Phase space measurement with forward modeling is one approach to address the scattering issue in biomedical imaging.
Scattering
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
is one of the biggest problems in biomedical imaging, given that scattered light is eventually defocused, thus resulting in diffused images.
[Elizabeth M. C. Hillman et al., (2007]
"Optical brain imaging in vivo: techniques and applications from animal to man"
/ref> Instead of removing the scattered light, this approach uses the information of scattered light to reconstruct the original light signals. This approach requires the phase space data of light in imaging system and a forward model to describe scattering events in a turbid medium. Phase space of light can be obtained by using digital micromirror device
The digital micromirror device, or DMD, is the microoptoelectromechanical system (MOEMS) that is the core of the trademarked DLP projection technology from Texas Instruments (TI). Texas Instrument's DMD was created by solid-state physicist and ...
(DMD)[Liu et al., 201]
"3D imaging in volumetric scattering media using phase-space measurements"
/ref> or light field microscopy.[Pegard et al., 201]
"Compressive light-field microscopy for 3D neural activity recording"
/ref> Phase space measurement with forward modeling can be used in neuroscience to record neuronal activity in the brain.
Concepts
Phase space of light is used to delineate the space and spatial frequency of light.[''M.J.Bastiaans et al., 2009 ]
Wigner distribution function applied to optical signals and systems"
/ref> As light propagates or scatters it will change its phase space as well. For example, as the position of light changes while staying in the same angle, simple propagation of light will shear the phase space of light. For scattering, since it diverges the light angle, the phase will be broadened after scattering. Therefore, scattering, and propagation of light can be modeled by the Wigner function which can generally describe light in wave optics. With a forward model to describe the propagation and scattering event in a scattering tissue, such as brain, a light field of a surface from point sources in a tissue can be estimated. To find the location of point sources of a target in a scattering medium, first, a light field of whole targets should be measured. Then simulated intensity plane is made by a phase space with all possible coordinates that may account for measured phase space. By applying optimization process with the non-negative least squares
In mathematical optimization, the problem of non-negative least squares (NNLS) is a type of constrained least squares problem where the coefficients are not allowed to become negative. That is, given a matrix and a (column) vector of response vari ...
and a sparsity constraint, a sparse vector set that would correspond to the locations of targets of interest would be obtained by getting rid of non-possible options.
An example of using a forward model for scattering events in a turbid medium
The Wigner quasiprobability distribution
The Wigner quasiprobability distribution (also called the Wigner function or the Wigner–Ville distribution, after Eugene Wigner and Jean-André Ville) is a quasiprobability distribution. It was introduced by Eugene Wigner in 1932 to study quan ...
can be used for a forward model
(1)
Eventually, scattering and propagation of light can be described as
(2)
The weight sum of decomposed contribution is
(3)
where is an coefficient that represents the intensity of light from a point source at the location
To obtain a sparse vector set , solve the lasso
A lasso ( or ), also called lariat, riata, or reata (all from Castilian, la reata 're-tied rope'), is a loop of rope designed as a restraint to be thrown around a target and tightened when pulled. It is a well-known tool of the Spanish an ...
problem
(4)
where is the actual measured phase space and is an arbitrary coefficient that favors sparsity.
Application
Phase space measurement with forward modeling can be used in neuroscience to record neuronal activity in the brain. Researchers have been widely using two-photon scanning microscopy to visualize neurons and their activity by imaging fluorescence emitted from calcium indicators expressed in neurons. However, two-photon excitation microscopy
Two-photon excitation microscopy (TPEF or 2PEF) is a fluorescence imaging technique that allows imaging of living tissue up to about one millimeter in thickness, with 0.64 μm lateral and 3.35 μm axial spatial resolution. Unlike traditional flu ...
is slow, because it has to scan all the pixels one by one in the target of interest. One advantage of using Phase space measurement with forward modeling is fast, which largely depends on the speed of camera being used. A light field camera can capture an image with all the pixels in one frame at a time to speed up the frame rate of their system. This feature can facilitate voltage imaging in the brain to record action potentials.
References
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Medical imaging