A Learning Approach to Optical Tomography

Abstract

Optical tomography has been widely investigated for biomedical imaging applications. In recent years optical tomography has been combined with digital holography and has been employed to produce high-quality images of phase objects such as cells. In this paper we describe a method for imaging 3D phase objects in a tomographic configuration implemented by training an artificial neural network to reproduce the complex amplitude of the experimentally measured scattered light. The network is designed such that the voxel values of the refractive index of the 3D object are the variables that are adapted during the training process. We demonstrate the method experimentally by forming images of the 3D refractive index distribution of Hela cells.

Diffraction tomography with Fourier ptychography

“…Subsequent work should also examine connections between FPT, multi-slice-based techniques for ptychography [33,34], and machine learning for 3D reconstruction [54]. While prior work already specifies sample conditions under which the first Born [43] and multi-slice [42] approximations remain accurate, it is not yet clear if this translates directly to reconstructions that require phase retrieval.…”

Tomographic phase microscopy: principles and applications in bioimaging [Invited]

“…A BPM-based tomographic reconstruction model, proposed by Kamilov et al [43,48], allows considering multiple scattering events by dividing the object into multiple layers and subsequently forming an artificial neural network geometry to model the RI distribution. Therefore, the BPM reconstruction model applies to thicker or highly inhomogeneous biological objects.…”

“…Therefore, the BPM reconstruction model applies to thicker or highly inhomogeneous biological objects. Instead of using iterative phase retrieval [59,74], the RI reconstruction in [43,48] uses complex field measurements from a typical angle scanning TPM system [18]. In the following paragraphs, we briefly introduce the concepts of retrieving RI distributions using the BPM model.…”

“…For example, regularized ODT models that use sample priori information, such as non-negativity and piecewise smoothness, have been implemented to alleviate the missing cone issue in TPM [24,46,47]. In 2015, a new physical model, based on the beam propagation method (BPM) to treat light diffraction, was demonstrated for 3D RI reconstruction in TPM [43,48]. This work has pioneered the machine learning concept for TPM [49].…”

3D x-ray imaging of continuous objects beyond the depth of focus limit

“…To do so, we simulate the propagation of probe function illumination waves at various probe positions and incident angles through a present guess of the 3D object so as to produce a set of assumed intensity patterns to be recorded on a far-field detector; we then adjust the guess of the object so as to minimize the difference between the actual detector plane Fourier magnitudes against our present guess of the same. Such an approach has been used with learning algorithms to guide the object updates [31, 32], as well as with the imposition of a sparsity regularizer [33]. In our case, we use a newly-developed proximal alternating linearized minimization algorithm for finding the object, as will be discussed below.…”