Despeckling Structural Loss(DSL):A New Metric for Measuring Structure­

Preserving Capability of Despeckling Algorithms

Xuezhi Yang, Li Jia, Yujie Wang, Yiming Tang School of Computer and Information, Hefei University of Technology, Hefei, Anhui, China

xzyang@hfut. edu. en

Abstract

In this paper, a new metric called despeckling

structural 10ss(DSL) is proposed for performance

assessment of despeckling algorithms with a focus on

the preservation of structural information. By taking

into account characteristics of the best and worst

structure preservation in despeckling, the DSL metric

examines the presence of image structures in ratio

images by using local correlations between the ratio

image and the noise-free reference image at edge

points, leading an objective and quantitative measure

of the structure-preserving capability of despeckling

algorithms. The DSL metric has been tested on

despeckling results of a simulated SAR image using

three types of algorithms and efficiency of the DSL has

been demonstrated. In comparison, the other five

commonly used despeckling metrics fail to keep a

consistency with the structural loss shown in

despeckling results as well as ratio images.

1. Introduction

Synthetic aperture radar (SAR) is a microwave

remote sensing system with the distinct feature of

imaging in all-day and all-weather conditions. The

acquired SAR images are known to be corrupted by

coherent speckle noise which forms an obstacle to

human interpretation as well as automated infonnation

extraction. To alleviate impacts of speckle noise, a

large number of despeckling algorithms have been

developed with focuses on speckle reduction in

homogeneous regions, preservation of radiometric

infonnation and preservation of structural information

including edges and textures[l].

Performance of despeckling algorithms needs to be

properly assessed according to the objectives of

speckle reduction, which is necessary for the objective

comparisons of algorithms. Since image structures are

critical to SAR image interpretation, structure­

preserving capability is the major concern in the

assessment of despeckling algorithms. Various metrics

have been designed for measuring despeckling

perfonnance which include mean-square error (MSE)

[2],[3] and its variations such as signal-to-mean-square

error ratio (S/MSE)[4], and peak signal-to-noise ratio

(PSNR)[5], edge correlations (EC)[4], Pratt's figure of

merit (FOM)[5],[6], structural similarity (SSIM)[3].

These despeckling metrics primarily measure

discrepancies or similarities between the despeckled

image and the noise-free reference image with respect

to some image characteristics such as intensity, local

variation and edge. However, changes of structural

information by despeckling are not properly taken into

account in defining the above metrics which cause

inaccurate measure of structure-preserving capability

of despeckling algorithms.

Another way to assessing preservation of structural

information is based on the ratio image of the original

SAR image to the despeckled image. According to the

multiplicative model of speckle noise, the ratio image

should ideally contains the noise removed by the

despeckling process while the presence of image

structures indicates the corresponding loss in the

despeckled results. For this reason, equivalent number

of looks of ratio image(ENLR)[2],[3],[4]is adopted

whose deviation from the nominal number of looks of

the SAR image is considered as a measure of structure

preservation. Although perfect despeckling

corresponds to the ENLR with the nominal value, the

degree of deviation may not uniquely indicate the

actual loss of structural infonnation. Currently, visual

inspection of structural information presented in ratio

images is adopted as a more reliable alterative to the

ENLR metric[2],[3], while which still has the

limitation of a subject and inaccurate assessment of

structure preservation.

In this paper, we propose a new metric called

despeckling structural loss (DSL) which takes into

account characteristics of the best and worst structure

preservation in despeckling. The DSL metric examines

the presence of structural information in ratio images

by using local correlations between the ratio image and

the noise-free reference image at edge points, which

offers an objective and quantitative measure of the

structure-preserving capability of despeckling

algorithms.

In the next section, definition of the DSL metric is

presented, followed by evaluations of the metrics in

Section III. Section IV concludes this paper.

2.The Proposed Metric-Despeckling

Structure Loss(DSL)

2.1. Ratio Image of SAR Image Despeckling

A SAR image corrupted by multiplicative speckle noise can be represented by the following model[I]:

y = XS, (1)

where y indicates the observed SAR image in

amplitude format, x denotes the magnitude of noise­

free image (backscattering coefficients) and s denotes

the speckle noise. Despeckling algorithms aim to

restore the noise-free image x from the SAR image y.

Based on the despeckled image denoted as u, a ratio

image r can be computed as

r = y/u (2)

As indicated by the multiplicative speckle noise

model (1), a perfect despeckling result in a ratio image

containing the speckle noise removed where the mean

of the ratio image should be close to unity and the

equivalent number of looks of the ratio image (ENLR)

should be close to the nominal number of looks of the

SAR image. On the other hand, structures found in the

ratio image are proportional to the loss of structural

information in the despeckled image.

2.2. The DSL Metric

We investigate two extreme cases of despeckling

with respect to structure preservation. One case named

Best Structure Preservation (BSP) perfectly restores the

noise-free image x and the ratio image is:

rBSp = y/u = y/x = s (3)

The other case named Worst Structure Preservation

(WSP) outputs a despeckled image of constant value

where image structures are completely removed. In

such a case, the ratio image becomes the original SAR

image:

rWSp =y/u=cy, (4)

where the constant c takes a value of lImean(y) if the

despeckled image is assumed to be the global mean of

uojBSPlWSP __ "::-' � E

Figure 1.Measurement of the DSL metric

the SAR image. According to the above defmitions, the

BSP case and the WSP case are determined by the

speckle noise and the SAR image respectively, both

independent of any despeckling algorithm.

From the BSP to the WSP, it is noted that contents

of the noise-free image x continuously increasing in the

ratio image. This motivates the development of a new

metric called DSL which characterizes the changing

structural information in the ratio image for measuring

the structure preserving capability of despeckling

algorithms. While the underlying noise-free image x is

normally unknown in real SAR images, the DSL

metric takes a full-reference approach as most existing

metrics by using simulated SAR images, which can be

generated by multiplying spatially uncorrelated speckle

noise to a noise-free reference image.

Measurement of the DSL metric, as illustrated in

Fig. 1, consists of the following steps:

1) Extract edge map E of the noise-free image x by

using the Canny edge detector [7] due to its simplicity

and efficiency (The two thresholds are 0.02 and 0.05,

and the width of the Gaussian filter is 0.1).

2) Compute the ratio image r of the despeckled image

to the SAR image.

3) At each edge point k of E, compute the correlation

between the reference image and the ratio image is:

where

CR(k) = 'f'(x-x,r-r)

(5) �'f'(x -X,X -x)· 'f'(r -r,r -r)

'f'(x,r)= I Xi' Ij , (6) ;EEnWin

x denotes the mean value in a local window Win,

whose size is set up as 11 x 11 in this work.

4) Compute the average correlation in the whole image:

CR = � ICR(k) (7) K k�1

where K is the number of edge points in E.

5) Compute the average correlation for the cases of

BSP and WSP, and obtain CRssp and CRwsp

respectively.

6) Compute the final DSL value by normalizing the

result CR with respect to CRBSP and CRwsp:

DSL = CR -CRBSP (8)

CRwsp -CRBSP

The DSL can be viewed as a combination of the EC,

the FOM as well as the ratio image. The edge map of

the noisy-free image is first detected as a representation

of the true image structures. Based on the edge map,

the DSL is computed as the correlation between the

noisy-free image and the ratio image, aiming at

detecting the presence of structures in the ratio image.

Ranging from zero to one, the DSL approaches zero

when the ratio image totally contains noise. The more

structures removed in the despeckling process or

equivalently presenting in the ratio image, the larger

the DSL value.

3. Testing and Results

3.1. Testing Setup

The DSL metric is tested on measuring the structure

preserving capability of several despeckling algorithms,

and compared with five commonly used despeckling

metrics including S/MSE, EC, FOM, SSIM and ENLR.

Three despeckling algorithms involved in the testing

are the enhanced Lee (EnLee) [1], the speckle reducing

anisotropic diffusion (SRAD) [6] and the nonlocal

means speckle reduction (NLMSR)[8]. A simulated SAR image is adopted for despeckling testing which is

generated by multiplying an aerial image (Fig. 2) with

spatially uncorrelated speckle noise in amplitude

format with the equivalent number of looks of 2.

Figure 2. An aerial Image

3.2. Testing Results and Discussions

The first testing is designed to validate the DSL

metric by comparing results of same type of

despeckling algorithm with varying degrees of

smoothing. Applying one despeckling algorithm on a

SAR image, larger smoothing degree means more loss

of structural information in the despeckling result.

Correspondingly, values of a metric desirable for

assessing structure-preserving capability should

monotonically change and be bounded in the range of

BSP and WSP. In this testing, each of the above three

despeckling algorithms is applied to the simulated SAR

image and generates 15 despeckled images with

increasing smoothing degrees by adjusting the

corresponding parameters of the algorithm. Fig. 3

illustrates the DSL values on despeckling images of the

EnLee (blue), the SRAD (black) and the NLMSR (pink)

respectively. For each type of despeckling, it can be

seen that the DSL value continuously goes up within

the range of BSP to WSP (i.e.,[O,I]) along with the

increase of smoothing degree. In comparison, the other

five metrics either do not change monotonically or

have values out of the range of BSP to WSP (Figures

of the results are not shown here due to the limited

space).

' .. ' ·· .. · .. · .. ' .. ·" · " · .. · .. ·· .. '·�N

......

-"'" . "'"

�:: . .... .. �� " r

I 1 , , s � , " , 10 I' U " 14 IS

Figure 3. The DSL for despeckling algorithms with

varying smoothing degrees

The second testing further validates the DSL metric

by comparing results from different types of

despeckling algorithms. Using the EnLee, the SRAD

and the NLMSR, four despeckling results marked by

boxes in Fig. 3 are picked out and shown in Fig. 4a to

4d which have increasing DSL values. The

corresponding ratio images are provided in Fig. 4e to

4h where more and more structures can be identified,

indicating a consistency with the DSL value. While as

shown in Table I, such a consistency is not followed in

using the other five metrics.

4. Conclusion

Preservation of structural information is of crucial

importance to despeckling algorithms while it still

cannot be properly assessed by various existing metrics.

The DSL metric proposed in this paper offers a new

means to measure structure preservation by

characterizing the loss of image structures as presented

in ratio images. Testing results have demonstrated the

usefulness of the DSL metric and its advantages over

existing metrics. Further work will focus on the

development of a new metric which combines the DSL

and the equivalent number of looks in homogeneous

regIOns for an overall assessment of despeckling

performance.

(a)NLMSR(DSL=0.427) (b)SRAD(DSL=0.467) (c) SRAD(DSL=0.517) (d) EnLee (DSL=0.600)

(e) ratio image of (a) (f) ratio image of (b) (g) ratio image of (c) (h) ratio image of (d)

Figure 4. Despeckling results using the NLMSR, the SRAD and the EnLee, with increasing DSL values

Table I. Various despeckling metrics measured on results shown in Fig.4a to 4d

Despeckling algorithms DSL S/MSE(dB)

NLMSR(Fig.4a) 0.427 13.8

SRAD(Fig.4b) 0.467 15.0

SRAD(Fig.4c) 0.517 14.8

EnLee(Fig.4d) 0.600 14.4

5. Acknowledgements

This work has been supported by the National

Natural Science Foundation of China (No. 41076120,

No. 60890075, No. 60672120, No. 61102154), Science

and Technological Fund of Anhui Province for

Outstanding Youth (10040606Y09), Provincial Natural

Science Research Project of Anhui Colleges (No.

KJ2011A242).

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