Signal Processing - September 2016 - 96

into the optical path [30]-[32], [48]. These methods all capfrom detailed spectra, acquisition systems for precise spectral
ture fewer measurements than full-sampling schemes and
measurements can be effective tools for scientific research
reconstruct spectra from incomplete data with the aid of
and engineering applications. For instance, spectral data can
regularized reconstruction theory (e.g., utilizing knowledge
greatly facilitate cancer detection and diagnosis, since certain
of signal sparsity in some basis).
types of cancer cells have spectral characteristics that differ
A diagram of several coded-aperture-based undersamfrom those of normal cells [1]. Spectral data can also yield a
pling snapshot schemes is shown in Figure 1. For better visurich set of features for image analysis. To take advantage of
alization, the target 3-D spectral data cube (x, y, m) is shown
this, spectral capture technology has become widely used in
military security, environmental monitoring, biological sciusing a two-dimensional (2-D) matrix representing both the
ences, medical diagnostics, scientific observation, and many
spatial (x) domain and the spectral (m) domain. Such a highother fields [1]-[7].
dimensional spectral data cube is not possible to capture in
Studies in spectrum acquisition have been conducted for
a single exposure using prevalent camera sensors. This has
decades. Early spectrometers acquire only a single beam of
motivated the aforementioned undersampling systems that
light at a time, which significantly limfirst capture a low-dimensional projection
its their utility for measuring full scenes.
of the original high-dimensional spectral
Since various material
Later work focused on efficient, high resodata. The projection process can be repand object properties can
lution capture of both the spectral and sparesented as a sensing matrix that projects
be inferred from detailed
tial dimensions. Recently, breakthroughs
the spectral and spatial information into a
spectra, acquisition
in temporal resolution have been achieved,
low-dimensional measurement, which is
which enable simultaneous acquisition of
then computationally decoded. To multisystems for precise
dynamic scenes in the spatial, temporal
plex the spectral and spatial information
spectral measurements
and spectral dimensions [8]-[10].
in a solvable manner, as shown in Figure 1,
can be effective tools for
Traditional sampling methods [11]-[17],
the coded aperture-based undersampling
scientific research and
which are based on the Nyquist-Shannon
schemes usually manipulate the original
engineering applications.
sampling theorem, measure the signal at a
data matrix in two ways: shearing and
certain constant sampling rate on each of
spatial modulation. These two transforms
the three dimensions. Each sample contains the signal inforeffectively reorganize the entries of the data matrix and are
mation at a single sampling location, time and wavelength.
operable in practice (shearing by a prism or diffraction gratSampling multispectral images in all three spatiospectral
ing, and spatial modulation by an occlusion mask, spatial light
dimensions requires measurement at a massive scale, and thus
modulator, or digital micromirror device).
making full-sampling schemes, such as those based on scanDepending on their optical configurations and exploiting
ning or interferometry, impractical in this scenario. That is
statistical properties of the spectrum data, the aforementioned
because scanning a scene on either the spatial dimension or
methods employ different sampling strategies, which result in
the spectral dimension entails a major sacrifice in the temporal
different sensing performance. In fact, the sampling scheme
sampling rate. As a result, a full-sampling approach can only
of a multispectral acquisition system has a significant effect
be applied in practice on static or slow-moving scenes.
on the reconstruction quality of spectra. On the other hand,
Capitalizing on recent advances in compressive sensin spectrometer design, sampling is also determined by the
ing theory, several techniques have been developed based
spectrometer optics and practical issues (e.g., calibration).
on undersampling and constrained reconstruction, such as
With the optical design flexibility that is possible through the
computed tomography imaging spectrometry (CTIS) [18]
combination of optical elements (e.g., gratings and prisms) and
and coded aperture snapshot imaging (CASSI). Within
computational elements (e.g., spatial light modulators or digital
the CASSI paradigm, there are single dispersive CASSI
micromirror devices), we posit that the effectiveness and effi[19], dual dispersive CASSI [20], [21], its dual-coded threeciency of the sampling scheme should become the principal
dimensional (3-D) version called the dual-coded snapshot
factor in the design of spectrometers.
imager (DCSI) [22], the colored 3-D version called the
Our intent in this article is to present a comprehensive discolored coded aperture spectral camera imager (CCASSI)
cussion and analysis of existing coded aperture-based multi[23]-[25], [47], prism-mask video imaging spectrometry
spectral snapshot systems, and link them to different sampling
(PMVIS) [26], [27], and single pixel camera spectrometry
schemes from the signal processing perspective. For each of
(SPCS) [28]. The aforementioned systems are all snapshot
these coded aperture-based undersampling schemes, efficienmultispectral cameras, which means that the spectral data
cy is examined based on the spectral sensing coherence inforare measured in a single exposure (shot) on the camera senmation between its sensing matrix and sparse spectral bases
sor. There are also other systems that capture multispectral
constructed from a multispectral image data set. In addition,
data at video rates, but with more than one measurement
the optical properties of the spectrometers, i.e., light throughper frame, by taking advantage of a rapidly varying optical
put, noise tolerance, feasibility, and complexity, are discussed
element such as a spatial light modulator (SLM) or digital
as well. We hope that these analyses and discussions not only
micromirror device (DMD), or by adding another camera
provide readers with fresh insight on multispectral imaging,
96

IEEE SIgnal ProcESSIng MagazInE

September 2016

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