# Direct Sampling Method for Diffusive Optical Tomography

@article{Chow2015DirectSM, title={Direct Sampling Method for Diffusive Optical Tomography}, author={Yat Tin Chow and Kazufumi Ito and Keji Liu and Jun Zou}, journal={SIAM J. Sci. Comput.}, year={2015}, volume={37} }

In this work, we are concerned with the diffusive optical tomography (DOT) problem in the case when only one or two pairs of Cauchy data is available. We propose a simple and efficient direct sampling method (DSM) to locate inhomogeneities inside a homogeneous background and solve the DOT problem in both full and limited aperture cases. This new method is easy to implement and less expensive computationally. Numerical experiments demonstrate its effectiveness and robustness against noise in the… Expand

#### 30 Citations

Learn an index operator by CNN for solving diffusive optical tomography: a deep direct sampling method

- Mathematics, Computer Science
- 2021

A deep direct sampling method (DDSM) to recover the inhomogeneous inclusions buried in a homogeneous background is developed and a convolutional neural network (CNN) is designed to approximate the index functional that mimics the underling mathematical structure. Expand

Locating small inclusions in diffuse optical tomography by a direct imaging method

- Physics
- 2020

Optical tomography is a typical non-invasive medical imaging technique, which aims to reconstruct geometric and physical properties of tissues by passing near infrared light through tissues for… Expand

Regularization of the factorization method applied to diffuse optical tomography

- Mathematics, Physics
- Inverse Problems
- 2021

In this paper, we develop a new regularized version of the factorization method for positive operators mapping a complex Hilbert space into it is dual space. The factorization method uses Picard’s… Expand

Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements

- Mathematics
- Computation
- 2021

In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a… Expand

Two effective post-filtering strategies for improving direct sampling methods

- Mathematics
- 2017

In this paper, we introduce two novel strategies to reduce artifacts in the direct sampling type methods (DSM). The newly proposed techniques can essentially reduce the artifacts and provide more… Expand

Direct sampling method for identifying magnetic inhomogeneities in limited-aperture inverse scattering problem

- Mathematics, Computer Science
- Comput. Math. Appl.
- 2020

It is demonstrated that the indicator function of DSM can be represented by an infinite series of Bessel functions of integer order and correspondingly examine various properties of DSM. Expand

Monostatic sampling methods in limited-aperture configuration

- Mathematics, Computer Science
- ArXiv
- 2021

This paper develops MSM in limited-aperture configuration and derive an asymptotic formula of the corresponding indicator function and proposes a modified numerical scheme with multi-frequency measurements that improve imaging performance, especially for small anomalies. Expand

Direct sampling method for imaging small anomalies: real-data experiments

- Mathematics
- 2018

In this paper, a direct sampling method (DSM) is designed for a real-time detection of small anomalies from scattering parameters measured by a small number of dipole antennas. Applicability of the… Expand

Application and analysis of direct sampling method in real-world microwave imaging

- Computer Science, Mathematics
- Appl. Math. Lett.
- 2019

Applicability of the DSM is theoretically demonstrated by proving that its indicator function can be represented in terms of an infinite series of Bessel functions of integer order, Hankel function of order zero, and the antenna configurations. Expand

Direct sampling method for anomaly imaging from scattering parameter

- Mathematics, Computer Science
- Appl. Math. Lett.
- 2018

A direct sampling method (DSM) is designed for imaging an anomaly and establishing a relationship between the indicator function of DSM and an infinite series of Bessel functions of integer order. Expand

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