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A Physics-based Noise Formation Model for Extreme Low-light Raw Denoising

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Abstract and Figures

Lacking rich and realistic data, learned single image denoising algorithms generalize poorly to real raw images that do not resemble the data used for training. Although the problem can be alleviated by the heteroscedastic Gaussian model for noise synthesis, the noise sources caused by digital camera electronics are still largely overlooked, despite their significant effect on raw measurement, especially under extremely low-light condition. To address this issue, we present a highly accurate noise formation model based on the characteristics of CMOS photosensors, thereby enabling us to synthesize realistic samples that better match the physics of image formation process. Given the proposed noise model, we additionally propose a method to calibrate the noise parameters for available modern digital cameras, which is simple and reproducible for any new device. We systematically study the generalizability of a neural network trained with existing schemes, by introducing a new low-light denoising dataset that covers many modern digital cameras from diverse brands. Extensive empirical results collectively show that by utilizing our proposed noise formation model, a network can reach the capability as if it had been trained with rich real data, which demonstrates the effectiveness of our noise formation model.
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A Physics-based Noise Formation Model for Extreme Low-light Raw Denoising
Kaixuan Wei1Ying Fu1Jiaolong Yang2Hua Huang1
1Beijing Institute of Technology 2Microsoft Research
Lacking rich and realistic data, learned single image de-
noising algorithms generalize poorly to real raw images
that do not resemble the data used for training. Although
the problem can be alleviated by the heteroscedastic Gaus-
sian model for noise synthesis, the noise sources caused by
digital camera electronics are still largely overlooked, de-
spite their significant effect on raw measurement, especially
under extremely low-light condition. To address this issue,
we present a highly accurate noise formation model based
on the characteristics of CMOS photosensors, thereby en-
abling us to synthesize realistic samples that better match
the physics of image formation process. Given the proposed
noise model, we additionally propose a method to calibrate
the noise parameters for available modern digital cameras,
which is simple and reproducible for any new device. We
systematically study the generalizability of a neural net-
work trained with existing schemes, by introducing a new
low-light denoising dataset that covers many modern dig-
ital cameras from diverse brands. Extensive empirical re-
sults collectively show that by utilizing our proposed noise
formation model, a network can reach the capability as if
it had been trained with rich real data, which demonstrates
the effectiveness of our noise formation model.
1. Introduction
Light is of paramount importance to photography. Night
and low light place very demanding constraints on photog-
raphy due to limited photon count and inescapable noise.
The natural reaction is to gather more light by, e.g., enlarg-
ing aperture setting, lengthening exposure time and open-
ing flashlight. However, each method is a tradeoff – large
aperture incurs small depth of field, and is unavailable in
smartphone cameras; long exposure can induce blur due to
scene variations or camera motions; flash can cause color
aberrations and is useful only for nearby objects.
A practical rescue for low-light imaging is to use burst
capturing [46, 28, 42, 40], in which a burst of images
are aligned and fused to increase the signal-to-noise ratio
Corresponding author:
(a) Input (b) G (c) G+P
(d) Paired real data (e) Ours (f) Reference
Figure 1: An image from the See-in-the-Dark (SID) Dataset [9],
where we present (a) the short-exposure noisy input image; (f)
the long-exposure reference image; (b-e) the outputs of UNets
[51] trained with (b) synthetic data generated by the homoscedas-
tic Gaussian noise model (G), (c) synthetic data generated by
the signal-dependent heteroscedastic Gaussian noise model (G+P)
[22], (d) paired real data of [9], and (e) synthetic data generated
by our proposed noise model respectively. All images were con-
verted from raw Bayer space to sRGB for visualization; similarly
(SNR). However, burst photography can be fragile, suffer-
ing from ghosting effect [28, 56] when capturing dynamic
scenes in the presence of vehicles, humans, etc. An emerg-
ing alternative approach is to employ a neural network to
automatically learn the mapping from a low-light noisy im-
age to its long-exposure counterpart [9]. However, such a
deep learning approach generally requires a large amount of
labelled training data that resembles low-light photographs
in the real world. Collecting rich high-quality training sam-
ples from diverse modern camera devices is tremendously
labor-intensive and expensive.
In contrast, synthetic data is simple, abundant and in-
expensive, but its efficacy is highly contingent upon how
accurate the adopted noise formation model is. The het-
eroscedastic Gaussian noise model [22], instead of the
commonly-used homoscedastic one, approximates well the
real noise occurred in daylight or moderate low-light set-
tings [5, 27, 28]. However, it cannot delineate the full pic-
ture of sensor noise under severely low illuminance. An
illustrative example is shown in Fig. 1, where the objec-
tionable banding pattern artifacts, an unmodeled noise com-
ponent that is exacerbated in dim environments, become
clearly noticeable by human eyes.
In this paper, to avoid the effect on noise model from
the image processing pipeline (ISP) [9, 5, 46] converting
raw data to sRGB, we mainly focus on the noise forma-
tion model for raw images. We propose a physics-based
noise formation model for extreme low-light raw denois-
ing, which explicitly leverages the characteristics of CMOS
photosensors to better match the physics of noise formation.
As shown in Fig. 2, our proposed synthetic pipeline derives
from the inherent process of electronic imaging by consid-
ering how photons go through several stages. It models sen-
sor noise in a fine-grained manner that includes many noise
sources such as photon shot noise, pixel circuit noise, and
quantization noise. Besides, we provide a method to cali-
brate the noise parameters from available digital cameras.
In order to investigate the generality of our noise model,
we additionally introduce an extreme low-light denoising
(ELD) dataset taken by various camera devices to evaluate
our model. Extensive experiments show that the network
trained only with the synthetic data from our noise model
can reach the capability as if it had been trained with rich
real data.
Our main contributions can be summarized as follows:
We formulate a noise model to synthesize realistic
noisy images that can match the quality of real data
under extreme low-light conditions.
We present a noise parameter calibration method that
can adapt our model to a given camera.
We collect a dataset with various camera devices to
verify the effectiveness and generality of our model.
2. Related Work
Noise removal from a single image is an extensively-
studied yet still unresolved problem in computer vision and
image processing. Single image denoising methods gener-
ally rely on the assumption that both signal and noise ex-
hibit particular statistical regularities such that they can be
separated from a single observation. Crafting an analytical
regularizer associated with image priors (e.g. smoothness,
sparsity, self-similarity, low rank), therefore, plays a critical
role in traditional design pipeline of denoising algorithms
[52, 48, 18, 16, 43, 15, 6, 26]. In the modern era, most
single image denoising algorithms are entirely data-driven,
which consist of deep neural networks that implicitly learn
the statistical regularities to infer clean images from their
noisy counterparts [53, 12, 45, 61, 24, 57, 10, 27]. Although
simple and powerful, these learning-based approaches are
often trained on synthetic image data due to practical con-
straints. The most widely-used additive, white, Gaussian
Figure 2: Overview of electronic imaging pipeline and visualiza-
tion of noise sources and the resulting image at each stage.
noise model deviates strongly from realistic evaluation sce-
narios, resulting in significant performance declines on pho-
tographs with real noise [49, 2].
To step aside the domain gap between synthetic images
and real photographs, some works have resorted to collect-
ing paired real data not just for evaluation but for train-
ing [2, 9, 54, 8, 33]. Notwithstanding the promising re-
sults, collecting sufficient real data with ground-truth la-
bels to prevent overfitting is exceedingly expensive and
time-consuming. Recent works exploit the use of paired
(Noise2Noise [38]) or single (Noise2Void [37]) noisy im-
ages as training data instead of paired noisy and noise-free
images. However, they can not substantially ease the bur-
den of labor requirements for capturing a massive amount
of real-world training data.
Another line of research has focused on improving the
realism of synthetic training data to circumvent the difficul-
ties in acquiring real data from cameras. By considering
both photon arrival statistics (“shot” noise) and sensor read-
out effects (“read” noise), the works of [46, 5] employed
a signal-dependent heteroscedastic Gaussian model [22] to
characterize the noise properties in raw sensor data. Most
recently, Wang et al. [59] proposes a noise model, which
considers the dynamic streak noise, color channel heteroge-
neous and clipping effect, to simulate the high-sensitivity
noise on real low-light color images. Concurrently, a
flow-based generative model, namely Noiseflow [1] is pro-
posed to formulate the distribution of real noise using la-
tent variables with tractable density1. However, these ap-
proaches oversimplify the modern sensor imaging pipeline,
especially the noise sources caused by camera electronics,
which have been extensively studied in the electronic imag-
ing community [36, 29, 25, 3, 17, 19, 30, 31, 4, 58, 14].
In this work, we propose a physics-based noise formation
model stemming from the essential process of electronic
imaging to synthesize the noisy dataset and show that size-
able improvements of denoising performance on real data,
particularly under extremely low illuminance.
1Note that Noiseflow requires paired real data to obtain noise data (by
subtracting the ground truth images from the noisy ones) for training.
3. Physics-based Noise Formation Model
The creation of a digital sensor raw image Dcan be gen-
erally formulated by a linear model
D=KI +N , (1)
where Iis the number of photoelectrons that is propor-
tional to the scene irradiation, Krepresents the overall sys-
tem gain composed by analog and digital gains, and Nde-
notes the summation of all noise sources physically caused
by light or camera. We focus on the single raw image de-
noising problem under extreme low-light conditions. In this
context, the characteristics of Nare formated in terms of
the sensor physical process beyond the existing noise mod-
els. Deriving an optimal regularizer to tackle such noise is
infeasible, as there is no analytical solver for such a noise
distribution2. Therefore, we rely on a learning-based neu-
ral network pipeline to implicitly learn the regularities from
data. Creating training samples for this task requires care-
ful considerations of the characteristics of raw sensor data.
In the following, we first describe the detailed procedures
of the physical formation of a sensor raw image as well as
the noise sources introduced during the whole process. An
overview of this process is shown in Fig. 2.
3.1. Sensor Raw Image Formation
Our photosensor model is primarily based upon the
CMOS sensor, which is the dominating imaging sensor
nowadays [50]. We consider the electronic imaging pipeline
of how incident light is converted from photons to electrons,
from electrons to voltage, and finally from voltage to digital
numbers, to model noise.
From Photon to Electrons. During exposure, incident
lights in the form of photons hit the photosensor pixel
area, which liberates photon-generated electrons (photo-
electrons) proportional to the light intensity. Due to the
quantum nature of light, there exists an inevitable uncer-
tainty in the number of electrons collected. Such uncer-
tainty imposes a Poisson distribution over this number of
electrons, which follows
(I+Np)∼ P (I),(2)
where Npis termed as the photon shot noise and Pdenotes
the Poisson distribution. This type of noise depends on the
light intensity, i.e., on the signal. Shot noise is a funda-
mental limitation and cannot be avoided even for a perfect
sensor. There are other noise sources introduced during the
photon-to-electron stage, such as photo response nonuni-
formity and dark current noise, reported by many previ-
ous literatures [29, 25, 58, 3]. Over the last decade, tech-
nical advancements in CMOS sensor design and fabrica-
tion, e.g., on-sensor dark current suppression, have led to
2Even if each noise component has an analytical formulation, their
summation can generally be intractable.
a new generation of digital single lens reflex (DSLR) cam-
eras with lower dark current and better photo response uni-
formity [23, 41]. Therefore, we assume a constant photo
response and absorb the effect of dark current noise Ndinto
read noise Nread, which will be presented next.
From Electrons to Voltage. After electrons are collected
at each site, they are typically integrated, amplified and read
out as measurable charge or voltage at the end of exposure
time. Noise present during the electrons-to-voltage stage
depends on the circuit design and processing technology
used, and thus is referred to as pixel circuit noise [25]. It
includes thermal noise, reset noise [36], source follower
noise [39] and banding pattern noise [25]. The physical ori-
gin of these noise components can be found in the electronic
imaging literatures [36, 25, 58, 39]. For instance, source
follower noise is attributed to the action of traps in silicon
lattice which randomly capture and emit carriers; banding
pattern noise is associated with the CMOS circuit readout
pattern and the amplifier.
By leveraging this knowledge, we consider the thermal
noise Nt, source follower noise Nsand banding pattern
noise Nbin our model. The noise model of Nbwill be pre-
sented later. Here, we absorb multiple noise sources into a
unified term, i.e. read noise
Nread =Nd+Nt+Ns.(3)
Read noise can be assumed to follow a Gaussian distribu-
tion, but the analysis of noise data (in Section 3.2) tells a
long-tailed nature of its shape. This can be attributed by the
flicker and random telegraph signal components of source
follower noise [25], or the dark spikes raised by dark current
[36]. Therefore, we propose using a statistical distribution
that can better characterize the long-tail shape. Specifically,
we model the read noise by a Tukey lambda distribution
(T L) [34], which is a distributional family that can approxi-
mate a number of common distributions (e.g., a heavy-tailed
Cauchy distribution):
Nread T L (λ; 0, σT L ),(4)
where λand σindicate the shape and scale parameters re-
spectively, while the location parameter is set to be zero
given the zero-mean noise assumption.
Banding pattern noise Nbappears in images as horizon-
tal or vertical lines. We only consider the row noise compo-
nent (horizontal stripes) in our model, as the column noise
component (vertical stripes) is generally negligible when
measuring the noise data (Section 3.2). We simulate the
row noise Nrby sampling a value from a zero-mean Gaus-
sian distribution with a scale parameter σr, then adding it as
an offset to the whole pixels within a single row.
From Voltage to Digital Numbers. To generate an im-
age that can be stored in a digital storage medium, the ana-
log voltage signal read out during last stage is quantized
Figure 3: Centralized Fourier spectrum of bias frames captured by
SonyA7S2 (left) and (right) NikonD850 cameras
into discrete codes using an ADC. This process introduces
quantization noise Nqgiven by
NqU(1/2q, 1/2q),(5)
where U(·,·)denotes the uniform distribution over the
range [1/2q, 1/2q]and qis the quantization step.
To summarize, our noise formation model consists of
four major noise components:
N=KNp+Nr ead +Nr+Nq,(6)
where K,Np,Nread,Nrand Nqdenotes the overall system
gain, photon shot noise, read noise, row noise and quantiza-
tion noise, respectively.
3.2. Sensor Noise Evaluation
In this section, we present a noise parameter calibration
method attached to our proposed noise formation model.
According to Eq. (2) (4) (6), the necessary parameters to
specify our noise model include overall system gain Kfor
photon shot noise Np; shape and scale parameters (λand
σT L) for read noise Nread ; scale parameter σrfor row noise
Nr. Given a new camera, our noise calibration method con-
sists of two main procedures, i.e. (1) estimating noise pa-
rameters at various ISO settings3, and (2) modeling joint
distributions of noise parameters.
Estimating noise parameters. We record two sequences
of raw images to estimate Kand other noise parameters:
flat-field frames and bias frames.
Flat-field frames are the images captured when sensor is
uniformly illuminated. They can be used to derive Kac-
cording to the Photon Transfer method. [32]Once we have
K, we can firstly convert a raw digital signal Dinto the
number of photoelectrons I, then impose a Poisson distribu-
tion on it, and finally revert it to D– this simulates realistic
photon shot noise.
Bias frames are the images captured under a lightless en-
vironment with the shortest exposure time. We took them
at a dark room and the camera lens was capped on. Bias
frames delineate the read noise picture independent of light,
blended by the multiple noise sources aforementioned. The
banding pattern noise can be tested via performing discrete
Fourier transform on a bias frame. In Fig.3, the highlighted
3Noise parameters are generally stationary at a fixed ISO.
Figure 4: Distribution fitting of read noise for SonyA7S2 (top)
and NikonD850 (bottom) cameras. Left: probability plot against
the Gaussian distribution; Middle: Tukey lambda PPCC plot that
determines the optimal λ(shown in red line); Right: probability
plot against the Tukey Lambda distribution. A higher R2indicates
a better fit. (Best viewed with zoom)
vertical pattern in the centralized Fourier spectrum reveals
the existence of row noise component. To analyze the dis-
tribution of row noise, we extract the mean values of each
row from raw data. These values, therefore, serve as good
estimates to the underlying row noise intensities, given the
zero-mean nature of other noise sources. The normality of
the row noise data is tested by a Shapiro-Wilk test [55]: the
resulting p-value is higher than 0.05, suggesting the null
hypothesis that the data are normally distributed cannot be
rejected. The related scale parameter σrcan be easily esti-
mated by maximizing the log-likelihood.
After subtracting the estimated row noise from a bias
frame, statistical models can be used to fit the empirical dis-
tribution of the residual read noise. A preliminary diagnosis
(Fig. 4 Left) shows the main body of the data may follow a
Gaussian distribution, but it also unveils the long-tail nature
of the underlying distribution. In contrast to regarding ex-
treme values as outliers, we observe an appropriate long-tail
statistical distribution can characterize the noise data better.
We generate a probability plot correlation coefficient
(PPCC) plot [20] to identify a statistical model from a
Tukey lambda distributional family [34] that best describes
the data. The Tukey lambda distribution is a family of distri-
butions that can approximate many distributions by varying
its shape parameter λ. It can approximate a Gaussian dis-
tribution if λ= 0.14, or derive a heavy-tailed distribution
if λ < 0.14. The PPCC plot (Fig. 4 Middle) is used to find
a good value of λ. The probability plot [60] (Fig. 4 Right)
is then employed to estimate the scale parameter σT L. The
goodness-of-fit can be evaluated by R2– the coefficient of
determination w.r.t. the resulting probability plot [47]. The
R2of the fitted Tukey Lambda distribution is much higher
than the Gaussian distribution (e.g., 0.972 vs. 0.886), indi-
cating a much better fit to the empirical data.
Although we use a unified noise model for different cam-
Real Bias Frame Gaussian Model Ours
(R2) (0.961) (0.978)
(R2) (0.880) (0.972)
Figure 5: Simulated and real bias frames of two cameras. A higher
R2indicates a better fit quantitatively. (Best viewed with zoom)
Figure 6: Linear least squares fitting from estimated noise param-
eter samples (blue dots) from a NikonD850 camera. Left and right
figures show the joint distributions of (K, σTL )and (K, σr)re-
spectively, where we sample the noise parameters from the blue
shadow regions.
eras, the noise parameters estimated from different cameras
are highly diverse. Figure 4 shows the selected optimal
shape parameter λdiffers camera by camera, implying dis-
tributions with varying degree of heavy tails across cameras.
The visual comparisons of real and simulated bias frames
are shown in Fig. 5. It shows that our model is capable of
synthesizing realistic noise across various cameras, which
outperforms the Gaussian noise model both in terms of the
goodness-of-fit measure (i.e., R2) and the visual similarity
to real noise.
Modeling joint parameter distributions. To choose noise
parameters for our noise formation model, we infer the joint
distributions of (K,σT L) and (K,σr), from the parame-
ter samples estimated at various ISO settings. As shown in
Fig. 6, we use the linear least squares method to find the
line of best fit for two sets of log-scaled measurements. Our
noise parameter sampling procedure is
log (K)Ulog( ˆ
Kmin),log( ˆ
log (σT L)|log (K)∼ N (aT L log(K) + bT L,ˆσT L),(7)
log (σr)|log (K)∼ N (arlog(K) + br,ˆσr),
where U(·,·)denotes a uniform distribution and N(µ, σ)
denotes a Gaussian distribution with mean µand standard
(a) Image capture setup (b) example images
Figure 7: Capture setup and example images from our dataset.
Table 1: Quantitative Results on Sony set of the SID dataset. The
noise models are indicated as follows. G: the Gaussian model for
read noise Nread;G: the tukey lambda model for Nread ;P: the
Gaussian approximation for photon shot noise Np;P: the true
Poisson model for Np;R: the Gaussian model for row noise Nr;
U: the uniform distribution model for quantization noise Nq. The
best results are indicated by red color and the second best results
are denoted by blue color.
×100 ×250 ×300
BM3D 32.92 / 0.758 29.56 / 0.686 28.88 / 0.674
A-BM3D 33.79 / 0.743 27.24 / 0.518 26.52 / 0.558
Paired real data 38.60 / 0.912 37.08 /0.886 36.29 /0.874
Noise2Noise 37.42 / 0.853 33.48 / 0.725 32.37 / 0.686
G36.10 / 0.800 31.87 / 0.640 30.99 / 0.624
G+P37.08 / 0.839 32.85 / 0.697 31.87 / 0.665
G+P38.31 / 0.884 34.39 / 0.765 33.37 / 0.730
G+P39.10 / 0.911 36.46 / 0.869 35.69 / 0.855
G+P+R39.23 / 0.912 36.89 / 0.877 36.01 / 0.864
G+P+R+U39.27 /0.914 37.13 /0.883 36.30 /0.872
deviation σ.ˆ
Kmin and ˆ
Kmax are the estimated overall sys-
tem gains at the minimum and maximum ISO of a camera
respectively. aand bindicate the fitted line’s slope and in-
tercept respectively. ˆσis an unbiased estimator of standard
deviation of the linear regression under the Gaussian error
assumption. For shape parameter λ, we simply sample it
from the empirical distribution of the estimated parameter
Noisy image synthesis. To synthesize noisy images, clean
images are chosen and divided by low light factors sampled
uniformly from [100,300] to simulate low photon count in
the dark. Noise is then generated and added to the scaled
clean samples, according to Eq. (6) (7). The created noisy
images are finally normalized by multiplying the same low
light factors to expose bright but excessively noisy contents.
4. Extreme Low-light Denoising (ELD) Dataset
To systematically study the generality of the proposed
noise formation model, we collect an extreme low-light
denoising (ELD) dataset that covers 10 indoor scenes
and 4 camera devices from multiple brands (SonyA7S2,
NikonD850, CanonEOS70D, CanonEOS700D). We also
record bias and flat field frames for each camera to calibrate
our noise model. The data capture setup is shown in Fig. 7.
For each scene and each camera, a reference image at the
base ISO was firstly taken, followed by noisy images whose
exposure time was deliberately decreased by low light fac-
tors fto simulate extreme low light conditions. Another
reference image then was taken akin to the first one, to en-
sure no accidental error (e.g. drastic illumination change or
accidental camera/scene motion) occurred. We choose three
ISO levels (800, 1600, 3200)4and two low light factors
(100, 200) for noisy images to capture our dataset, resulting
in 240 (3×2×10×4) raw image pairs in total. The hardest
example in our dataset resembles the image captured at a
“pseudo” ISO up to 640000 (3200×200).
5. Experiments
5.1. Experimental setting
Implementation details. A learning-based neural network
pipeline is constructed to perform low-light raw denoising.
We utilize the same U-Net architecture [51] as [9]. Raw
Bayer images from SID Sony training dataset [9] are used
to create training data. We pack the raw Bayer images
into four channels (R-G-B-G) and crop non-overlapped
512 ×512 regions augmented by random flipping/rotation.
Our approach only use the clean raw images, as the paired
noisy images are generated by the proposed noise model
on-the-fly. Besides, we also train networks based upon
other training schemes as references, including training
with paired real data (short exposure and long exposure
counterpart) and training with paired real noisy images (i.e.,
Noise2Noise [38]).
Our implementation5is based on PyTorch. We train
the models with 200 epoch using L1loss and Adam opti-
mizer [35] with batch size 1. The learning rate is initially
set to 104, then halved at epoch 100, and finally reduced
to 105at epoch 180.
Competing methods. To understand how accurate our pro-
posed noise model is, we compare our method with:
1. The approaches that use real noisy data for training,
i.e. “paired real data” [9]6and Noise2Noise [38];
2. Previous noise models, i.e. homoscedastic (G) and het-
eroscedastic Gaussian noise models (G+P) [22, 21];
3. The representative non-deep methods, i.e. BM3D [15]
and Anscombe-BM3D (A-BM3D) [44]7.
4Most modern digital cameras are ISO-invariant when ISO is set higher
than 3200 [13].
5Code is released at
6[9] used paired real data to perform raw-to-sRGB low-light image pro-
cessing. Here we adapt its setting to raw-to-raw denoising.
7The noise level parameters required are provided by the off-the-shelf
image noise level estimators [22, 11].
(a) Noise2Noise (b) Paired real data (c) Ground Truth
(d) G(e) G+P(f) G+P+R+U
Figure 8: Visual result comparison of different training schemes.
Our final model (G+P+R+U) suppresses the “purple” color
shift, residual bandings and chroma artifacts compared to other
5.2. Results on SID Sony dataset
Single image raw denoising experiment is firstly con-
ducted on images from SID Sony validation and test sets.
For quantitative evaluation, we focus on indoor scenes illu-
minated by natural lights, to avoid flickering effect of alter-
nating current lights [2] 8. To account for the imprecisions
of shutter speed and analog gain [2], a single scalar is cal-
culated and multiplied into the reconstructed image to min-
imize the mean square error evaluated by the ground truth.
Ablation study on noise models. To verify the efficacy
of the proposed noise model, we compare the performance
of networks trained with different noise models developed
in Section 3.1. All noise parameters are calibrated using the
ELD dataset, and sampled with a process following (or sim-
ilar to) Eq. (7). The results of the other methods described
in Section 5.1 are also presented as references.
As shown in Table 1, the domain gap is significant be-
tween the homoscedastic/heteroscedastic Gaussian models
and the de facto noise model (characterized by the model
trained with paired real data). This can be attributed to
(1) the Gaussian approximation of Possion distribution is
not justified under extreme low illuminance; (2) horizontal
bandings are not considered in the noise model; (3) long-
tail nature of read noise is overlooked. By taking all these
factors into account, our final model, i.e.G+P+R+U
gives rise to a striking result: the result is comparable to
or sometimes even better than the model trained with paired
real data. Besides, training only with real low-light noisy
data is not effective enough, due to the clipping effects (that
violates the zero-mean noise assumption) and the large vari-
ance of corruptions (that leads to a large variance of the
Noise2Noise solution) [38]. A visual comparison of our fi-
nal model and other methods is presented in Fig. 8, which
8Alternating current light is not noise, but a type of illumination that
breaks the irradiance constancy between short/long exposure pairs, making
the quantitative evaluation inaccurate.
Table 2: Quantitative results (PSNR/SSIM) of different methods on our ELD dataset containing four representative cameras.
Camera fIndex Non-deep Training with real data Training with synthetic data
BM3D [15] A-BM3D [44] Paired data [9] Noise2Noise [38] G G+P [22] Ours
×100 PSNR 37.69 37.74 44.50 41.63 42.35 42.46 45.36
SSIM 0.803 0.776 0.971 0.856 0.893 0.889 0.972
×200 PSNR 34.06 35.26 42.45 37.98 38.93 38.88 43.27
SSIM 0.696 0.721 0.945 0.775 0.813 0.812 0.949
×100 PSNR 33.97 36.60 41.28 40.47 39.57 40.29 41.79
SSIM 0.725 0.779 0.938 0.848 0.823 0.845 0.912
×200 PSNR 31.36 32.59 39.44 37.98 36.68 37.26 39.69
SSIM 0.618 0.723 0.910 0.820 0.757 0.786 0.875
×100 PSNR 30.79 31.88 40.10 38.21 40.59 40.94 40.62
SSIM 0.589 0.692 0.931 0.826 0.925 0.934 0.937
×200 PSNR 28.06 28.66 37.32 34.33 37.49 37.64 38.17
SSIM 0.540 0.597 0.867 0.704 0.871 0.873 0.890
×100 PSNR 29.70 30.13 39.05 38.29 39.77 40.08 39.84
SSIM 0.556 0.640 0.906 0.859 0.884 0.897 0.921
×200 PSNR 27.52 27.68 36.50 34.94 37.67 37.86 37.59
SSIM 0.537 0.579 0.850 0.766 0.870 0.879 0.879
Input BM3D A-BM3D G G+P Noise2Noise Paired real data Ours
Figure 9: Raw image denoising results on both indoor and outdoor scenes from SID Sony dataset. (Best viewed with zoom)
Input BM3D A-BM3D G G+P Noise2Noise Paired real data Ours
Figure 10: Raw image denoising results on our ELD dataset. (Best viewed with zoom)
shows the effectiveness of our noise formation model.
Though we only quantitatively evaluate the results on in-
door scenes of the SID Sony set, our method can be applied
to outdoor scenes as well. The visual comparisons of both
indoor and outdoor scenes from SID Sony set are presented
in Fig. 9. It can be seen that the random noise can be sup-
(a) Input (b) Paired real data (c) Ours
Figure 11: Denoising results of a low-light image captured by a
Huawei Honor 10 camera.
SonyA7S2 NikonD850 CanonEOS70D CanonEOS70D
PSNR values (dB)
x 100
x 200
SID only
SonyA7S2 NikonD850 CanonEOS70D CanonEOS70D
PSNR values (dB)
x 100
x 200
w/o. target camera noise parameters
w. target camera noise parameters
Figure 12: (a) Performance boost when training with more synthe-
sized data. (b) Noise parameter sensitivity test.
pressed by the model learned with heteroscedastic Gaussian
noise (G+P) [22], but the resulting colors are distorted, the
banding artifacts become conspicuous, and the image de-
tails are barely discernible. By contrast, our model pro-
duces visually appealing results as if it had been trained
with paired real data.
5.3. Results on our ELD dataset
Method comparisons. To see whether our noise model
can be applicable to other camera devices as well, we assess
model performance on our ELD dataset. Table 2 and Fig. 10
summarize the results of all competing methods. It can be
seen that the non-deep denoising methods, i.e. BM3D and
A-BM3D, fail to address the banding residuals, the color
bias and the extreme values presented in the noisy input,
whereas our model recovers vivid image details which can
be hardly perceived on the noisy image by human observers.
Moreover, our model trained with synthetic data even often
outperforms the model trained with paired real data. We
note the finding here conforms with the evaluation of sen-
sor noise presented in Section 3.2, especially in Fig. 4 and
5, where we show the underlying noise distribution varies
camera by camera. Consequently, training with paired real
data from SID Sony camera inevitably overfits to the noise
pattern merely existed on the Sony camera, leading to sub-
optimal results on other types of cameras. In contrast, our
model relies on a very flexible noise model and a noise cali-
bration process, making it adapts to noise characteristics of
other (calibrated) camera models as well. Additional evi-
dence can be found in Fig. 11, where we apply these two
models to an image captured by a smartphone camera. Our
reconstructed image is clearer and cleaner than what is re-
(a) SID only (b) SID + MIT5K (c) Ground Truth
Figure 13: Denoising results of a low-light image captured by a
NikonD850 camera.
stored by the model trained with paired real data.
Training with more synthesized data. A useful merit of
our approach against the conventional training with paired
real data, is that our model can be easily incorporated with
more real clean samples to train. Fig. 12(a) shows the rel-
ative improvements of our model when training with the
dataset synthesized by additional clean raw images from
MIT5K dataset [7]. We find the major improvements, as
shown in Fig. 13, are owing to the more accurate color and
brightness restoration. By training with more raw image
samples from diverse cameras, the network learns to infer
picture appearances more naturally and precisely.
Sensitivity to noise calibration. Another benefit of our
approach is we only need clean samples and a noise cali-
bration process to adapt to a new camera, in contrast to cap-
turing real noisy images accompanied with densely-labeled
ground truth. Besides, the noise calibration process can be
simplified once we already have a collection of parameter
samples from various cameras. Fig. 12(b) shows models
can reach comparable performance on target cameras with-
out noise calibration, by simply sampling parameters from
other three calibrated cameras instead.
6. Conclusion
We have presented a physics-based noise formation
model together with a noise parameter calibration method
to help resolve the difficulty of extreme low-light denois-
ing. We revisit the electronic imaging pipeline and inves-
tigate the influential noise sources overlooked by existing
noise models. This enables us to synthesize realistic noisy
raw data that better match the underlying physical process
of noise formation. We systematically study the efficacy
of our noise formation model by introducing a new dataset
that covers four representative camera devices. By train-
ing only with our synthetic data, we demonstrate a convolu-
tional neural network can compete with or sometimes even
outperform the network trained with paired real data.
Acknowledgments We thank Tianli Tao for the great help
in collecting the ELD dataset. This work was partially sup-
ported by the National Natural Science Foundation of China
under Grants No. 61425013 and No. 61672096.
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Conference Paper
Full-text available
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