Signal Processing - January 2017 - 57

recently, there have also emerged multipixel multiplexing-based
cameras that completely get rid of the lens and replace the lens
with a mask and computational reconstruction algorithms [2].

In essence, at F = Fmin we can obtain the measurement rate of
a full-frame sensor but using a device with potentially a fraction of the number of photodetectors. This can be invaluable
for sensing in many wavebands, for example, SWIR.
As a case study, consider an SMC with a DMD pattern rate R DMD = 10 kHz and an ADC with a sampling rate
R ADC = 10 MHz. Then, for a sensor with Fmin = 1, 000 pixels,
we can acquire 10 million measurements per second. An SPC, in
comparison, would acquire only 10,000 measurements per second. Consequently, multipixel SMCs can acquire videos at significantly higher spatial and temporal resolutions than an SPC.
There have been many multipixel extensions to the SPC
concept. The simplest approach [46] maps the DMD to a
low-resolution sensor array, as opposed to a single photodetector, such that each pixel on the sensor observes a nonoverlapping
patch or a block of micromirrors on the DMD. SMCs based on
this design have been proposed for sensing in the visible [78],
SWIR [19], and MWIR [54]. Figure 2 shows an example of
the increased measurement rates offered by the LiSens camera
[78], which uses a linear array of 1,024 photodetectors. More

TMCs
TMCs apply CS multiplexing in time to boost the temporal resolution of videos obtained from sensor arrays with low temporal resolution. Again, let V [x, y, t] be a three-dimensional (3-D)
signal representing a time-varying scene. Due to the assumed
low frame rate of the sensor, we obtain a scene measurement
once every T seconds, where T is too large. If the SLM has an
operational speed of one pattern every TSLM seconds, then each
measurement of a TMC takes the form of a coded image:
y [x, y, t 0] =

C-1

/ z [x, y, j] V [x, y, t 0 + jTSLM],

j=0

where z [x, y, j] is the attenuation pattern on the SLM at spatial
location (x, y) and time jTSLM. Here, each coded image measured by the TMC multiplexes C frames of the high-speed

107

Relay Lens

SPC

RADC

Objective
Lens
DMD

105
104
100

∗R

DM

D

106

F

Measurement Rate

108

Fmin

Line
Sensor

102
104
Number of Pixels F
(a)

(b)

LiSens

SPC
64 × 64

128 × 128

256 × 256

Capture Duration
0.11 s
0.88 s

768 × 1,024

Cylindrical Lens

106

(c)

FIGURE 2. The multipixel SMCs support significantly higher sensing rates than an SPC. (a) The measurement rate as a function of the number of sensor
pixels. An optimized SMC with F min pixels delivers the highest possible measurement rate. (b) Lab prototypes of the SPC and LiSens cameras, each placed
on the one arm of a single DMD. The measurement rate of the LiSens camera is nearly 1 MHz, while that of the SPC is 20 kHz. (c) Comparisons between
LiSens, which uses 1,024 sensor pixels, and an SPC for a static scene. Each row corresponds to a different capture duration, defined as the total amount
of time that the cameras have for acquiring compressive measurements. The larger measurement rate of the LiSens camera enables it to sense scenes
with very high spatial resolution even for small capture durations. (Photos courtesy of [78].)

IEEE SIgnal ProcESSIng MagazInE

|

January 2017

|

57
Table of Contents for the Digital Edition of Signal Processing - January 2017
