Three-stage Unstructured Filter for Removing Mixed Gaussian plus

Random Impulse Noise

Fitri Utaminingrum

1,2

, Keiichi Uchimura

and Gou Koutaki

Computer Science and Electrical Engineering, Graduate School of Science and Technology,

Kumamoto University, 2-39-1 Kurokami, Chuo-ku, 860-8555 Kumamoto, Japan

Brawijaya University, Information Technology and Computer Science Programs,

Jl. Veteran No.8 Malang, 65145 East Java, Indonesia

Priority Organization for Innovation and Excellence, Kumamoto University,

2-39-1 Kurokami, Chuo-ku, 860-8555 Kumamoto, Japan

Keywords:

K-SVD Method, Noise Removal, Mixed Noise.

Abstract:

Digital image processing is often contaminated by more than one type of noise, such as mixed noise. In this

paper, we propose a three-stage process to develop K-SVD method not only for reducing Gaussian noise but

also for mixed Gaussian and impulse noise with optimizing input system and preserving edge structure. A

three-stage process is combining of impulse noise removal, edge reconstruction and image smoothing. Press-

ing of an impulse noise in the early stages by Decision Based Algorithm (DBA) and repairing edge structure

by an edge-map are able to optimize the performance of the K-SVD method for smoothing an image. The

performance of the ﬁlter is analysed in terms of Peak Signal to Noise Ratio (PSNR), Mean Structural Simi-

larity (MSSIM) index and Blind Image Quality Index (BIQI). The simulation result is obtained a signiﬁcant

improvement over the previous research.

1 INTRODUCTION

The quality of an image may decrease due to distur-

bance or unwanted signals, which is called with noise.

The corrupted image with noise is one of the main

problems in the image processing and computer vi-

sion. Two common type of image noise are Gaussian

noise and Impulse noise. Contamination image with

noise makes a user difﬁcult to recognize the original

image data. In such adverse conditions, it is needed an

implementation to restore the noisy image to become

an image that has a better quality. Noise removal is

necessary in image processing to acquire useful im-

portant information that we want (Fitri et al., 2012b).

Gaussian and impulse noises are caused by imper-

fection of camera sensors and communication chan-

nel, error in the data-acquisition system, interference

from the outside instrumentation and error in the

transmission channel, etc (Bogdan, 2010; Fitri et al.,

2012a). Several previous papers have been proposed

to suppress both of noises. Denoising method that

only used for reducing one type of noise is much eas-

ier than the mixed noise removal.

There are two cases of noise distributions for im-

pulse noise: ﬁxed-valued impulse noise (salt-and-

pepper) and random-valued impulse noise (Wenbin,

2007). A large number of algorithms have been pro-

posed to reduce impulse noise from corrupted images.

One of the most popular method to reduce impulse

noise is median ﬁlter (Astola and Kuosmanen., 1997).

These algorithms remove the impulsive noise but they

were unable to preserve the sharpness of the edges.

Median ﬁlter performs well at low noise density, but it

fails at medium and high densities (Veerakumar et al.,

2013). Moreover, various modiﬁed median ﬁlters are

also proposed, e.g. the Vector Median Filter (VMF)

(Laskar et al., 2009) and the Spatial Median Filter

(SMF) (Church et al., 2008). Although these ﬁlters

obtain a better performance in lesser execution time,

VMF approaches still have the drawbacks like blur-

ring and low performances when the noise ratio is

high (Lezoray et al., 2008), while SMF cannot pre-

serve the original local features and maintain the edge

area. The other one is Gaussian noise removal. Addi-

tive Gaussian noise is characterized by adding a value

to each image pixel and the values obey a zero-mean

Gaussian distribution with noise variance σ (Yingyue

et al., 2013). Some researchers are often used total-

Utaminingrum F., Uchimura K. and Koutaki G..

Three-stage Unstructured Filter for Removing Mixed Gaussian plus Random Impulse Noise.

DOI: 10.5220/0005051400990106

In Proceedings of the 11th International Conference on Signal Processing and Multimedia Applications (SIGMAP-2014), pages 99-106

ISBN: 978-989-758-046-8

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

variation methods to develop their research (Tony and

Ke, 2006; Chan et al., 2005). The main drawback

of the total variation methods is the texture informa-

tion over-smooth in the image (Buades et al., 2005).

Sparse land model and K-Singular Value Decomposi-

tion (K-SVD) algorithms (Michal and Michael, 2006)

are also used to reduce Gaussian noise (Michael and

Michal, 2006). K-SVD is an iterative method that al-

ternates between sparse coding of examples based on

the current dictionary and a process of updating the

dictionary atoms to better ﬁt the data. This algorithm

is ﬂexible and works in conjunction with any pursuit

algorithm.

Rarely, an image is only contaminated by one type

of noise (Gaussian or random impulse noise). Digi-

tal image processing is often contaminated by more

than one type of noise, such as mixed noise. Some

representative mixed noise removals are Two-phase

method (TP) (Jian et al., 2008) and Fast two-phase

image deblurring (FTPID) (Jian et al., 2010) which

can work well in the reducing Gaussian and impulse

of noise. The two-phase method uses variational

methods involving an L1 shaped data-ﬁdelity term.

These methods can handle salt-and-pepper noise, but

not optimal for random impulse noise.

To overcome the problem of the previous meth-

ods, we propose a three-stage process to develop K-

SVD method not only for reducing Gaussian noise but

also for mixed Gaussian and impulse noise with opti-

mizing input system and preserving edge structure. A

three-stage process develops the connection between

an impulse noise removal, an edge reconstruction and

the smoothing image methods. Pressing of an impulse

noise in the early stages by Decision Based Algorithm

(DBA) and repairing edge structure by an edge-map

are able to optimize the input of the K-SVD method

for smoothing an image.

The rest of the paper is organized as follows: Sec-

tion II describes about the detailed explanation of the

proposed method, Section III shows the experimental

result of our simulation program, and Section IV is a

conclusion.

2 PROPOSED METHOD

We propose a three-stage process to remove mixed

Gaussian and impulse in the image F. The ﬁrst stage

is impulse noise removal. The second stage is the re-

pairing edges region on the image. The third stage is

the smoothing image.

2.1 Impulse Noise Removal

Impulse noise removal is only applied to the pixels

that are detected as the impulse noise. The ﬁltering

process just conducted on the noisy pixel known as a

Decision Based Algorithm (DBA).

We make an impulse noise detector which is

capable for detecting both types of impulse noise.

There are salt-and-pepper and random-valued im-

pulse noises. The impulse noise ﬁltered image (

is obtained by placing the free impulse noise pixel

and new pixel from

F at (i, j) position.

F is the

average value of two free-noisy pixels that are lo-

cated around (i, j). Detection of salt-and-pepper and

random-valued impulse noise at each position (i, j) in

the corrupted image (F) is presented in Eq.(1).

i j

{

i j

if F

i j

= 0 or F

i j

= 255 or F

i j

≤ τ

or F

i j

≥ τ

i j

other

(1)

and τ

are the minimum and maximum limits of

threshold value respectively, which is calculated by

Eqs.(2) and (3).

= MIN(W) +

MED(W) − MIN(W)

(2)

= MED(W) +

MAX(W) − MED(W)

(3)

where MIN, MED and MAX are operators to obtain

minimum, median and maximum value respectively.

W is the 3 × 3 sample pixel window.

Observations of two pixels are performed in the

horizontal, vertical, left and right-diagonal directions.

If the observations are not found free-noisy pixels, we

average values of two pixels

i, j−1

and

i−1, j

2.2 Edge Reconstruction

The edge reconstruction process is guided by an edge-

map that is obtained from the threshold results of the

edge image detection. We use two Sobel kernels to

detect the edge area from an image there are horizon-

tal (H

) and vertical (H

) derivative kernel.

The horizontal and vertical gradients of the image

intensity function can be written in Eq.(4).

G =

(

X ∗ H

)

(4)

X is an image that contains no impulse noise. ∗

denotes the 2-dimensional convolution operation.

Meanwhile, the edge-map is resulted from the

threshold that has two intensity conditions there are

bright (1) and dark (0). The threshold image result is

a binary image (

G). The bright intensity (1) is given,

when the pixel values of G

i j

is greater than the thresh-

old (τ) and vice versa. We only repair the area that are

SIGMAP2014-InternationalConferenceonSignalProcessingandMultimediaApplications

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detected as edges and ignores the non-edge regions.

We scan

G by using 5 × 5 window (W

). If in the

scanning process, elements of the window contain an

edge, then check the direction of an edge in the win-

dow as follows:

1 If an edge position in the W

window is at the

horizontal direction, then the

X image at the three

coordinates in the horizontal direction

X(i, j+k) is

updated with an average of three pixels from these

direction as illustrated in Eq.(5). k=[-1,0,1].

X(i, j +k) =

∑

k=−1

X(i, j +k) (5)

2 If an edge position in the W

window is at the

vertical direction, then we use Eq.(6) to repair the

edge image.

X(i + k, j) =

∑

k=−1

X(i + k, j) (6)

3 If an edge position in the W

window is at

the left-diagonal direction, then the

X(i − 1, j +

1),

X(i, j) and

X(i +1, j −1) are updated by using

Eq.(7).

X(i + k, j −k) =

∑

k=−1

X(i + k, j −k) (7)

4 If an edge position in the W

window is at

the right-diagonal direction, then the

X(i − 1, j −

2),

X(i, j) end

X(i +1, j +1) are updated by using

Eq.(8).

X(i − k, j +k) =

∑

k=−1

X(i − k, j +k) (8)

Finally, the

X image that has been reconstructed based

on four rules symbolized by X.

2.3 Image Smoothing Based on K-SVD

K-SVD method is a combination of K-mean clus-

tering process and Singular Value Decomposition

(SVD). K-SVD is denoising method based on a sparse

representation with learning dictionary which con-

tains a prototype signal-atom (Michal and Michael,

2006). It is limited in handling small patches. In or-

der to maximize performance for K-SVD method, we

minimize an impulse noise and reconstruct the edge

area on the input part, ﬁrstly. The X is an image that

has undergone reconstruction in the early stage with

eliminating impulse noise and improving edge area.

Denoising procedure using Eq.(9) is based on dic-

tionary learned patches from the corrupted image, that

are described as follows. Input image is symbolized

by X

i j

and output image is reconstruction image (Y

i j

min

Y,D,α

{

λ ∥ X

i j

−Y

i j

∥ +

∑

i j

∥ α

i j

∥

∑

i j

∥ Dα

i j

− R

i j

∥

}

(9)

λ is regulation parameter, µ

i j

is a patch-speciﬁc

weight that are determined by the optimization pro-

cedure, α

i j

is a size k column vector, D is the learn

dictionary with matrix size n × k and R

i j

is a size n

column vector.

There are several parameters that are used in K-

SVD methods. These parameters are n (the block size

of image patches), k (size of dictionary), J (number

of iterations), λ (weight of the noisy image), σ (stan-

dard deviation of Gaussian noise) and C (multiplier

coefﬁcient). We use the default parameters for de-

noising procedure that will be a good starting point

by using the original K-SVD are as follows: n=8, J=4,

k = J × n

, λ=

and C=1.15.

Description of K-SVD method uses the setting pa-

rameters which are deﬁned in Eq.(9). The detail infor-

mation about denoising procedure of K-SVD is ex-

plained in the several steps.

1. Initialization: set Y

i j

= X

i j

and D are some initial

dictionary.

2. Repeat J times

(a) Sparse Coding Stage: Use any pursuit algo-

rithm to compute the representation vectors

i j

for each patch R

i j

. The mathematical

aproach can be formulated as follows:

∀

i j

min

i j

||α

i j

subject to

||Dα

i j

− R

i j

Y ||

≤ n(Cσ)

(b) Dictionary Update Stage: for each column

l=1,2,...,k in D.

- Find the patches ω

that use in this atom

, ω

= {(i j)|α

i j

(l) ̸= 0}

- For each patch (i, j) ∈ ω

compute its repre-

sentation error

i j

= R

i j

−

∑

m̸=l

i j

(m)

- Set E

= (e

i j

)

i j∈ω

- Apply SVD decomposition and update d

and

i j

(l)

(i, j)∈ω

pose matrix and I is an identity square matrix.

i j

λX

i j

∑

i j

Dα

i j

λI +

∑

i j

Three-stageUnstructuredFilterforRemovingMixedGaussianplusRandomImpulseNoise

101

(a) (b)

(e) (f)

Figure 1: Denoising results of different algorithms on Lena

image corrupted by noise variance (σ=15) and impulse

noise density (p = 50%). (a) Original image, (b) Corrupted

image, (c) TP (Jian et al., 2008), (d) FTPID (Jian et al.,

2010), (e) AF, (f) Proposed Method.

(a) (b)

Figure 2: SSIM-map of Fig.1. (a) TP (Jian et al., 2008), (b)

FTPID (Jian et al., 2010),(c) AF, (d) Proposed Method.

3 EXPERIMENTAL RESULT

We have tested the performance of our proposed

method on a different image sample, some of which

are Cameraman, Lena, Man and Pepper. Different

density of Gaussian noise plus random-valued im-

pulse noise has been tested in our research. We de-

note the random-valued impulse noise by p as density

level (30%, 50% and 70%) and Gaussian noise by σ

as standard deviation (5, 10 and 15). It means that

p + σ is the corrupted image by the mixed Gaussian

and impulse noise.

Simulation result is obtained from MATLAB 7.5.0

release 2007b. We use a Personal Computer (PC) that

has speciﬁcation of CPU 3.3 GHz and 4GB RAM.

The performance of our proposed method is evaluated

by Qualitative and Quantitative parameters. Both pa-

rameters were used since they complement each other

for more complete analysis.

3.1 Qualitative Parameter

Qualitative parameter by visual observation is more

subjective than the quantitative parameter, where it

can be observed but not measured. We compare our

proposed method with many other well-known algo-

rithms published in the (Jian et al., 2008; Jian et al.,

2010) literatures and Adaptive Fuzzy (AF).

3.1.1 Visual Observation

The test image used for this comparison is Lena orig-

inal image (512×512) as shown in Fig.1(a), which

is corrupted by mixed Gaussian and impulse noise

(p=50% plus σ=15) as shown in Fig.1(b). Further-

more, Fig.1(c) and (d) are the ﬁltering results of TP

and FTPID methods, respectively. The ﬁltering result

of TP is almost similar to FTPID method. However,

FTPID method is a little smoother than TP method.

Meanwhile, the ﬁltering result of AF method is pre-

sented in Fig.1(e). In this paper, the visual quality

ﬁlters of AF method is better than both methods. The

ﬁltering result of the proposed method is visualized

in Fig.1(f). The proposed method is highly effective

for removing impulse noise plus Gaussian noise from

the corrupted image. By comparing TP and FTPID,

we can see clearly that the proposed method success-

fully suppresses the noise and preserves the edge de-

tails and texture very accurately.

3.1.2 The Structural Similarity-map

(SSIM-map)

In addition, we also use SSIM-map in the qualitative

evaluation. SSIM-map is a local perceptual quality in-

dicator that is used to measure the similarity between

original image and the ﬁltering image result. If the

pixels have the similarities, it will produce high in-

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tensity and vice versa. SSIM-map results from Lena

image are presented in Fig.2.

Figures.2(a), (b), (c) and (d) are the SSIM-map

of TP, FTPID, AF and our proposed method respec-

tively. Regarding to Fig.2, the level contrasts of

SSIM-map image results from lowest to highest are

TP, FTPID, AF and our proposed method respec-

tively.

Generally, our method has more contrast than all

comparison methods that has been used in this pa-

per (TP, FTPID and AF). In this case, our proposed

method produces the highest intensity, that is related

to the condition of pixel between proposed method,

and original image that has the similarity value in ev-

ery coordinates.

3.2 Quantitative Parameter

Quantitative measurement is an important because

qualitative measurement by visual assessment of the

image is subjective. Quantitative assessment in the

numerical variable is used for measurement, compar-

ison or to track performance. They represent a mea-

surable quantity that make it easy to analysis.

Qualitative measurement involves gathering data

that is absolute, such as numerical data. In order to

provide quantitative measures on the performance of

the ﬁltering result, we used Peak Signal-to-Noise Ra-

tio (PSNR), Mean Structural Similarity (MSSIM) in-

dex and Blind Image Quality Index (BIQI).

3.2.1 Peak Signal-to-Noise Ratio (PSNR)

The quality of the restored images is measured by

Peak Signal-to-Noise Ratio (PSNR). It uses a stan-

dard mathematical model to measure the quality im-

age. The higher PSNR value, the better quality image

and vice versa.

PSNR is usually expressed in terms of a logarith-

mic decibel (dB) scale as illustrated in Eq.(10). M is

represented as row of an image; N is a column of an

image; x

i j

is an original image and y

i j

is the ﬁltering

result.

PSNR = 20 log

255.M.N

∑

j=1

∑

i=1

i j

− y

i j

)

(10)

Table 1 presents the PSNR results of the three

comparative denoising algorithms on all test images.

PSNR values of the proposed method demonstrate

much better performance than TP, FTPID and AF,

when the level noise (30% ≤ p ≤ 70%) and (5 ≤ σ ≤

15)

3.2.2 Mean Structural Similarity (MSSIM)

Index

The structural similarity (SSIM) index is a method for

measuring the similarity between two images (origi-

nal image as reference image and the ﬁltering image

results as the reconstructed image) (Zhou et al., 2004).

An image quality MSSIM index is calculated by

computing the average of SSIM value over all win-

dows as deﬁned in Eq.(11)

MSSIM(I, F) =

∑

j=1

SSIM(i

, f

) (11)

I and F are reference and the ﬁltered images, re-

spectively. The i

and f

are the image contents at the

jth local window. M is the number of local windows

of the image. We use Eq.(12) to obtain SSIM value.

SSIM(i, f ) =

(2µ

)(2σ

i f

)

(µ

+ µ

)(σ

+ σ

)

(12)

and µ

are the mean intensity of image i and f re-

spectively. σ

and σ

are standard deviation of image

i and f respectively. σ

i f

is covariance.

The response of MSSIM value is similar with

PSNR. MSSIM value is ranging between 0 and 1. The

higher MSSIM index value, the better quality of the

ﬁltering image result. In this case, if the results of

MSSIM index value close to 1 indicates that the ﬁlter-

ing image result almost similar with original image.

The MSSIM index result in the several methods

are presented in Table 2. Referring to Table 2, the

proposed method has a highest value than TP, FTPID

and AF methods. The MSSIM index value of the pro-

posed method is close to one. It means, the quality

ﬁlter of the proposed method is better than all com-

parison methods.

3.2.3 Blind Image Quality Index (BIQI)

In another hand, we also use BIQI (Blind Image Qual-

ity Index) to evaluate on the quality image assessment

by using distortion-speciﬁc image quality measure as

well as a distortion-type classiﬁer. It is obvious that

BIQI performs well in terms of correlation with hu-

man perception, and it is competitive with that of full-

reference PSNR across distortion types and the data-

base. (Anush and Alan, 2010).

Blind image quality index is calculated by using

Eq.(13)

(BIQI) = Σ

i=n

(13)

is the probability of each distortions in the image

and q

the quality score corresponding to the distor-

tions (Anna et al., ).

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103

Table 1: Comparison result of PSNR value.

Images

σ = 5 σ = 10 σ = 15

p (%)

Methods Methods Methods

TP FTPID AF Proposed TP FTPID AF Proposed TP FTPID AF Proposed

Cameraman

29.31 29.90 29.93 31.49 26.70 27.71 29.49 30.58 25.65 26.10 28.88 29.58

Lena 33.08 34.15 31.09 34.19 30.66 31.33 30.55 32.49 29.12 29.67 29.88 31.39

Man 31.98 33.06 34.24 34.82 29.80 30.35 32.55 32.73 28.57 28.29 30.66 31.28

Pepper 32.68 33.87 35.28 37.15 30.64 31.66 33.44 35.19 29.63 30.25 31.19 33.42

Cameraman

26.92 27.40 29.04 30.10 25.45 25.99 28.61 29.37 24.10 24.69 27.99 28.69

Lena 31.40 32.30 30.46 32.54 29.23 29.88 29.91 31.29 27.93 28.42 29.19 30.32

Man 30.91 31.08 32.78 33.15 28.74 29.21 31.32 31.49 27.64 28.01 29.58 30.16

Pepper 30.96 31.83 33.72 35.48 29.37 30.24 32.15 34.09 28.22 28.85 30.12 32.49

Cameraman

24.69 24.67 27.37 27.57 23.35 23.45 26.98 27.24 22.41 22.67 26.39 26.79

Lena 29.56 29.73 29.09 30.07 27.75 28.11 28.59 29.46 25.87 26.48 27.89 28.87

Man 29.56 29.73 30.32 30.50 27.38 27.64 29.29 29.50 26.27 26.57 27.95 28.58

Pepper 29.35 29.58 31.18 32.67 27.83 28.43 30.03 31.70 26.82 27.07 28.45 30.53

Table 2: Comparison result of MSSIM index value.

Images

σ = 5 σ = 10 σ = 15

p (%)

Methods Methods Methods

TP FTPID AF Proposed TP FTPID AF Proposed TP FTPID AF Proposed

Cameraman

0.81 0.83 0.95 0.97 0.58 0.60 0.87 0.93 0.42 0.44 0.87 0.90

Lena 0.82 0.85 0.87 0.92 0.62 0.65 0.84 0.88 0.46 0.49 0.81 0.85

Man 0.84 0.86 0.94 0.96 0.63 0.66 0.88 0.92 0.47 0.50 0.80 0.88

Pepper 0.81 0.83 0.95 0.97 0.56 0.58 0.87 0.95 0.38 0.41 0.78 0.94

Cameraman

0.79 0.85 0.94 0.96 0.56 0.64 0.85 0.92 0.42 0.49 0.84 0.88

Lena 0.78 0.84 0.85 0.90 0.59 0.67 0.83 0.86 0.44 0.53 0.79 0.83

Man 0.80 0.87 0.92 0.94 0.61 0.69 0.86 0.90 0.46 0.54 0.77 0.86

Pepper 0.80 0.86 0.94 0.96 0.55 0.64 0.86 0.95 0.38 0.47 0.75 0.93

Cameraman

0.74 0.87 0.91 0.93 0.52 0.69 0.83 0.90 0.38 0.55 0.81 0.86

Lena 0.70 0.83 0.83 0.86 0.53 0.70 0.80 0.83 0.40 0.58 0.75 0.80

Man 0.73 0.86 0.89 0.90 0.55 0.73 0.82 0.86 0.41 0.60 0.73 0.83

Pepper 0.76 0.89 0.93 0.95 0.53 0.72 0.84 0.93 0.37 0.56 0.73 0.91

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Table 3: The quality score of the ﬁltering image result.

Images

σ = 5 σ = 10 σ = 15

p (%)

Methods Methods Methods

TP FTPID AF Proposed TP FTPID AF Proposed TP FTPID AF Proposed

Cameraman

38.92 41.65 36.64 35.79 53.60 55.94 52.52 40.38 56.22 56.74 53.08 42.67

Lena 34.56 35.95 38.86 31.05 49.02 49.44 47.91 35.33 54.13 54.53 54.43 34.89

Man 41.05 37.40 40.72 40.45 52.22 54.65 53.14 38.72 55.16 56.40 54.47 39.83

Pepper 57.86 59.13 55.78 40.41 64.49 67.66 65.43 44.79 65.32 66.91 66.40 45.67

Cameraman

34.57 35.89 43.43 35.36 47.30 53.64 47.21 41.87 52.92 56.34 51.43 44.47

Lena 30.20 31.96 31.23 31.92 45.32 46.77 45.38 36.53 51.58 52.82 52.75 35.53

Man 40.07 47.17 44.07 39.75 52.46 61.36 57.04 39.01 54.01 60.75 60.69 40.98

Pepper 64.27 66.18 59.36 40.56 65.27 67.24 66.61 44.82 67.90 67.79 66.92 45.90

Cameraman

27.34 40.25 42.83 34.49 46.79 50.71 46.67 42.87 44.74 55.60 52.92 44.74

Lena 31.50 37.33 40.44 35.56 40.41 45.53 47.72 38.82 46.65 55.59 55.91 37.34

Man 34.82 43.63 44.81 40.36 46.63 54.69 55.53 40.20 56.15 58.21 57.21 43.09

Pepper 44.39 50.94 46.44 38.82 66.68 68.33 65.72 44.72 67.94 69.28 67.07 46.70

A quality score of the ﬁltering image result is pre-

sented in Table 3. The score typically has a value be-

tween 0 and 100. In this case, 0 represents the best

quality and, 100 as the worst.

Referring to Table 3, the quality of the proposed

method in some experiments data has a lowest value

than TP, FTPID and AF as the comparison methods.

However, in the small variance noise, the proposed

method is not always obtained the lowest BIQI value.

In this case, the smallest BIQI value was obtained

in the FTPID or TP methods in condition (σ=5 and

p=30%, 50% and 70%).

The lowest value indicates the better quality of the

ﬁltering result. Even though the ﬁnal BIQI value of

the proposed method was not close to zero, that result

is enough to consider that noise was reduced.

4 CONCLUSION

A three-stage process method that develops the con-

nection between an impulse noise removal, an edge

reconstruction and the smoothing image methods for

reducing the mixed Gaussian plus random impulse

noise in the corrupted image is proposed. Pressing

of an impulse noise in the early stages by Decision

Based Algorithms (DBA) and repairing edge structure

by an edge-map are able to optimize the performance

of the K-SVD method for smoothing an image.

The qualitative parameters show that our proposed

method cannot only remove most of the mixed noise,

but also preserve the edge details, smooth quality and

maintain textures of an image. Our simulation result

is obtained a signiﬁcant improvement over the pre-

vious research. The proposed method is capable of

overcoming the drawback of previous studies and pro-

vides a satisfactory result.

For future work, we will give an attention on the

computing time process. Hence, the next method not

only optimal to reduce the mixed Gaussian plus im-

pulse noise in many variation density, but also pro-

duces a faster computational time process in several

noise densities.

ACKNOWLEDGEMENTS

The work of the ﬁrst author is supported by Direc-

torate of Higher Education (DGHE) of Indonesia and

Brawijaya University, Indonesia.

Three-stageUnstructuredFilterforRemovingMixedGaussianplusRandomImpulseNoise

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