Signal Processing - September 2016 - 97

Conventional
Camera

Modulation

Projection

λ
x

Modulation

Shearing

PMVIS

λ
x

SD-CASSI

Modulation
λ
x

3-D-CASSI
(CCASSI and DCSI)

DD-CASSI

Shearing

λ
x

Projection
λ

Shearing

Spatial Modulation
λ
x

Modulation

Projection
λ

Shearing
x

Shearing

λ
x

Projection

Spectral Modulation

Projection

Shearing
λ
x

Figure 1. Sensing matrices of existing sampling schemes for multispectral acquisition. The spectral and spatial data matrix is high dimensional,
and current camera sensors can capture only a low-dimensional projection of the spectral data. The projection process can be regarded as a sensing
matrix for the high-dimensional spectral data cube, and state-of-the-art computational multispectral imaging methods can be summarized as different
sensing matrices.

but also serve as guidance for designing new multispectral
cameras and conducting further study of existing methods.

Full-sampling systems
While mostly focusing on undersampling techniques for multispectral capture, we also paint a fuller picture of multispectral
imaging by first reviewing systems designed for full-sampling
schemes. Conventional multispectral image acquisition systems are generally based on the Nyquist-Shannon sampling
theorem, and thus they sample the signal at twice its maximal
frequency. Therefore, due to the considerable amount of data, a
sacrifice in either spatial or temporal resolution is needed for
these cameras. Such a sacrifice may make full-sampling
schemes less practical, thus motivating systems based on compressive measurements.
In spite of the low latency of capture, full-sampling methods for multispectral image acquisition have become widely
used in practice. We introduce the basic principles and analyze
the performance of full-sampling multispectral acquisition

systems in this section, including three conventional multispectral cameras: filter-based spectrometers, scanning spectrometers, and interferometry-based methods.
Filter-based spectrometers record a sequence of images
using a different color filter with each imaging exposure,
which effectively samples a set of full spatial resolution images
over the spectral range at the expense of temporal resolution.
These spectrometers can be easily implemented using a rotating wheel of gel filters, or electronically tunable filters that are
typically based on birefringent liquid crystal plates. The measurement scheme of filter-based spectrometers can be viewed
as spectral sampling over the temporal domain, with the spatial resolution fully preserved. In such a system, it is important
for the color filters to be fabricated with an antireflective coating, to minimize reductions in light throughput.
Instead of varying the filters temporally, scanning spectrometers sweep a spectral sensing device over the scene, sacrificing
temporal resolution to gain spatial resolution. Typically, scanning is performed in a whiskbroom or a pushbroom manner.

IEEE SIgnal ProcESSIng MagazInE

September 2016

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