Noise Suppression in Low-light Images through Joint Denoising and Demosaicing
Priyam Chatterjee∗
Univ. of California, Santa Cruz

Neel Joshi
Sing Bing Kang
Microsoft Research

Yasuyuki Matsushita
Microsoft Research Asia

priyam@soe.ucsc.edu{neel,sbkang}@microsoft.com

yasumat@microsoft.com

Abstract
We address the effects of noise in low-light images in thispaper. Color images are usually captured by a sensor witha color filter array (CFA). This requires a demosaicing process to generate a full color image. The captured images
typically have low signal-to-noise ratio, and the demosaicing step further corrupts the image, which we show to be
the leading cause of visually objectionable random noise
patterns (splotches). To avoid this problem, we propose a
combined framework of denoising and demosaicing, where
we use information about the image inferred in the denoising step to perform demosaicing. Our experiments showthat such a framework results in sharper low-light images
that are devoid of splotches and other noise artifacts.

(a) RGB image(b) Demosaiced image

Figure 1. Effect of demosaicing on low-light noise characteristics:(a) RGB image with spatially independent Poisson noise; (b) demosaiced version of the noisy image. The simulated noisy RGB
image was subsampled to form the Bayer pattern image. Notice
how the demosaiced image demonstrates more splotches.

are observed) to form a full color image. With advancesin optical and electronic systems, current cameras can produce high quality images when the images are well exposed.
However, under low-light conditions, when the number ofphotons entering the imaging system is low, the raw image
captured in the CFA has a low signal-to-noise ratio (SNR).
Most cameras then produce quite noisy images. Cameras
typically adapt to such low signal levels by increasing their
sensitivity (ISO level) to the input signal, which amplifies
the input noise. Such noise usually manifests itself in theform of splotches that are very salient to the human visual system (Fig. 1(b)). In our work, we concentrate on
suppressing such visually unpleasant artifacts that typicallycorrupt light-limited images.

1. Introduction
Low-light noise is a significant problem in photography.
Most consumer cameras have poor low-light characteristics,
which typically result in images with noticeable noise artifacts. Taking longer exposures reduces noise; however,this is only useful for static cameras and scenes, otherwise
a blurry image is obtained. Active lighting in the form ofa flash is not always viable as it causes color aberrations
and is effective only for nearby objects. Recently, camera manufacturers have started addressing the problem of
low-light photography by introducing cameras with larger
photon sensors to accumulate more light at shorter exposures. In this paper, we propose a software-based approachto suppress the random mid-frequency texture patterns (orsplotches) and other noise effects in low-light images, making it possible to capture sharp as well as noise-free images
with short exposures.
Most modern consumer cameras capture images on asingle sensor with a color filter array (CFA), of which theBayer pattern [2] (Fig. 5(a)) is the most popular. A demosaicing algorithm is then used to interpolate the missing colors (e.g., red and blue values wherever only green samples

Our paper has two major contributions. First, we show,
through simulations, that demosaicing is the main cause of
the splotches commonly observed in low-light images. Thisfinding leads us to our second contribution: a framework
for combined denoising and demosaicing specifically targeting low-light images. To efficiently solve the joint problem, we pose the problem as that of vector upsampling in
the presence of noise. This vector upsampling is carried out
in a two-step framework that is motivated by Locally Linear
Embedding (LLE) [23]. In the first step (denoising), embedding information is learned about the image from the noisy∗ The work presented in this paper was done while the author was visiting Microsoft Research, Redmond.

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Figure 2. Outline of our denoising and demosaicing framework.

Bayer image, which is then enforced in an unknown low
resolution image to perform the second step (demosaicing).

Figure 3. Histograms of noise values in different color channels of
two different flat regions of the Macbeth color chart captured as
Bayer pattern. The image was captured under low-light conditionsat shutter speed 0.1 sec. and ISO 1600. In the plot to the right, thehistograms for the green and blue channels are very similar.

2. Related Work
Image denoising is a well-studied problem that has seen
considerable performance improvement in recent years (see[6] for a survey). Broadly, denoising techniques can be classified as either transform-domain-based or spatial. Portilla
et al. [21] proposed a wavelet-based method that was widely
regarded as the state-of-the-art until recently. The recently
proposed method of BM3D [8] employs a hybrid approachby first identifying similar patches within the noisy image.
The similar patches are then denoised collaboratively in atransform-domain (e.g., DCT) leading to remarkable denoising performance.
Spatial-domain methods can vary significantly in theirapproaches. Techniques range from denoising using image statistics [3, 7] or dictionaries [10] to using priors on
the noise in a segmentation-based framework [17]. Another popular class of methods is based on directional filters [4, 24, 25] where denoising is performed by learning anembedding of the image in a local neighborhood. Locality can be defined either spatially [24, 25] or in the patch
space [4], with the latter taking advantage of patch redundancy in the input image.
Mathematically, denoising in Non-Local Means(NLM) [4] is performed by representing each patch in
the image as bzi = Ywi , where Y is a matrix (or dictionary) of patches created from the noisy image, with thecoefficients wi being a measure of similarity between thereference noisy patch yi and column elements in Y. The
self-similarity based framework has also been extended todemosaicing [5]. Instead of using a fixed Y, Elad et al. [10]proposed to iteratively update the over-complete dictionary
Y and sparse coefficients wi to improve performance.
This framework was later adapted for different restoration
problems by Mairal et al. [18, 19].
Although dictionary-based methods have been applied toa variety of image restoration tasks, they rely on the presence of the ground truth to act as a prior on the desired output. This is especially true for image demosaicing [18, 19].
They are, thus, not applicable to our problem where suchground truth cannot be obtained without making simplistic
assumptions about low-light image generation. Moreover,restoration can be adversely affected if the input image is
not described well by the dictionary.

Prior techniques do not explicitly target the removal of
splotchy artifacts in low-light images. To remove such artifacts, it is essential to account for Poisson nature of thenoise in the CFA (typically Bayer) image. The methods
discussed thus far, and most CFA image denoising methods [11, 27], assume the noise to be Gaussian, and notsignal-dependent. Deledalle et al. [9] recently extended
NLM for Poisson noise by redefining the similarity measure
between noisy grayscale patches. However, it is not clear
how that work can be extended to Bayer images with nonhomogeneous noise in different subsampled color channels.
In the class of denoising approaches that use color information, Hirakawa et al. [15] proposed an interpolation
filter with the assumption that the color channels have similar higher frequencies. Zhang et al. [28] proposed a PCAbased approach for color reproduction from noisy raw data.
Bennett et al.’s approach [3] assumes the true color at eachpixel to be a combination of two colors which are estimated from a neighborhood. Although noise is accounted
for in [3, 28], learning the basis colors and PCA vectors
respectively can be challenging under low SNR. Anotherspace-varying method for joint denoising and demosaicing
was proposed by Menon et al. [20]. However, the noise
there, as in [3, 28], is assumed to be independent and identically distributed Gaussian. As a result, they are not welltuned to handle low-light images.
In contrast to prior approaches, we are specifically interested in suppressing splotchy effects that are typical in
low-light images. In order to design an effective techniqueto remove these artifacts, we first need to understand how
they are generated. The next section describes our findings.

3. Splotch Artifacts in Low-Light Images
Images are typically captured using a CFA (e.g., Bayerpattern), where each sensor element is capable of capturing
light within specific wavelengths. The light (or photons) incident on a sensor element is accumulated over a period oftime controlled by the shutter speed setting. Due to this photonic nature of light, the voltage resulting from the photon
counting process is noisy. This noise is called shot noise.
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(a) 14 bits/pixel,(b) 14 bits/pixel,
RGB imagedemosaiced image(c) Gradient orientations in color channels of (a)(d) Gradient orientation in color channels of (b)(e) 8 bits/pixel,(f) 8 bits/pixel, deRGB image
mosaiced image(g) Gradient orientation in color channels of (e)(h) Gradient orientation in color channels of (f)Figure 4. Directionality of Poisson noise visualized with gradient orientations histograms for images with various quantization levels.

Although modern cameras are capable of storing raw intensities with high precision (bits per pixel), we still study theeffects of such quantization in low-light images.

The voltage in each sensor element is usually magnified
by a gain factor based on the ISO setting of the camera.
While this increases sensitivity to the input signal, it also
results in amplification of the noise. The voltage is thenquantized to obtain the raw intensity values. Although imperfect electronic components also contribute to the noise
affecting the image, the dominant noise at lower intensities
has been shown to be shot and quantization noise [1].

In our study, we ran simulations to study the combined effects of different processes in the image formation
pipeline, namely, quantization and demosaicing. Our simulator is designed to study the effects of different levels ofPoisson distributed noise on different quantization levels of
mainly constant-intensity images. The effect was studied
when noise was added independently in each color channelof color images, as well as in the demosaiced image obtained from subsampling the noisy color image according
to the Bayer pattern. The synthetically generated noisy images were visually inspected and analyzed (by computing
gradient and orientation histograms).

Next, the camera demosaics the noisy Bayer image to
produce a color image. Since most demosaicing algorithms
do not account for noisiness of the raw data, a denoisingprocess is often applied to the resulting image. This is followed by other non-linear operations such as gamma correction, color tone-mapping, and even sharpening before thefinal color image is stored in the camera. Here we are interested in identifying the chief causes of the splotches in
low-light images.

In our simulations over multiple flat images, the effectof quantization level on the splotches was visually indiscernible for the full color as well as demosaiced images(Figures 4(a)-(d)). However, the histogram of gradient orientations (Figures 4(e)-(h)) exhibit stronger directionality
along vertical and horizontal directions as quantization is
reduced to 8 bits per pixel. Considering that even lower-end
commercial cameras record information in at least 8 bits per
pixel and the fact that this does not lead to any visually detectable increase in splotches, we eliminate quantization asa significant factor of image noise artifacts. Henceforth, we
consider Poisson distributed shot noise as the major sourceof low-light noise.

We start by studying the noise characteristics of such images. As mentioned earlier, shot noise is a result of photonic nature of light. Since the intensity values are a result of a counting process, the noise is Poisson distributed,
and can be assumed to be spatially independent. We confirmed this experimentally by capturing multiple images ofa static scene (e.g., Macbeth color chart) under various shutter speeds and ISO settings. We found that in any given flat
region, the variance of the noise is proportional to the mean
intensity of the flat region obtained by averaging the intensities of each color channel, the constant of proportionality
being dependent on the camera’s ISO setting (gain factor).
Moreover, the histogram of the noise in each color channel in each flat area fits a Poisson density function. Thisis shown in Fig. 3 for two different flat regions of the color
chart captured under low-light conditions with shutter speed
0.1 second and ISO 1600. This Poisson distribution is attributed to the shot noise [12, 14]. The quantization noise,on the other hand, is due to the digitization of the voltage.

Our simulations with varying levels of Poisson noise led
to two important conclusions: (1) even when the noise is independent in each channel, patterns are visible in the noisy
image (gradient orientation histograms do not show any bias
in edge direction); (2) the visual patterns (splotches) are
more pronounced in demosaiced images, irrespective of thedemosaicing method employed. Interestingly, demosaicing
does not seem to alter the approximately uniform distribu323

tion of gradient orientations. This leads us to believe thatthe noisy patterns in the image are a result of humans being adept at identifying patterns in any image [26], and thatsuch patterns are noticeably enhanced by the demosaicing
process. An example of such enhanced splotches is illustrated in Fig. 1 showing a house image with simulated Poisson noise added independently in each color channel and its
demosaiced version obtained from the simulated CFA noisy
image sampled according to the Bayer pattern.
Although modern demosaicing techniques (see [13, 16]
for comprehensive reviews) take into account inter-channel
dependencies, most do not account for noise in the observed
Bayer samples. Interpolating across noisy color channels
corrupts the noise characteristics in the demosaiced image, enhancing splotches in the process. Such artifacts arethen propagated further in the imaging pipeline. Hence, it
is important to suppress the Bayer domain Poisson noise
before demosaicing. Most Bayer domain denoising methods [11, 27] do not handle Poisson noise. Moreover, thedemosaicing method usually has no information about thedenoising process and errors in denoising can be propagatedeasily. Motivated by this, we propose a method based on
LLE [23] that we adapt to perform combined denoising anddemosaicing in a vector upsampling framework.

of similar blocks to obtain a denoised Bayer image. This
embedding is then enforced in the demosaicing step throughan optimization framework. This implicitly enforces the
cross-color correlation in demosaicing as the embeddings
are learned simultaneously from all color channels.

4.1. Denoising Step
As mentioned earlier, denoising of the Bayer blocks is
performed by representing each noisy block as a linear combination of similar blocks. To learn such an embedding, we
first need to identify similar blocks. However, under lowlight conditions, the weak signal corrupted by noise leads to
low signal-to-noise ratios (SNR), making it difficult to identify similar blocks. To add robustness, we consider larger
regions consisting of multiple spatially collocated blocks toform patches. Blocks with similar neighborhoods to any
given reference patch are identified and the linear embedding weights are learned. The denoising step thus consistsof learning a local embedding of a patch in the Bayer domain and using it to perform denoising. Below we provide
an outline for the denoising process (Fig. 6):
1. Form patches centered at each [R, G, G, B] node. For
any given patch centered at yi identify the K-mostsimilar patches (centers denoted by yj ) within the image subject to noise corruption.

4. Denoising–Demosaicing as Upsampling

2. Represent the center node of the patch b
zi under consideration of similarity to yi as a linear combination of
the similar patches to be of the form
K
X
b
zi =
wij yj = Yi wi ,(1)

In our proposed framework, we pose the problem
of denoising and demosaicing as that of vector upsampling (Fig. 5). The task of demosaicing is to estimate
the unknown color information at each pixel location.
We consider this problem as estimating the unobserved
blocks (Fig. 5(b)), at exact one pixel shifts in horizontal,
vertical and diagonal directions. For example, consider thenumbered regions in Fig. 5(a), estimating the horizontallyshifted image results in estimating the green channel information at locations where only a red value was observed. Ina similar manner, vertical and diagonally shifted image estimates result in obtaining estimates of different color channels. As a result, red, blue and two green color estimates areaccumulated at each pixel location, from which a full color
RGB image is obtained. Thus, we show that vector upsampling with an appropriate choice of vectors ([R, G, G, B]
patterns shown in the figure) can lead to demosaicing. As
such, any method that performs 2-D upsampling of vectorvalued functions can be used for this purpose. However,such interpolation methods must account for noise contamination of the samples, as well as the correlation between
the observations ([R, G, G, B] vector elements).
Here we propose to perform vector interpolation bylearning local embeddings of each Bayer block (see Fig. 2),
where locality is in terms of similarity of block intensities (vector magnitudes). This is performed by representing
each observed block (black nodes) as a linear combination

j=1

where Yi is the matrix formed by concatenating thevectorized center nodes of the similar patches yj , wij
are the weights that measure the confidence of a patch
centered at yj being similar to that centered at yi , andwi is a vector containing the wij entries. The weights
are calculated in an optimization framework as
b i = arg min kyi − Yi wi kp ,
w
(2)
wi

with p chosen to fit the error distribution.
3. Repeat the process for blocks with different patterns,
namely, [G, R, B, G], [G, B, R, G], & [B, G, G, R].
Note that with blocks of a certain pattern, we match
blocks with the same pattern only. The embedding learning process is carried out for each such pattern to obtain
multiple denoised estimates of the Bayer image. The final
estimate is obtained as an average of the multiple estimates.
This secondary averaging process reduces the residual noisein the initial estimates to produce the final denoised raw image. More importantly, doing so allows us to obtain multiple embeddings of each pixel, which provides more constraints for the optimization in the demosaicing step.
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(a) Demosaicing by estimating(b) Equivalent
shifted images
vector upsampling
Figure 5. Demosaicing of noisy Bayer data as vector upsampling:(a) single pixel shifts in horizontal, vertical, and diagonal (notshown) directions fill-in missing color information at different
locations; (b) corresponding visualization of vector upsamplingwhere the black nodes are observed noisy Bayer patterns and graynodes marked H, V, and D are filled-in through horizontal, verticaland diagonal shifted image estimation respectively.

Figure 6. Our combined denoising and demosaicing framework.

enforce the embedding on it to obtain the final output. However, such a method relies heavily on the performance of theinitial demosaicing. To counter that effect, we propose toperform demosaicing in an optimization framework.
The motivation of our optimization framework arises
from the relation between a high resolution (HR) image andits corresponding low resolution (LR) version. Consider theBayer image as an incomplete observation of an unknown
HR image that we wish to estimate. A 2× downsampled LR
image could then be formed by first averaging each color
channel of the HR image in a 2 × 2 region and then subsampling the smoothed image. Thus, the color information at any pixel at location i of the LR image is obtained
from averaging of the colors at the i-th block of the HR image, only some of which are observed in the Bayer image.
Without loss of generality, consider the red color channel inFig. 5(a). We can see that the red value in the LR image corresponding to the numbered block (indexed by i) is obtained
unfrom the observed ri1 and unobserved ril
for l = 2, 3, 4.
For notational convenience, we denote ri1 as ri . The embeddings for each block in the Bayer domain can thus bethought to be similar to the embedding for the corresponding pixel in the (unknown) LR image. This is in keepingwith the spirit of LLE [23], where dimensionality reduction
is performed by enforcing local embeddings learned in thehigher dimension to data in the lower dimensional space. In
our context, we learn the local embeddings in the partiallyobserved HR (Bayer) image and enforce them in the downsampled LR image. Thus, we can write
4
4
X
X
X
un
un
ri +
ril
=
wij (rj +rjl)∀ i. (4)In order to apply this scheme, we first need to identify
similar patches, given only their noisy observations. Under
low-light conditions, the noise has been shown to be Poisson distributed which is dependent on the (unknown) true
intensity of the Bayer pattern image. Similarity measures
based on such Poisson noise has been proposed by Alteret al. [1]. However, in our case we found that using an `2
distance measure between noisy patchesd(yi , yj ) = kyi − yj k22 ,(3)

to identify similar patches works reasonably well for our
purposes. This is because we are merely interested in ranking noisy patches based on similarity to a reference patch
to identify the K = 30 most similar patches. The weightcalculation mechanism of Eq. (2) then implicitly rejects dissimilar patches by giving them low weights.
The patch-based embedding of each block allows us toperform denoising of the raw data as outlined in Fig. 6. Demosaicing this image using any demosaicing method results
in a denoised color image. However, further noise suppression is achieved when the demosaicing step makes use of
the local linear embedding information learned in the denoising step.

4.2. Demosaicing step

l=2

Once the raw image is denoised, the missing color information needs to be estimated to form the final image. This
process is known as demosaicing. One can use any existing
method to perform demosaicing of the denoised raw image.
However, demosaicing being a special form of interpolation inherently leads to reduced sharpness in the final image. Moreover, for images with low SNR as in our case, thenoise may not be sufficiently removed by denoising. One
way to further suppress the noise is to use any existing demosaicing algorithm to obtain an initial color estimate andjl=2

Rewriting the above equation in terms of all the observed
and unobserved samples of the HR image in a vector form(r and run respectively) we obtainr + Drun = W(r + Drun )⇒ e
r = (W − I)Dr

un

un

f
= Wr

(5)
,

(6)

where D is a matrix operator where each row implements asummation of the unobserved samples corresponding to theobserved samples r, W is a sparse matrix with wij as its
325

5. Resultsi, j-th entry, er = r − Wr is a function of observed samf = (W − I)D with I as the identity
ples only, and W
matrix. In the demosaicing step, we are interested in esf and e
timating run given the estimated W
r. Note that there
are many more unobserved red values than observed ones
making the problem ill-posed. Hence, we employ a regularization framework to reduce the solution space. We use
Eq. (6) as our data fitting term and an initial demosaicing of
the denoised Bayer image as prior information (run0 ). The
final estimate for the demosaiced image is obtained by solving for the unknown intensities as
f un kp + kΛ(run − run )kq , (7)bker − Wrrun = arg min0
runwhere Λ is a diagonal matrix with varying diagonal entries
that allow us to control the penalty of deviating from the initial estimate, and p, q are chosen according to the distribution of the error for the data fitting and regularization terms.
We use p = q = 0.65, since the histogram of the data fitting error fits a hyper-Laplace distribution for our simulated
experiments (see the following section). This also allows
us to avoid over-fitting at the higher intensities and oversmoothing in the low-intensity regions [22].
As mentioned earlier, noise may still be present in the denoised Bayer image. Such noise is more perceptible in thesmoother regions. Thus, allowing the final estimate in thesmoother regions to deviate from the initial estimate can beadvantageous. On the other hand, enforcing the prior can begood in the textured regions where there may be fewer similar patches. The diagonal entries of Λ can thus be chosen to
be inversely related to the number of similar blocks (large
wij values) found in the embedding stage which serves asa good measure of the reliability of the learned embedding.
However, we found that simply using a fixed Λ = 0.1 I in
the optimization framework leads to satisfactory suppression of noise and splotches in low-light images, as demonstrated in Sec. 5.

To validate our method, we perform experiments withreal-world images captured with different cameras, under
different low-light conditions. In Fig. 7, we compare ourmethod to straight demosaicing results – we use the ‘demosaic’ function in Matlab. The noise artifacts are significantly
reduced by our approach across a large range of SNR, image content, and lighting conditions (indoor, outdoor, daytime, nighttime, and flash), without any parameter tuning
or user input to handle the change in the noise levels andimage content. The images in these results were shot witha Canon 1Ds Mark III and Rebel Xti, which have very different image sensors, showing that our method generalizes
across camera types. Note how the extremely high-textured
splotch patterns seen in the straight demosaiced results do
not appear in our results – the smooth areas appear smooth,
yet textures are largely retained.
In Fig. 8 we compare our results to several existing techniques. For our comparisons, we choose two methods that
perform denoising after demosaicing, as is commonly done.
The methods used are Neat Image and BM3D [8] (state-ofthe-art denoiser [6]). Since our method performs denoisingon Bayer images, we also compare to a recent Bayer denoising method [27]. Finally, we show results from a joint
denoising and demosaicing method proposed by Menon etal. [20]. For fair comparisons, we tuned the parameters ofeach method to obtain the most visually pleasing results.
From Fig. 8, it can be seen that our method maintains agood balance of denoising smooth regions while retaining
textured regions. For previous methods, a trade-off must
be made. Either the support-region needs to be large to remove the splotches, which then blurs the image detail, or
vice versa. Moreover, with many of the previous methods, even when the high and mid-frequency splotches are
removed, lower frequency components of the artifacts remain, where smooth regions appear to have a low-frequency
low-intensity color pattern. The benefits of our method are
best seen when viewing the images on a computer screen.

4.3. Poisson Noise Model and Error Norm
The form of the error norm in our LLE framework is dependent on the image noise distribution. While it is known
that low-light noise is Poisson distributed, without further
analysis, it is not obvious what the error distributions would
be on the terms in Equations 2 and 7. We empirically measured the distributions, by generating Poisson distributed
samples in a low-intensity range from a set of known samples with known coefficients. We fit a generalized Gaussian to this distribution and found it to be hyper-Laplacian(p = 0.65 < 1), with the variance proportional to the meanvalue of the samples. This distribution is consistent with amean subtracted Poisson distribution as it is sparser than aGaussian, which is to be expected for a Poisson distribution
at low-intensity levels, and its variance is proportional to theoriginal mean of the distribution. We minimized this norm
using iterative re-weighted least-squares.

6. Conclusions
We proposed a framework for combined denoising anddemosaicing of low-light images, specifically targeted at reducing the splotches and noise effects in such images. For
this we make use of a local linear embedding framework
where a linear embedding is learned in the denoising step.
This local embedding is then enforced within an optimization framework to perform refinement of an initial demosaicing of the denoised image. We showed that the proposed method is able to considerably improve the qualityof the final output image over the traditional approaches ofdemosaicing and then denoising and also performs better326

Figure 7. Comparisons of real images captured under various conditions to those obtained by straight demosaicing. The low-light images
are shot with different cameras (Canon 1Ds Mark III and Rebel Xti)

than recently proposed joint denoising and demosaicing approaches.
Our method assumes access to the raw image data before
it is corrupted by various stages in the image formation process. However, such raw data is not easily accessed for aconsiderable number of consumer cameras. For those cases
and for existing images, it is necessary to invert the demosaicing and other in-camera processing to estimate the raw
data before applying our algorithm. This is a direction of
our future work.

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