Rapid Light Flash Localization in SWIR using Compressed Sensing

Andreas Brorsson

, Carl Br

annlund

, David Bergstr

and David Gustafsson

FOI - Swedish Defence Research Agency, C4ISR , Link

oping, Sweden

Keywords:

Compressive Sensing, CS, Single Pixel Imaging, Flash Localization,Single Pixel Target, SWIR, Total

Variation, Muzzle Flash.

Abstract:

A high-resolution single pixel camera for long range imaging in the short-wave infrared has been evaluated

for the detection and localization of transient light ﬂashes. The single pixel camera is based on an InGaAs

photodiode with a digital micromirror device operating as a coded aperture. Images are reconstructed using

compressed sensing theory, with Walsh-Hadamard pseudo-random measurement matrices and fast Walsh-

Hadamard transform for localization. Our results from experiments with light ﬂashes are presented and the

potential use of the camera for muzzle ﬂash detection and localization is discussed.

1 INTRODUCTION

The primary signal modalities used to detect snipers

are acoustic signal, optical signal from the muzzle

ﬂash (visual and IR) and pre-shot laser retro-reﬂection

from the optical sight. In the visual spectrum, the

muzzle ﬂash can be extremely weak and hard to de-

tect, especially in daylight and in particular with sig-

nature suppressors mounted. The MWIR range (3

- 5 µm) would therefore be seen as the best choice

for a hostile ﬁre indication (HFI) system (Trzaskawka

et al., 2010; Kastek et al., 2011). The MWIR range

is however associated with larger size, weight, power

requirements and cost (e.g. higher SWaP-C). Systems

operating in the short-wave infrared (SWIR) bands

0.8 - 1.7 µm and 1.1 - 2.5 µm have advantages of po-

tentially lower SWaP-C. The former SWIR band is

usually preferred due to the availability of uncooled

InGaAs FPAs in this spectral range. An example of

the spectral distribution of a 50 caliber gun and im-

ages of a sniper riﬂe at 1000 meters in SWIR and

MWIR can be seen in Figure 1.

This paper presents an initial concept of an HFI

and sniper sight optics detection system, using Com-

pressive sensing (CS) and a low cost single pixel cam-

era (SPC) with a background subtraction method im-

plemented. Because a very fast photo diode collects

the light in the SPC, the temporal resolution of the

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muzzle ﬂash is not limited by the frame rate. SWIR

images of a scene, including the sniper, can be gen-

erated while it also can detect and localize fast events

such as muzzle ﬂashes. Also, the unique temporal

signature of the ﬂash can be measured directly in the

detector signal, thus suppressing false alarms which

is important for an operational system. Background

reduction is performed directly on the raw data with

data captured just before or after the fast event, mak-

ing the data of the ﬂash even sparser. Because the

data of the ﬂash is highly sparse, reconstruction of

the image is possible using TVAL3 (Total Variation

Augmented Lagrangian Alternating Direction Algo-

rithm). Restoration of the image to locate the ﬂash is

performed after it is detected and discriminated, thus

minimizing the power usage. The system may also

be used for optics (or cat’s eye) detection if a laser

is irradiating the scene, which means that a sniper

may be detected and localized pre-shot. (Trzaskawka

et al., 2010; Br

annlund et al., 2013) This functionality

is to some degree demonstrated in the paper, when a

small reﬂector is irradiated with a 1550 nm laser. It

may also be possible to ﬁnd the distance to the target

by measuring the time-of-ﬂight of the reﬂection, but

this functionality is not demonstrated as the focus of

this paper is on muzzle ﬂash detection. The temporal

signature of a muzzle ﬂash in various spectral bands

can be seen in Figure 2. As can be seen, the ﬂashes

in SWIR are typically less than 1 ms long (Svensson

et al., 2011).

566

Brorsson, A., Brännlund, C., Bergström, D. and Gustafsson, D.

Rapid Light Flash Localization in SWIR using Compressed Sensing.

DOI: 10.5220/0010386605660573

In Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2021) - Volume 4: VISAPP, pages

566-573

ISBN: 978-989-758-488-6

Figure 1: Left: The spectral distribution from a secondary ﬂash. The weapon has a caliber of 0.5 (barrel length 36 in).

(Trzaskawka et al., 2010) Top right: Muzzle ﬂash from a sniper riﬂe at 1000 meters recorded in SWIR (0.8-1.7 µm). Bottom

right: Same ﬂash in MWIR (3-5 µm). The red rectangles show enlargements at the riﬂe position (Krieg et al., 2016).

Time [s]

0.42 0.43 0.44 0.45 0.46

0.4

0.8

0.4

0.8

Band 4

Band 5

Band 1

Band 3

0.4

0.8

0.4

0.8

Intensity

Figure 2: The intensity recorded for a 7.62 cal gun for multiple spectral bands, shown during a 40 ms duration and normalized

to the peak value. Band 1 is 0.35 - 0.65 µm, band 3 is 1.46 - 1.79 µm, band 4 is 2.13 - 2.57 µm and band 5 is 3.0 - 4.80 µm. In

the 0.35 - 0.65 µm band, only scattered light from the sun and the ﬂash itself was observed (Svensson et al., 2011).

Rapid Light Flash Localization in SWIR using Compressed Sensing

567

2 RELATED WORK

In (Br

annlund et al., 2013), a combined hostile ﬁre

and optics detection system was tested, using a laser

illuminator and a high speed FPA camera in SWIR.

In (Krieg et al., 2016), a system using 19 single ele-

ment detectors to detect muzzle ﬂashes was demon-

strated. Additionally, two acoustic sensors were in-

tegrated to reduce false alarms. Gil Tidhar proposes

a hostile ﬁre indication (HFI) system with two FPA

sensors, the ﬁrst operating in SWIR and the second

one in the visible band. With this solution sun-glints

and other light sources such as car headlamps can be

cancelled out, as the spectra of such sources is typi-

cally different to that of a muzzle ﬂash (Tidhar et al.,

2009). Trzaskawka et al. presents an initial concept

of a cooled electro-optical sensor unit in MWIR for

sniper detection purposes and discuss the characteris-

tics of muzzle ﬂashes (Trzaskawka et al., 2010).

Conventional cameras capture the scene by mea-

suring the light at each of the thousands or millions

of pixels. In Compressed Sensing (CS), a relatively

small number of measurements from the scene is

combined with sparse reconstruction procedures to

recover an image using only a single or a reduced

number of pixel detectors. CS exploits the fact that

natural images are compressible or sparse in some ba-

sis and therefore only a few measurements relative

to the image resolution are needed (sub-Nyquist) to

reconstruct the image. Two constraints must be ful-

ﬁlled in order to utilize CS sampling: the image in-

formation needs to be compressible and the measure-

ment matrix need to be incoherent with the sparse

transform. The ﬁrst constraint is fulﬁlled because it

is known that natural images are compressible, us-

ing for example JPEG or JPEG2000 compression al-

gorithms. The second constraint is fulﬁlled using a

measurement matrix with a random characteristic. In

CS, a high resolution image can be acquired at sub-

Nyquist sampling rates while using smaller, cheaper

and lower bandwidth components but with the ex-

pense of a longer acquisition time compared to stan-

dard cameras (Wakin et al., 2006; Takhar et al., 2006;

Takhar et al., 2008).

In (Chen et al., 2017) a method to detect light

ﬂashes in raw data using a CS-based single pixel cam-

era (SPC) and a sliding window calculation process is

presented. They succeed in detecting 25 ms anoma-

lies with an intensity 4 times higher than the back-

ground. In previous work Br

annlund et al. presented

an SPC in SWIR which can detect and localize light

ﬂashes from a minimal number of measurements and

discuss a muzzle ﬂash detection system using a high

speed DMD (Br

annlund et al., 2019).

3 SINGLE PIXEL CAMERA

ARCHITECTURE

Our platform consists of a digital micromirror device

(DMD) (Vialux V-7000, 1024 ×768, 22.7 kHz) and

a large area detector InGaAs photodiode (Thorlabs

PDA20C/M, 0.8-1.7 µm). The light from the ”active”

micromirrors is collected by a ”light bucket” - the de-

tector and a 50 mm ﬁxed focal length lens (f/1.4, 0.8-

2.0 µm). A single plano-convex lens (Thorlabs, f=200

mm, D=75mm, 1.05-1.7 µm) focusing the scene onto

the DMD, see Figure 3. A visual spectrum reference

camera is also mounted viewing the DMD to simplify

focusing of the system.

The single pixel sensor captures the scene by mea-

suring the light intensity focused onto the detector re-

ﬂected from the DMD (Digital Micromirror Device),

or another SLM (Spatial Light Modulator). The DMD

can quickly change patterns to obtain new measure-

ments. M measurements are sampled to reconstruct

an image with N pixels, where M  N. Each ele-

ment in the measurement matrix is encoded as one or

zero (or negative one, with two sensors) which corre-

sponds to the individual DMD mirror state. The CS

sampling model is deﬁned as

y = Φx +ε, (1)

where x is the scene considered as an image rear-

ranged as a one-dimensional array with N pixels, y

is the sampled signal with M measurements, Φ is the

measurement matrix and ε is the noise. CS states

that M can be relatively small compared to N, where

the number of measurements needed to reconstruct an

image depends on the sparsity of the image. Using

an SPC where noise contaminates the signal and the

scene may not be completely stationary, the number

of measurements needed will increase in proportion to

the noise and the dynamics in the scene. Permutated

Sequence Ordered Walsh-Hadamard matrix (WHM)

are used as measurement matrices, which replaces

matrix multiplication in Equation 1 with the fast

Walsh-Hadamard transform (FWHT). The FWHT is

both faster than matrix multiplication and eliminating

the need to store the measurement matrices in com-

puter memory. WHM has approximately the same

characteristics and properties as an independent and

identically distributed (i.i.d.) random matrix but gen-

erally needs a higher number of measurements for ex-

act reconstruction of the image. Research has how-

ever shown that there is no signiﬁcant loss in recov-

ery of the image relative to the i.i.d. random mea-

surement matrix (Cai Zhuoran et al., 2013). The total

variation (TV) based TVAL3 is used for image recon-

struction. Natural images often contain sharp edges

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

568

Figure 3: The single pixel camera architecture used in this

work. The optics, DMD, reference camera, the single pixel

sensor and laser are shown.

and piecewise smooth areas which the TV regulariza-

tion algorithm is good at preserving. The main differ-

ence between TV and other reconstruction algorithms

is that TV considers the gradient of signal to be sparse

instead of the signal itself, thus ﬁnding the sparsest

gradient (Li, 2010).

The SPC architecture is also built with an optional

secondary detector which measure the complement of

the ﬁrst sensor. Previous research show that similar

reconstruction results can be achieved with approxi-

mately half the number of patterns compared to one

sensor. The research also show that the reconstruc-

tion became more stable with dynamics in the scene

and vibrations on the camera itself compared to only

one sensor. In summary, by using two sensors, the in-

formation of the scene sampled is doubled while the

noise increases by

√

2 in the combined signal. The

beneﬁt of using two sensors in the context of light

ﬂash localization is that on average a detector only

sees half of the light event per DMD pixel. If it is de-

sired to identify the signal based on a signature, half

of the information is lost, but can be complemented

using the other detector (Oja and Olsson, 2019).

Figure 4: Two images of cars at 512x512 (top) and 256x256

(bottom) pixel resolutions at 350 m. Subsampling ratios are

30% and 40%, respectively. In the bottom image a fence can

be seen in the foreground (seen as thin horizontal lines).

4 TARGET DETECTION AND

LOCALIZATION SYSTEM

The localization systems and target application de-

scribed in this article rests on an edge case of CS the-

ory and is enabled by the high speed DMD pattern

rate. The spatial resolution of the signal to be located

is bound to the temporal resolution (the length of the

signature) by

M ≥ k log(N/k ), (2)

Rapid Light Flash Localization in SWIR using Compressed Sensing

569

where k is the number of ”pixels” the light ﬂash is vis-

ible in and M is the minimum number of patterns re-

quired to reconstruct the signal without noise (Takhar

et al., 2008). The minimum temporal length of the

light ﬂash is

t ≥

DMD pattern rate

, (3)

which for example means t ∼0.3−1.0 ms, depending

on the pixel spread in 32 ×32 resolution. In Equa-

tion 2 it is assumed that the only information in the

signal is the light ﬂash, in order to extract the signal a

method with background reduction was implemented

which is described in Section 4.1. With the help

of the background reduction, in principle, all back-

ground information from static objects in the scene is

removed, while dynamic information in the scene that

has a longer temporary signature than the light phe-

nomenon can be ﬁltered out. After the background

reduction, the signal is analyzed by a detection algo-

rithm. The detection algorithm can for example use

a matched ﬁlter to compare the background reduced

signal against a known signature, which is described

in Section 4.2. Only if a match with high probability

is found the signal is reconstructed for localization. In

the localization step, different reconstruction methods

can be used depending on the signals temporal length

and pixel spread, which is described in Section 4.3.

4.1 Background Subtraction

The background reduction has been implemented by

repeating a ﬁxed number of patterns on the DMD dur-

ing the measurement. The number of patterns in the

repeating window is set to double the temporal length

of the light phenomenon. It is desirable that the win-

dow is as small as possible so that potential dynamics

in the scene is keept to a minimum. From the mea-

sured data y, a new vector is created that contains

background-reduced data by calculating the residual

between two corresponding patterns according to,

ρ(i)

= |y

−y

i+w

|, (4)

where y

is the background reduced signal and w is

the number of patterns in the window. Assuming that

a light ﬂash has occurred in one of the windows the

equation can be expanded to

ρ(i)

= |y

−y

i+w

= |(y

δ(i)

+ y

β(i)

+ ε

(i)

) −(y

β(i+w)

+ ε

(i+w)

)|,

(5)

where y

is a pattern with a light ﬂash, y

is back-

ground information of the scene and ε is the noise,

assumed to be additive white Gaussian noise. With

the relative small time frame between y

β(i)

and y

β(i+w)

(e.g. 1.76 ms, with window size of 40 @ 22.7 kHz)

we can assume,

β(i)

' y

β(i+w)

⇒

ρ(i)

= y

δ(i)

+ ε

(i)

−ε

(i+w)

= y

δ(i)

+ ε

∆

(6)

The only components after the background reduc-

tion is the signal of interest and combined noise, as

seen in Figure 5a. The combined noise affect the σ

(standard deviation) of the reduced signal by a factor

√

2 compared to the linear signal. The system can

also be complemented with a second detector which

samples the compliment of the ﬁrst detector in the

scene, which can be seen in Figure 5b. The advan-

tages of using two detectors is that the measurements

can be combined in order to get the envelope of the

whole light ﬂash, which increases the likelihood of a

successful detection and localization even with lower

SNR. Alternatively using two sensors with different

wavelengths corresponding to two known spectrums

of the target and therefore are more robust to natural

occurring light phenomenon and thus reducing false

positives.

4.2 Light Flash Detection

Detection of light ﬂashes can be performed by thresh-

olding the background-reduced signal, which can be

done without reconstructing an image of the scene.

The temporal signature of the fast event can also be

compared with the known signature of the desired

light ﬂash, separating it from other natural events us-

ing a matched ﬁlter. Given the temporal resolution

that the signal can be sampled (at least an order of

magnitude faster than the DMD pattern rate), it might

even be possible to distinguish between unique light

ﬂashes depending on length and characteristic enve-

lope. As seen in Figure 5c, the light ﬂash envelope is

revealed with basic signal processing techniques such

as moving mean even in noisy signals.

4.3 Scene Reconstruction

When a desired light ﬂash has been detected the back-

ground reduced signal of interests is cut out and re-

constructed using a suitable method. The sparse

background-reduced signal during the ﬂash (acquired

using only a few patterns) can be restored to an im-

age using TVAL3. If the method is successful a noisy

image will be restored, where the brightest pixel is

located at the position of the light ﬂash. Test on

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

570

(a)

0 50 100 150 200 250 300 350 400

-2

Background reduced signal, combined

(b)

(c)

Figure 5: In (a) top plot the simulated signal with the com-

ponents broken apart for clarity, blue line is the informa-

tion from the background in the scene which is repeated

after 200 samples, red is information from a light ﬂash

(represented as half period of sin

, indices 0-100) added to

background, green line is background, light ﬂash and added

noise. (a) bottom is the background reduced signal. In (b)

the combined background reduced signal from two detec-

tors is plotted. (c) shows plot of moving mean of the com-

bined signal in (b).

simulated light ﬂashes show that the strongest recon-

structed pixels using TVAL3 was the same pixels as

only using the inverse FWHT (IFWHT). Therefore,

only the IFWHT is used in the reconstruction and

localization. The difference between using TVAL3

i.e. CS-reconstruction and IFWHT is that TVAL3 will

suppress false positives i.e reconstruct a ﬁner picture,

but it does not change the strongest initial guesses

given by the IFWHT which is performed at the be-

ginning of the TVAL3 algorithm.

5 EXPERIMENTS

To link the research and the experimental set-up to

a concrete problem, we choose to simulate a muz-

zle ﬂash. Munitions ﬂashes, such as gunshots, ex-

plosions, missile launches and kinetic ammunition are

high-speed phenomena with time durations from sub-

milliseconds to a fraction of a second. Standard cam-

eras with typical frame rates of 30 or 60 Hz are not

fast enough for detection of snipers and the problem

therefore requires non-standard high-speed imaging

solutions. But even if the frame rate is high, it still

needs to be signiﬁcantly higher than 1 kHz to resolve

the temporal signature, which is normally beyond the

capability of most sensors (Svensson et al., 2011).

The ﬂash can be detected with such a device, but it

may only be resolved in a single frame thus making

it susceptible to false alarms. The high data rate of a

FPA is also a problem, because the algorithm needs to

analyse all the pixels in each frame and compare it to

the previous one to detect the fast rise in pixel value.

By comparison the SPC with a high speed pattern rate

(> 22 kHz) is both capable of resolving the temporal

signature (> 100 kHz DAQ) and locate the ﬂash.

To simulate the muzzle ﬂash, a small reﬂector was

placed in the scene and was irradiated by a pulsed

laser placed next to the SPC. The laser parameters

in the measurement was 7 W @ 1550 nm, 20 mrad

divergence, 10 Hz pulse repetition frequency and a

pulse length of 1 ms (a square wave with a duty cy-

cle of 1%). The simulation of the muzzle ﬂash is far

from perfect. The size of the reﬂector (Ø7 cm) may

be much smaller compared to a real muzzle ﬂash and

the temporal and spectral signatures will also differ

to some extent. We simulated a ∼ 1 ms muzzle ﬂash

that at the current pattern rate is resolved by approxi-

mately 22 patterns. Given Equation (2), and factoring

in nose and dynamics in the scene (which increases

M) and possible pixel spread (1 ≤ k ≤ 4) the resolu-

tion was set to N = 32 ×32. In all the measurements

(images), the FOVs are increased by binning the mi-

cromirrors, so the resolution of the patterns used was

1024 ×1024 and effective reconstructed resolution of

32 ×32. The reﬂector was placed in different envi-

ronments and at different length from the camera. In

the results presented in Section 6, the reﬂector was

placed on a three trunk ca. 350 m from the camera.

This scene contains dynamics in the form of grass and

branches from the trees that moves with the wind, tur-

bulence as well as natural lightning from the sun.

Rapid Light Flash Localization in SWIR using Compressed Sensing

571

500 1000 1500 2000 2500 3000

Raw sampled signal

Channel 1

Channel 2

Moving mean of Ch1

(a)

(b)

Figure 6: (a) Raw sampled signal with light ﬂash (notice

the repetitions for each window which shows that the back-

ground is static). (b) Background reduced and quantized

signal from (a), by combining the signals and calculate

moving mean the light ﬂash envelope becomes clear.

6 RESULTS

An example of the signals when an outdoor reﬂector

is pulsed with the laser can be seen in Figure 6. With

adequate SNR and number of patterns are sampled

during the pulse, the result will be a dark image with

the brightest pixel at the position of the light source.

In Figure 7, the restored 32 ×32 image (using 20

patterns) of the simulated light ﬂash is superimposed

in red over the outdoor scene. 20 consecutive patterns

during a part of the 1 ms laser pulse are used to re-

store the red overlay image. The outdoor scene is also

captured at 128x128 resolution (3000 patterns with a

subsampling ratio of 18%), when the light source is

continuously on, thus visible as a small bright light.

Tests were made to evaluate the number of pat-

terns needed to locate a small light source, in this test

only one sensor was used. Instead of using a small

window for background reconstruction 500 unique

patterns was repeated. The laser was synced in such

a way that the laser was active for 500 patterns and

then inactive for 500 patterns. Thus we could cal-

culate background reduction for the whole signal and

wide range of pattern combinations (different sections

Figure 7: B/W image of the outdoor scene at 128x128 pixel

resolution, reconstructed using a subsampling ratio of 18%.

The Ø7 cm reﬂector, seen as a bright dot when the laser

is continuously on, is mounted on a tree at 350 m range.

The red overlaid image of the simulated 1 ms light ﬂash is

reconstructed to 32x32 pixel resolution using 20 consecu-

tive patterns (during a pulse) and illustrates the capability

to detect and localize the ﬂash at the same position as the

reﬂector (ground-truth).

of the signal) could be reconstructed to test if the

strongest pixel in fact was the light source for each

individual image. From the measurements, 500 pat-

terns were analysed and (M ≤ 40) different consecu-

tive patterns were used to reconstruct a large number

of images. The results from the experiments are pre-

sented in Figure 8. As can be seen, the probability to

locate the ﬂash is almost zero below ﬁve patterns but

then rises quickly and after 25 patterns reaches almost

100. Because the patterns displayed on the DMD are

random, the probability to ﬁnd the light source is de-

pendent on the speciﬁc pattern combinations during

the light ﬂash and the SNR.

The same test was conducted both in- and out-

doors with variable length to the target, backgrounds

and resolutions. The trails showed that the key fac-

tor in order to detect and localize the signal was

SNR. With higher SNR the probability and number

of measurements needed for a successful localization

increased respectively lowered.

7 CONCLUSIONS

Conventional FPA-based solutions to high speed light

ﬂash detection are challenging, due to limitations in

frame rates, signal processing demands as well as

transmission bandwidth requirements. The sparse na-

VISAPP 2021 - 16th International Conference on Computer Vision Theory and Applications

572

0 5 10 15 20 25 30 35 40

M, number of measurements

100

Optimal simulated

Outdoor

Indoor

Figure 8: Probability to ﬁnd the correct pixel (illuminated

reﬂector) in the reconstructed image given M number of

samples, using one sensor. Green line shows simulated light

ﬂash without noise, blue line from illuminating the reﬂector

indoors in a dark room from ca. 40 m, red line from outdoor

trials ca. 350 m.

ture of the transient and highly localized events how-

ever suggests that CS-based approaches might be use-

ful. Results of our initial experiments, based on long

range detection of 1 ms laser pulses with our DMD-

based SWIR SPC, show great potential of both detec-

tion and localization of ﬂashes with the high sampling

rate provided by the DMD. A high (99%) localization

probability have shown to be provided after only 25-

30 samples, corresponding roughly to the pulse width

of the laser and to 2-3% sampling ratio of a recon-

structed image at 32x32 pixel resolution. Although

the initial focus has been given to muzzle ﬂash detec-

tion, it is also conceivable that the system could be

used for sniper optics detection by using active CW

or pulsed laser irradiation, using similar techniques

as described in the paper. Detection of other transient

and spatially limited events of military interest could

be explosions and missile launches at longer ranges.

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