An Adaptive Richardson-Lucy Algorithm for Single

Image Deblurring Using Local Extrema Filtering

Jiunn-Lin Wu*, Chia-Feng Chang and Chun-Shih Chen

Department of Computer Science and Engineering, National Chung Hsing University,

Taichung, Taiwan 402, R.O.C.

Abstract

Motion Blur is one of the common artifacts in digital photographing. With the population of

handheld camera and smart phone, image deblurring becomes an important problem. Richardson-

Lucy algorithm is well-known deconvolution algorithm. But the ringing artifacts usually appear while

the estimated point spread function is not accurate. In this paper, we proposed an improved

Richardson-Lucy deconvolution algorithm. Before deconvolution step, we separate the blurred image

into smooth part and edge part which is called the edge map. The blurred image and edge map are then

used for image deblurring. By using the proposed edge map, the ringing artifacts in the deblurred

image are significantly reduced while preserving the sharp edge information.

Key Words: Motion Blur, Deconvolution, Richardson-Lucy, Ringing Artifacts, Edge Map

1. Introduction

Motion Blur is common artifact which produces dis-

appointing blurred image under dim light in digital pho-

tography. It is caused by camera shaking or the target

object moving during exposure time. Recently, handheld

camera and smart phone are getting more and more po-

pular; restoring a blurred image is becoming an important

issue. Figure 1 shows the example of image deblurring.

In general, motion blur can be separated into two

types. The first one is camera shake caused the image

blurred; the second one is the target object moving. A

blurred image can be viewed as an unblurred image con-

volution with point spread function (PSF) which is the

movement of camera or the movement of target object. If

the point spread function is shift-invariant, the image

deblurring problem can be transformed into image de-

convolution. According to the point spread function is

known or not, the deconvolution can be classified into

non-blind deconvolution [1�4] and blind deconvolution

[5�8]. Blind deconvolution is an ill-pose problem, it uses

only blurred image to restore image. Therefore image-

pair deblurring method [9,10] is proposed to solve mo-

tion blur problem, but the additional image is hard to ac-

quire. Nonblind deconvolution uses known point spread

function and blurred image to restore deblurred image.

Wiener filter [11] and Richardson-Lucy deconvolution

[2] are well-known nonblind deconvolution algorithms

which are good at image deblurring. But if the point

spread function is not accurate, the deblurring result will

appear undesired ringing artifacts at the smooth region

around edges. To solve this problem, Wang et al. [3] pro-

posed using different weight values for smooth region

and edge region during the deblurring process to sup-

press ringing. But it still failed around some edges. Zhao

et al. [12] suggested that using only two weight values

for describing smoothness information of image is not

enough.

Journal of Applied Science and Engineering, Vol. 16, No. 3, pp. 269�276 (2013) DOI: 10.6180/jase.2013.16.3.06

*Corresponding author. E-mail: jlwu@cs.nchu.edu.tw Figure 1. Example of image deblurring.

In this paper, we proposed an adaptive image de-

blurring algorithm using local extrema filtering. To re-

duce ringing artifacts from deblurred image, the ex-

trema-based multiscale decomposition filter is used to

distinguish the edge region and smooth region, and then

edge map is obtained. According to Zhao et al. sugges-

tion, it is better that existing more than two weight values

in edge map instead of only two weight values in edge

map. Thus we use blurred image and edge map which

contains more than two weight values are both used to

deconvolution procedure. Finally the deblurred image is

obtained with less ringing.

The rest of the paper are organized as follows. Re-

lated works which is mentioned in Introduction are de-

scribed in detail. Then according to related works our

proposed method is presented. And then experiments are

designed for verifying our deblurring algorithm. Finally,

we conclude this paper.

2. Related Works

In general, a blurred image can be modeled as

(1)

where I is blurred image; L is latent unblurred image; k

is point spread function; n is noise and � is convolution

operator. According to point spread function is known

or not, image deconvolution can be separated into non-

blind deconvolution and blind deconvolution.

Richardson-Lucy algorithm [2] is a well-known it-

erative deconvolution method for image deblurring. A

more clearly deblurred image is generated for each time

of iteration. After several iterations, a sharp and un-

blurred result image can be obtained. According to Bayes’

theorem, (1) can be transform into

(2)

Then the formulation of Richardson-Lucy algorithm

can be defined as

(3)

where * is correlation coefficient operator, � is convo-

lution operator, t is the tth of iteration, Lt is current itera-

tion deblurred image, Lt+1 is the next iteration deblurred

image, k is PSF and I is blurred image. If the point

spread function is not accurate enough, the ringing ar-

tifacts will appear in the result image. Figure 2 shows

that if the point spread function is not precise enough,

then the ringing artifacts will be generated in the result

image. Therefore, to reduce ringing artifacts is an im-

portant issue for image deblurring. Several methods

have been proposed to solve this problem.

Shan et al. [13] suggested that the smooth region in

the blurred image is also smooth in deblurred image.

Therefore, Shan included a constraint about the smooth

region called local prior during the restoration process.

The formulation of local prior is defined as

(4)

where i is pixel position in image, L is latent unblurred

image, I is blurred image � is the standard deviation and

� is smooth region in image. Figure 3 shows the corre-

sponding smooth region of original image.

For this reason Wang et al. proposed improved Rich-

ardson-Lucy algorithm using local prior. It includes an

adaptive weight map called edge map during deblurring

process. Before deconvolution, the blurred image is used

to extract the edge map which indicates where the smooth

or edge region it. And then the edge map and blurred

270 Jiunn-Lin Wu et al.

Figure 2. Example of the ringing artifacts. (a) Original im-age. (b) Blurred image. (c) The result of Richard-son-Lucy algorithm.

Figure 3. Example of edge map. (a) Blurred Image. (b) Thecorresponding smooth region of blurred image.

image are used as inputs for each time of iteration. When

the ringing is appear during deconvolution process, the

edge map will reduce the effect of ringing by assigning

the smooth region where ringing appeared large weight

to update it. Then the ringing artifacts can be efficiently

reduced from result.

From Figure 4, we can notice that Wang’s method

reduces most ringing artifacts, but the ringing artifacts

around the region where between two edges is not re-

duced successfully. In next section, we will discuss this

problem, and then proposed our deblurring algorithm.

3. Proposed Method

In this section, we will propose an adaptive Richard-

son-Lucy deconvolution algorithm using local extrema

filtering. Observe on the result which is deblurred by

Wang et al, the region between two edges is not fully

described by Wang’s edge map. Consequently, the ring-

ing artifacts still exist in deconvolution result. To get an

appropriate edge map is an important issue for obtaining

a good deconvolution result. As a result, there are two

problems for extracting edge map, first is well descrip-

tion edge map about the smooth and edge region; the

other is only two weight values in edge map is not enough.

Extrema-based multiscale decomposition (EMD) [14]

is good at separating detail and mean layer. Compare

with existing edge-preserving image decomposition al-

gorithms, EMD can extract the detail from input image

while preserving edge mean and contrast properly. Its

idea is getting the local extrema such that maxima or

minima, and then getting the mean layer by averaging

maximum layer and minima layer, the mean layer is also

called smooth layer. Then we extract the detail layer by

subtracting smooth layer from input image.

As mentioned before the edge map must have good

description at smooth region, thus we improved EMD

algorithm for purpose. First EMD is used for separating

the detail layer and mean layer, and then the contour is

extracted from mean layer by calculate the gradient of

input image, called smooth map. For further edge map

information, the gradient of detail layer is also used for

describing the detail part called detail map. Finally,

Combining the detail map into smooth map, then the

result map is the proposed edge map. The flowchart of

our improved EMD method is shown in Figure 6.

In Figure 7(a), we can observe that the smooth map

contains most contours, so we can extract the contours

which are strong edges (Figure 7(c)) from smooth map.

And the detail map (Figure 7(b)) contains most texture

information, thus we extract further detail information

(Figure 7(d)) from detail map. But the detail map also

contains undesired noise information, so a simple thre-

shold method is used for filtering out the noise. Compare

proposed edge map with the edge map extracted by

Wang’s method in Figure 8; the region between two

strong edges is clear defined in our proposed edge map.

Wang’s edge map only separate the blurred image into

smooth region and edge region, it is too strict to define

Adaptive Richardson-Lucy Algorithm for Single Image Deblurring 271

Figure 4. Comparison of deblurring results. (a) The resultusing Richardson-Lucy. (b) The result using Wang’smethod. (c) The corresponding magnitude of (a).(d) The corresponding magnitude of (b).

Figure 5. Overview of extrema-based multiscale decomposi-tion algorithm [12].

the edge map using only two weight values. For exam-

ple, some regions contain ringing artifacts or noise may

be classified as an edge region. As a result, the ringing

artifacts will still exist in result image. On the other hand,

our edge map defines the smooth region and edge region

more flexible, so the deblurring result can be reduced

more ringing artifacts.

After obtained a reasonable edge map, blurred image

and edge map are both used as inputs for deconvolution.

During the deconvolution process, the edge map is used

as the local prior of Richardson-Lucy algorithm, and then

the cost function Epl (L) = �log(pl (L)) can be defined as

(5)

where L is latent unblurred image, I is blurred image,

M is edge map which describes the smoothness infor-

mation of the image, �x is the partial derivative operator

in x direction and �y is partial derivative operator in y

direction.

Combine (5) with Richardson-Lucy algorithm, it can

be defined as

(6)

where �Epl (Lt) is defined as

(7)

where * is correlation coefficient operator, �x* is conju-

gate matrix of �x, �y* is conjugate matrix of �y, t is the

number of iteration, Lt is current deblurred image, Lt+1

is the deblurred image of next iteration, k is PSF, I is

blurred image, M is edge map and � is the predefined

parameter. The comparison of the proposed method

with Wang’s approach is shown in Figure 9; we observe

that the ringing artifacts within red rectangle are sig-

272 Jiunn-Lin Wu et al.

Figure 6. Flowchart of our improved EMD method. Figure 7. Intermediate results of our improved EMD. (a)Smooth map. (b) Detail map. (c) The result of gra-dient of smooth map and then use threshold me-thod. (d) The gradient of detail map.

Figure 8. Comparison between our method and others. (a)Proposed edge map. (b) Wang’s edge map.

nificantly reduced in our result. In the other word, our

deblurred image has better visual result than Wang’s

method with similar PSNR. It is obvious that the ring-

ing artifacts can be efficiently reduced by using the pro-

posed edge map in the deconvolution step. The flow-

chart of our proposed method is shown in Figure 10.

4. Experiments and Discussions

The aim of the proposed method is to reduce the

ringing artifacts in the deblurred images. Therefore, in

this section, we will use several well-known natural im-

ages which failed in Richardson-Lucy algorithm, and the

synthesis images to demonstrate the effectiveness of the

proposed method.

For all test images, at first the traditional Richard-

son-Lucy algorithm is used as a failed example with

ringing artifacts. Then several deconvolution methods

with edge map are used to recover blurred image and re-

duce ringing artifacts. Then we will compare our result

with the traditional Richardson-Lucy result and other

methods in detail. For the first experiment, we use the

blurred image “old man” which its size is 800 � 532 and

PSF which its size is 27 � 27 to verify our method. There

are many wrinkles on the old man face and hands, so we

can observe these two parts to verify our method. Figure

11 shows the undesired result of Richardson-Lucy algo-

rithm. And then we compare our result and edge map

with Wang’s method in Figure 12. We can observe that

compare with Wang’s method, our edge map provides

more edge information. Therefore we can reduce more

ringing artifact while preserving the edge.

Figure 13 is a magnitude view of our result and

others. Compare with traditional Richardson-Lucy al-

gorithm, our proposed method and Wang’s method can

efficient reduce the ringing artifacts, but our method has

better image vision than Wang’s. Next experiment we

Adaptive Richardson-Lucy Algorithm for Single Image Deblurring 273

Figure 9. Comparison of deconvolution result (a) Originalimage (512 � 512). (b) PSF (21 � 21). (c) Wang’method with 40 times iteration (PSNR is 27.16). (d)Our proposed method with 40 times iteration(PSNR is 26.72).

Figure 10. The flowchart of our proposed method.

Figure 11. The result of traditional Richardson-Lucy decon-volution algorithm using “Old man”. (a) Blurredimage and PSF. (b) Deblurred result.

use blurred image “flower” which its size is 701 � 494

and bigger PSF which its size is 35 � 35 to verify our

method. The “flower” has more texture then “old man”.

Figure 14 is the result of Richardson-Lucy algorithm.

We can observe that Figure 15(a) has less ringing ar-

tifacts, but some region is failed to recover sharp edge. In

contrast, our result in Figure 15(c) has sharper result.

From Figure 16, we can see that our method has the best

image vision of the three. Next, we want use an image

which contains a lot of narrow detailed to verify the ro-

bustness of proposed method. So we use he blurred im-

age “doll” which its size is 800 � 558 and bigger PSF

which its size is 41 � 41 to verify our method. Figure 17

is the result of Richardson-Lucy algorithm. From Figure

18, the detail part is well preserved, and the ringing ar-

tifacts are reduced successfully.

274 Jiunn-Lin Wu et al.

Figure 12. Comparison results with other methods using “Oldman” (a) Wang’s result. (b) Wang’s edge map. (c)Our proposed method. (d) Our corresponding edgemap.

Figure 13. Close-ups which is extracted from Figures 11(b)and 12(a), (c). (a) Richardson-Lucy algorithm. (b)Wang’s method. (c) Our proposed method.

Figure 14. The result of traditional Richardson-Lucy decon-volution algorithm using “Flowers”. (a) Blurredimage and PSF. (b) Deblurred result.

Figure 15. Comparison results with other methods using“Flowers” (a) Wang’s result. (b) Wang’s edge map.(c) Our proposed method. (d) Our correspondingedge map.

Figure 16. Close-ups which is extracted from Figures 14(b)and 15(a), (c). (a) Richardson-Lucy algorithm. (b)Wang’s method. (c) Our proposed method.

The close-ups show proposed method reduces more

ringing artifacts where near the contour of the doll’s face

than other deconvolution methods.

The processing time of deblurring using all natural

images is show in Table 1.

Finally, we use the synthesis images shown in Figure

20 to verify our proposed method. The synthesis images

include, “Lena”, “Airplane” and “Fruit”. The image size

of burred “Lena”, burred “Airplane” and burred “Fruit”

are 490 � 490, 486 � 486 and 490 � 458 respectively. The

size of corresponding PSF are 23 � 23, 19 � 19 and 23 �

23 respectively. The result comparisons of the proposed

method with Wang’s algorithm are shown in Figure 20. It

is obvious that the proposed method has better visual re-

sult than Wang’s approach. Table 2 shows that the pro-

posed method has similar PSNR with Wang’s method.

The processing times for deblurring examples is shown in

Table 2. We implemented our method with Visual C++.

Net language. The testing environment was as PC running

Window 7 64 bit version with AMD Phenom II X4 945

3.4 GHz. 4 GB Ram. The processing time of the proposed

method is too long to be waiting for. The FFT (Fast Fou-

rier transform) which is mentioned in many existence

deconvolution methods can be used to solve this problem.

Adaptive Richardson-Lucy Algorithm for Single Image Deblurring 275

Figure 17. The result of traditional Richardson-Lucy decon-volution algorithm using “Doll”. (a) Blurred imageand PSF. (b) Deblurred result.

Figure 18. Comparison results with other methods using“Doll” (a) Wang’s result. (b) Wang’s edge map. (c)Our proposed method. (d) Our corresponding edgemap.

Figure 19. Close-ups which is extracted from Figures 17(b)and 18(a), (c). (a) Richardson-Lucy algorithm. (b)Wang’s method. (c) Our proposed method.

Table 1. The comparison of processing time between the

proposed method and other approaches

Processing time (second)

Image Proposed

method

Wang’s

methodRichardson-Lucy

Old man 610.5927 178.457 139.32

Flower 556.0106 200.890 170.90

Doll 816.6494 342.269 0302.936

Figure 20. Deblurring result of synthesis image. First row:blurred image and its PSF. Second row: the result ofproposed method. Third row: the result of Wang’smethod. (a) “Lena”. (b) “Airplane”. (c) “Fruit”.

To reduce time complexity of the proposed algo-

rithm will be the main task for future work. Our method

shares common limitation with others deconvolution

method. Huge PSF, bright spot, severe noise, and non-

uniform blur will cause the deblurring failed. To solve

these problems in the proposed method will be interest-

ing future work.

5. Conclusions

In this paper, we proposed an adaptive Richardson-

Lucy deconvolution algorithm using local extrema filter-

ing. First, the local extrema filtering called EMD is used

to extract the edge map of the image which contains well

definition on smooth regions, and then the edge map and

blurred image are both used as inputs for deblurring al-

gorithm. With the effort of edge map, the ringing artifact

can be reduced for each time of iteration. Finally, a shaper

deblurred image without ringing can be obtained. The

experiments show that our proposed method can reduce

the ringing artifacts effectively while preserving the edge

of the image.

Acknowledgements

This research is partially supported by National Sci-

ence Council Grant NSC 101-2221-E-005-088.

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276 Jiunn-Lin Wu et al.

Table 2. The comparison between the proposed method

and Wang’s method

PSNR (dB)Processing time

(second)Image

Proposed

method

Wang’s

method

Proposed

method

Wang’s

method

Lena 28.9105 29.2214 320.7099 77.227

Airplane 27.7854 27.7699 298.3994 61.108

Fruit 30.7137 30.8389 298.7241 71.791