Neural Networks (CNN) to capture patterns' scale and…
In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding…
Single photon emission computed tomography (SPECT) is a well established clinical tool for functional imaging. A limitation of current SPECT systems is the use of mechanical collimation, where only a small fraction of the emitted photons is…
In this article we study the inverse problem of thermoacoustic tomography (TAT) on a medium with attenuation represented by a time- convolution (or memory) term, and whose consideration is motivated by the modeling of ultrasound waves in…