Signal Processing - September 2016 - 11

470 nm

497 nm

524 nm

551 nm

578 nm

605 nm

632 nm

578 nm

605 nm

632 nm

578 nm

605 nm

632 nm

(a)
470 nm

497 nm

524 nm

551 nm

(b)
497 nm

524 nm

551 nm

dror Baron

470 nm

(c)

Figure 3. Images at wavelengths 470-632 nm within image cubes were reconstructed by the new algorithms from North Carolina State University and
the University of Delaware. (a) represents the ground truth, (b) shows the output of the new algorithm, and (c) shows the output of the other algorithm.

it may consume approximately one or two
megabytes of memory or storage space.
Yet, a hyperspectral image file might be
several orders of magnitude larger, making data storage and file transmission
cumbersome, inconvenient, or, in some
instances, completely impractical. Furthermore, capturing hyperspectral images
across dozens of wavelengths is currently a time-consuming process, requiring
conventional imaging technology to snap
a series of images-each capturing a different suite of wavelengths or subsets of
pixels with their corresponding wavelengths-and then combining the images
into a single file. A final hyperspectral
image is actually an image cube comprised of a collection of images (slices),
where each two-dimensional image depicts one wavelength.
Earlier this year, researchers at North
Carolina State University and the University of Delaware announced the creation
of an algorithm that works with a popular
compressive spectral imager to quickly
acquire and accurately reconstruct hyperspectral images in less time and then
store those images using less memory.
According to researcher Dror Baron, an
assistant professor of electrical and computer engineering at North Carolina State

University, the coded aperture snapshot
spectral imager (CASSI) used in the research can acquire image data from different wavelengths simultaneously,
which significantly accelerates the imaging process. Recognizing that CASSI
provides significant improvements in
both imaging quality and acquisition
speed over conventional spectral imaging
techniques, the researchers worked to
further improve the system by accelerating the three-dimensional (3-D) image
cube reconstruction process. They began
by turning to an approximate message
passing (AMP) framework.
"Our proposed AMP-3-D-Wiener used
an adaptive Wiener filter as a 3-D image
denoiser within the AMP framework,"
Baron notes. "AMP-3-D-Wiener was faster than existing image cube reconstruction
algorithms and also achieved better reconstruction quality" (Figure 3).
"A big challenge was that AMP typically converts a noisy linear inverse problem where an unknown signal is observed
through multiplying it by a matrix and adding noise into a much simpler problem
where noise is added directly to the signal,"
Baron explains. The noise getting added to
the signal in the new problem is supposed
to be Gaussian and independent of the
IEEE Signal Processing Magazine

September 2016

signal. "However," Baron notes, "AMP has
these properties when the matrix is well
behaved, and, in our hyperspectral system,
the matrix was very poorly behaved." This
meant that the noise added to the signal in
the new problem was not Gaussian and
was also statistically dependent on the signal. "Therefore, we had to make some
changes to the algorithm that gave a more
desired performance."
"We were able to reconstruct image
quality in 100 seconds of computation
that other algorithms couldn't match in
450 seconds," Baron states. He's confident that computational time can be even
further reduced.
The researchers' next step, Baron says,
is to run the algorithm in a real-world system to gain insights into how the algorithm
functions and identify potential room for
improvement. "We're also considering
how we could modify both the algorithm
and the hardware to better compliment
each other," Baron says.

Author
John Edwards (jedwards@john
edwardsmedia.com) is a technology writer based in the Phoenix, Arizona, area.

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http://www.edwardsmedia.com

Table of Contents for the Digital Edition of Signal Processing - September 2016