# 6.6 Hyperspectral imaging

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This module provides an overview of architectures and methods for hyperspectral imaging using the ideas of compressive sensing.

Standard digital color images of a scene of interest consist of three components – red, green and blue – which contain the intensity level for each of the pixels in three different groups of wavelengths. This concept has been extended in the hyperspectral and multispectral imaging sensing modalities, where the data to be acquired consists of a three-dimensional datacube that has two spatial dimensions $x$ and $y$ and one spectral dimension $\lambda$ .

In simple terms, a datacube is a 3-D function $f\left(x,y,\lambda \right)$ that can be represented as a stacking of intensities of the scene at different wavelengths. An example datacube is shown in [link] . Each of its entries is called a voxel. We also define a pixel's spectral signature as the stacking of its voxels in the spectral dimension $f\left(x,y\right)={\left\{f\left(x,y,\lambda \right)\right\}}_{\lambda }$ . The spectral signature of a pixel can give a wealth of information about the corresponding point in the scene that is not captured by its color. For example, using spectral signatures, it is possible to identify the type of material observed (for example, vegetation vs. ground vs. water), or its chemical composition.

Datacubes are high-dimensional, since the standard number of pixels present in a digitized image is multiplied by the number of spectral bands desired. However, considerable structure is present in the observed data. The spatial structure common in natural images is also observed in hyperspectral imaging, while each pixel's spectral signature is usually smooth.

Compressive sensing (CS) architectures for hyperspectral imaging perform lower-dimensional projections that multiplex in the spatial domain, the spectral domain, or both. Below, we detail three example architectures, as well as three possible models to sparsify hyperspectral datacubes.

## Single pixel hyperspectral camera

The single pixel camera uses a single photodetector to record random projections of the light emanated from the image, with the different random projections being captured in sequence. A single pixel hyperspectral camera requires a light modulating element that is reflective across the wavelengths of interest, as well as a sensor that can record the desired spectral bands separately  [link] . A block diagram is shown in [link] .

The single sensor consists of a single spectrometer that spans the necessary wavelength range, which replaces the photodiode. The spectrometer records the intensity of the light reflected by the modulator in each wavelength. The same digital micromirror device (DMD) provides reflectivity for wavelengths from near infrared to near ultraviolet. Thus, by converting the datacube into a vector sorted by spectral band, the matrix that operates on the data to obtain the CS measurements is represented as

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

This architecture performs multiplexing only in the spatial domain, i.e. dimensions $x$ and $y$ , since there is no mixing of the different spectral bands along the dimension $\lambda$ .

how environment affect demand and supply of commodity ?
Wht at the criteria for market ?
Amos
what is difference between monitory policy and fiscal policy?
monetary policy is a policy thrust by National Govt(CBN) to influence government spending, purchase &taxes
Frank
necessity of economics
I will say want,choice,opportunity cost,scarcity,scale of preference
Alao
what is monopoly market.How price output are determined under monopoly market
bisham
b) Monopoly market is an impecfect market where s single firm having the innovation to produce a particular commodity.Prices are determined through output since there are no other competitive.
Frank
Monopoly market:firm has market power & does not respond to market price
Frank
Explain the process of price determination under perfect competition market with suitable diagram
Price determination under perfect competition via this process :firms have no market power to influence price rather firms respond to market price.
Frank
price is different from demand- demand is amount of commodity
demand is amount /quantity of commodity a potential buyer is willing to buy at a given price at market
Frank
demand is a desire of customer on commodity with the ability to pay it and willing to buy it at given price of commodity
Harika
demand is price of what
show that shortrun average cost
what is economics
what is money
Mbah
what is money
Mbah
Difine macro economics
agaba
money is a medium of exchange between goods and services,maybe inform of currency.
Wesonga
Economics is study of how human beings strive to satisfy numerous wants using limited available resources.
Wesonga
how do you find the maximum number of workers the firms should employ order to produce where there are increasing returns
Jane
what are implications of computing national income?.
agaba
pl
MUDASIRU
what is the formulae for calculating national income
MUDASIRU
it calculated by value added method
Praveen
classify the production units like agriculture, banking, transport etc
Praveen
money is anything that is generally acceptetable for human
Ogbaji
Estimate the net value added(NVA) at fixed cost by each industrial structure
Praveen
definition of unemployment
what are the causes of unemployment?
The main causes of unemployment are listed below. 1. Frictional unemployment 2. Cyclical unemployment 3. Structural unemployment
assani
We can also categorize the causes on a broader sense as: 1. Political and 2. Social cause As unemployeement root causes are embaded in this two.
Yonathan
would opportunity cost exist if there was no scarcity?
assani
yes just because the opportunity cost arose when there is Alternative to choose among the alternatives.
I am thinking that, if our resources were unlimited, then there wouldn't be any need to forgo some wants. Hence the inexistence if opportunity cost
assani
Politics
Job
politics has done what?
assani
consider time assani
Mary
I'm Emmanuel,...I taught the main cause is the change in gov't.
Emmanuel
...Lack of capital to set up a firm respectively
Emmanuel
🙈
Emmanuel
I would like to bring in Educational levels can also be the cause the cause of the problem respectively
Emmanuel
I think the main causes of unemployment is lack of INFRASTRUCTURAL DEVELOPMENT OVER POPULATION OVER DEPENDENT ON GOVERNMENT LACK OF SELF EMPOWERMENT...
ananti
lack of skills among the new generation is the serious issue.
Vishal
Where I come from , I don't see why education or personal aspects seem to do with unimployment, technically the motivation and eigerness in all works of live is there , dispite the cultural influence and physical bearriors;the thing we lacking is Government Support and open market ethics.
Joe
sorry about that-(repation). We have a over powering ethical political system that's displacing the marketing asspects of economy and causing large scale unemployment right across the board...
Joe
can someone Explain Expansionary Monetary Policy and Contractionary Monetary Policy Using one of the instrument of Monetary Policy? Please am kinda lost here?. ta
using a graph show the case of substitute and compliment goods
can anyone give me a simple explanation to Five Sector Macroeconomics?
Emmanuel
Can someone please define what economics is
economics simply is a social science subject that study human behavior.
dajan
economics is a social science which studies human behaviour as a relationship between ends and scarce means that has alternative uses
Alao
Can someone please tell me how to calculate GDP
Emmanuel
emmanual kapal to calculate GDP (Gross Domestic Product) has three method in calculating it (1)income approach (2) expenditure approach (3) value added method
Alao
thanks Alae
Emmanuel
u are welcome
Alao
in basic terms economics is revered to as battery system, it date back to when Men sees the need to exchange sapless goods and produce to gain , either wealth , basic necessities or to establish trading ties for personal benefit or social asspects in terms of coexistence and continuity, future .
Joe
what is the law of demand
keep other thing constant, when the price increases demand decrease when the price decreases demand increases of the commodity.
sj
all things being equal,quantity demanded decrease as price increase and increase as price decrease
Seth
there's practial joke to it ..." the higher the demand ; scarcity, increase in production and drop in quality"... quite the controversy - for example China vs Europe, United States and we are all boxed up in between somewhere...
Joe
Other thing remain constant the low price of commodity the high quantity of commodity and vice versa is true
Baraka
Explain Effective demand
What is effective demand
Anita
like Modi is in demand...best example of effective demand
Pranav
Don't get you
Anita
Anita you mean you don't get me or who?
Onyeking
level of demand that represents a real intention to purchase by people with the means to pay
Pranav
Difference between extinct and extici spicies
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
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