<< Chapter < Page Chapter >> Page >
Aerial view of the single-pixel camera in the lab.

The single-pixel design reduces the required size, complexity, and cost of the photon detector array down to a single unit, which enables the use of exotic detectors that would be impossible in a conventional digital camera. Example detectors include a photomultiplier tube or an avalanche photodiode for low-light (photon-limited) imaging, a sandwich of several photodiodes sensitive to different light wavelengths for multimodal sensing, a spectrometer for hyperspectral imaging, and so on.

In addition to sensing flexibility, the practical advantages of the single-pixel design include the facts that the quantum efficiency of a photodiode is higher than that of the pixel sensors in a typical CCD or CMOS array and that the fill factor of a DMD can reach 90% whereas that of a CCD/CMOS array is only about 50%. An important advantage to highlight is that each CS measurement receives about N / 2 times more photons than an average pixel sensor, which significantly reduces image distortion from dark noise and read-out noise.

The single-pixel design falls into the class of multiplex cameras. The baseline standard for multiplexing is classical raster scanning, where the test functions { φ j } are a sequence of delta functions δ [ n - j ] that turn on each mirror in turn. There are substantial advantages to operating in a CS rather than raster scan mode, including fewer total measurements ( M for CS rather than N for raster scan) and significantly reduced dark noise. See  [link] for a more detailed discussion of these issues.

[link] (a) and (b) illustrates a target object (a black-and-white printout of an “R”) x and reconstructed image x ^ taken by the single-pixel camera prototype in [link] using N = 256 × 256 and M = N / 50 [link] . [link] (c) illustrates an N = 256 × 256 color single-pixel photograph of a printout of the Mandrill test image taken under low-light conditions using RGB color filters and a photomultiplier tube with M = N / 10 . In both cases, the images were reconstructed using total variation minimization, which is closely related to wavelet coefficient 1 minimization   [link] .

Sample image reconstructions from single-pixel camera. (a) 256 × 256 conventional image of a black-and-white “R”. (b) Image reconstructed from M = 1300 single-pixel camera measurements ( 50 × sub-Nyquist). (c) 256 × 256 pixel color reconstruction of a printout of the Mandrill test image imaged in a low-light setting using a single photomultiplier tube sensor, RGB color filters, and M = 6500 random measurements.

Discrete formulation

Since the DMD array is programmable, we can employ arbitrary test functions φ j . However, even when we restrict the φ j to be { 0 , 1 } -valued, storing these patterns for large values of N is impractical. Furthermore, as noted above, even pseudorandom Φ can be computationally problematic during recovery. Thus, rather than purely random Φ , we can also consider Φ that admit a fast transform-based implementation by taking random submatrices of a Walsh, Hadamard, or noiselet transform  [link] , [link] . We will describe the Walsh transform for the purpose of illustration.

We will suppose that N is a power of 2 and let W log 2 N denote the N × N Walsh transform matrix. We begin by setting W 0 = 1 , and we now define W j recursively as

W j = 1 2 W j - 1 W j - 1 W j - 1 - W j - 1 .

This construction produces an orthonormal matrix with entries of ± 1 / N that admits a fast implementation requiring O ( N log N ) computations to apply. As an example, note that

W 1 = 1 2 1 1 1 - 1


W 2 = 1 2 1 1 1 1 1 - 1 1 - 1 1 1 - 1 - 1 1 - 1 - 1 1 .

We can exploit these constructions as follows. Suppose that N = 2 B and generate W B . Let I Γ denote a M × N submatrix of the identity I obtained by picking a random set of M rows, so that I Γ W B is the submatrix of W B consisting of the rows of W B indexed by Γ . Furthermore, let D denote a random N × N permutation matrix. We can generate Φ as

Φ = 1 2 N I Γ W B + 1 2 D .

Note that 1 2 N I Γ W B + 1 2 merely rescales and shifts I Γ W B to have { 0 , 1 } -valued entries, and recall that each row of Φ will be reshaped into a 2-D matrix of numbers that is then displayed on the DMD array. Furthermore, D can be thought of as either permuting the pixels or permuting the columns of W B . This step adds some additional randomness since some of the rows of the Walsh matrix are highly correlated with coarse scale wavelet basis functions — but permuting the pixels eliminates this structure. Note that at this point we do not have any strict guarantees that such Φ combined with a wavelet basis Ψ will yield a product Φ Ψ satisfying the restricted isometry property , but this approach seems to work well in practice.

Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where is the latest information on a no technology how can I find it
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
why its coecients must have a power-law rate of decay with q > 1/p. ?
Nader Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now

Source:  OpenStax, Introduction to compressive sensing. OpenStax CNX. Mar 12, 2015 Download for free at http://legacy.cnx.org/content/col11355/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introduction to compressive sensing' conversation and receive update notifications?