# 6.6 Hyperspectral imaging  (Page 2/2)

 Page 2 / 2

## Dual disperser coded aperture snapshot spectral imager

The dual disperser coded aperture snapshot spectral imager (DD-CASSI), shown in [link] , is an architecture that combines separate multiplexing in the spatial and spectral domain, which is then sensed by a wide-wavelength sensor/pixel array, thus flattening the spectral dimension  [link] .

First, a dispersive element separates the different spectral bands, which still overlap in the spatial domain. In simple terms, this element shears the datacube, with each spectral slice being displaced from the previous by a constant amount in the same spatial dimension. The resulting datacube is then masked using the coded aperture, whose effect is to "punch holes" in the sheared datacube by blocking certain pixels of light. Subsequently, a second dispersive element acts on the masked, sheared datacube; however, this element shears in the opposite direction, effectively inverting the shearing of the first dispersive element. The resulting datacube is upright, but features "sheared" holes of datacube voxels that have been masked out.

The resulting modified datacube is then received by a sensor array, which flattens the spectral dimension by measuring the sum of all the wavelengths received; the received light field resembles the target image, allowing for optical adjustments such as focusing. In this way, the measurements consist of full sampling in the spatial $x$ and $y$ dimensions, with an aggregation effect in the spectral $\lambda$ dimension.

## Single disperser coded aperture snapshot spectral imager

The single disperser coded aperture snapshot spectral imager (SD-CASSI), shown in [link] , is a simplification of the DD-CASSI architecture in which the first dispersive element is removed  [link] . Thus, the light field received at the sensors does not resemble the target image. Furthermore, since the shearing is not reversed, the area occupied by the sheared datacube is larger than that of the original datacube, requiring a slightly larger number of pixels for the capture.

## Sparsity structures for hyperspectral datacubes

This sparsity structure assumes that the spectral signature for all pixels in a neighborhood is close to constant; that is, that the datacube is piecewise constant with smooth borders in the spatial dimensions. The complexity of an image is then given by the number of spatial dyadic squares with constant spectral signature necessary to accurately approximate the datacube; see [link] . A reconstruction algorithm then searches for the signal of lowest complexity (i.e., with the fewest dyadic squares) that generates compressive measurements close to those observed  [link] .

## Spatial-only sparsity

This sparsity structure operates on each spectral band separately and assumes the same type of sparsity structure for each band  [link] . The sparsity basis is drawn from those commonly used in images, such as wavelets, curvelets, or the discrete cosine basis. Since each basis operates only on a band, the resulting sparsity basis for the datacube can be represented as a block-diagonal matrix:

$\Psi =\left[\begin{array}{cccc}{\Psi }_{x,y}& \mathbf{0}& \cdots & \mathbf{0}\\ \mathbf{0}& {\Psi }_{x,y}& \cdots & \mathbf{0}\\ ⋮& ⋮& \ddots & ⋮\\ \mathbf{0}& \mathbf{0}& \cdots & {\Psi }_{x,y}\end{array}\right].$

## Kronecker product sparsity

This sparsity structure employs separate sparsity bases for the spatial dimensions and the spectral dimension, and builds a sparsity basis for the datacube using the Kronecker product of these two  [link] :

$\Psi ={\Psi }_{\lambda }\otimes {\Psi }_{x,y}=\left[\begin{array}{ccc}{\Psi }_{\lambda }\left[1,1\right]{\Psi }_{x,y}& {\Psi }_{\lambda }\left[1,2\right]{\Psi }_{x,y}& \cdots \\ {\Psi }_{\lambda }\left[2,1\right]{\Psi }_{x,y}& {\Psi }_{\lambda }\left[2,2\right]{\Psi }_{x,y}& \cdots \\ ⋮& ⋮& \ddots \end{array}\right].$

In this manner, the datacube sparsity bases simultaneously enforces both spatial and spectral structure, potentially achieving a sparsity level lower than the sums of the spatial sparsities for the separate spectral slices, depending on the level of structure between them and how well can this structure be captured through sparsity.

## Summary

Compressive sensing will make the largest impact in applications with very large, high dimensional datasets that exhibit considerable amounts of structure. Hyperspectral imaging is a leading example of such applications; the sensor architectures and data structure models surveyed in this module show initial promising work in this new direction, enabling new ways of simultaneously sensing and compressing such data. For standard sensing architectures, the data structures surveyed also enable new transform coding-based compression schemes.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!