Remote Sensing Image Restoration Using Various Techniques: A Review

Inte rnatio nal Jo urnal o f Sc ie ntific & Eng inee ring Re se arc h, Vo lume 3, Issue 1, January -2012 1

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Remote Sensing Image Restoration Using

Various Techniques: A Review

Er.Neha Gulati,Er.Ajay Kaushik

Abs tract—In the imag ing process of the remote sensing ,there w as degradation phenomenon in the acquired images. In order to reduce the image blur caused by the degradation, the remote sensing images w ere restored to give prominence to the characteristic objects in the images.the images w ere restored. IMAGE restoration is an important issue in high-level image processing..The purpose of image restoration is to estimate the origina l image f rom the degraded data. It is w idely used in various f ields of applications, such as medical imaging, astronomical imaging, remote sensing, microscopy imaging, photography deblurring, and f orensic science, etc. Restoration is benef icia l to interpreting and analyzing the remote sensing images. Af ter restoration, the blur phenomenon of the images is reduced. The characters are highlighted, and the visual eff ec t of the images is clearer. In this paper diff erent image restoration techniques like Richardson-Lucy algorithm, Wiener f ilter, Neural Netw ork,Blind Deconvolution.

Ke ywords —Image Restoration,Degradation model, Richardson-Lucy algorithm,Wiener f ilter, Neural Netw ork,Blind Deconvolution.

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I. INTRODUCTION
For the space r emote sensing camera, many factors w ill cause image degradation dur ing the image acquisition pr ocess,such as aberration of the optical system, per formance of CCD sensors, motion of the satellite platform and atmospher ic turbulence [14]. The degradation r esults in image blur , affecting identification and extraction of the useful information in the images.The degradation phenomenon of the acquir ed images causes serious economic loss. Ther efor e, r estor ing the degraded images is an ur gent task in order to expand uses of the images.Ther e ar e sever al classical image r estor ation methods, for example Wiener filtering, r egularized filter ing and Lucy-Richardson algor ithm. These methods r equir e the prior knowledge of the degradation phenomenon [16][19], which be denoted as the degr adation function of the imaging system, i.e.,the point spr ead function (PSF). As the operational envir onment of the r emote sensing camera is
special and the atmospher ic condition dur ing image
acquisition is var ious, it is usually impossible to obtain accur ate degr adation function.The field of image r estoration (sometimes r eferr ed to as image deblurr ing or image deconvolution) is concer ned with the r econstruction or estimation of the uncorrupted image fr om a blurr ed and noisy one. Essentially, it tries to per form an operation on the image that is the inver se of the
imper fections in the image formation system. The r emote sensing images dealt w ith in this paper have high r esolution. W ith the PSF as parameter , the images can be r estor ed by the var ious techniques.
II. RELATED W ORK
The task of deblurr ing an image is image deconvolution; if
the blur ker nel is not known, then the pr oblem is said to be “b lind”.For a survey on the extensive literatur e in this ar ea, see [Kundur and Hatzinakos 1996]. Existing blind deconvolution methods typically assume that the blur ker nel has a simple parametric form, such as
a Gaussian or low-fr equency Four ier components. How ever , as illustr ated by our examples, the blur kernels induced dur ing camera shake do not have simple for ms, and often contain very shar p edges.Similar low-fr equency assumptions ar e typically made for the inputimage, e.g., applying a quadratic r egular ization. Such assumptions can pr event high fr equencies (such as edges) fr om appear ing in the r econstr uction. Car on et al. [2002] assume a power -law distr ibution on the image fr equencies; pow er-laws ar e a simple form of natural image statistics that do not pr eserve local str uctur e. Some methods [Jalobeanu et al. 2002; Neelamani et al. 2004] combine power -laws with wavelet domain constraints but do not wor k for the complex blur ker nels in our examples.
Deconvolution methods have been developed for astr onomical im-ages [Gull 1998; Richar dson 1972 ; Tsumuraya et al. 1994; Zar owin 1994], which have statistics quite differ ent from the natural scenes w e addr ess in this paper . Per forming blind deconvolution in this do-main is usually str aightforwar d, as the blurry image of an isolated star r eveals the point-spr ead-function.
Another appr oach is to assume that ther e ar e multiple images avail-able of the same scene [Bascle et al. 1996; Rav- Acha and Peleg 2005]. Hardwar e appr oaches include: optically stabilized lenses [Canon Inc. 2006], specially designed CMOS sensor s [Liu andGamal 2001],and hybrid imaging systems [Ben-Ezra and Nayar 2004]. Since w e

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would like our method to w or k w ith existing cam-er as and imagery and to wor k for as many situations as possible, we do not assume that any such har dwar e or extra imagery is available.
Recent w or k in computer vision has shown the usefulness of heavy-tailed natur al image pr ior s in a var iety of applications, including denoising [Roth and Black 2005], superr esolution [Tappen et al.2003], intr insic images [W eiss
2001], video matting [Apostoloff and Fitzgibbon 2005],
inpainting [Levin et al. 2003], and separating
r eflections [Levin and W eiss 2004]. Each of these methods is
effectively “non-blind”, in that the image formation pr ocess (e.g., the blur ker nel in superr esolution) is assumed to b e known in advance.Miskin and MacKay [2000] per form blind deconvolution on line art images using a prior on raw
pixel intensities. Results ar e shown for small amounts of synthesized image blur . W e apply a similar var iational scheme for natur al images using image gr adients in place of intensities and augment the algorithm to achieve r esults for photo-graphic images with significant blur .
III. IMAGE DEGRADATION
B. Image r estoration theory
The obj ective of image r estor ation is to r educe the image
blur during the imaging pr ocess. If w e know the prior know ledge of the degr adation function and the noises, the inver se pr ocess against degradation can be applied for
r estoration, including denoising and deconvolution. In fr equency domain, the r estoration pr ocess is given by the expr ession
F(u,v)=G(u,v)- N(u,v) (3) H(u,v)
Because r estoration w ill enlar ge the noises, denoising is done befor e r estor ation to r emove the noises. Denoising can be per formed both in the spatial domain and in the fr equency domain. The usual method is to select an appropr iate filter accor ding to the characters of the noises to filter out the noises. Spatial convolution is defined as multiplication in the fr equency domain, and its inverse operation is division.
Ther efor e, deconvolution is carr ied out in the fr equency
domain as a rule. At last, the inver se Four ier transform is
done to F(u,v) to complete the r estoration.
THEORY
A. Image degradation model
As Fig 1 shows, image degradation pr ocess can be modeled
as a degr adation function together with an additive noise,
operates on an input image f(x,y) to pr oduce a degr aded image g(x,y) [4]. As a r esult of the degr adation pr ocess and noise inter fusion, the or iginal image becomedegr aded image, r epr esenting image blur in differ ent degr ees.If the degradation function h(x, y) is linear and spatially invariant, the degradation pr ocess in the spatial domain is expr essed as convolution of the f(x,y) andh(x, y) , given by
g(x,y)=f(x,y) * h(x,y)+n(x,y) (1)

Figur e1. Image degradation model
Accor ding to the convolution theor em , convolution of two spatial functions is denoted by the pr oduct of their Four ier transfor ms in the fr equency domain.Thus,the degradation pr ocess in fr equency domain can be written as
G(u,v)=F(u,v)H(u,v)+N(u,v) (2)
C. Blurring
Blur is unshar p image ar ea caused by camer a or subj ect movement, inaccur ate focusing, or the use of an apertur e that gives shallow depth of field [7]. Blur
effects ar e filter s that make smooth transitions and decr ease contr ast by averaging the pixels next to har d edges of defined lines and ar eas wher e ther e ar e significant color tr ansition [15].
D. Blur ring Types
In digital image ther e ar e 3 common types of Blur effects:
 Average Blur
The Aver age blur is one of sever al tools you can use to
r emove noise and specks in an image. W e can use this tool when noise is pr esent over the entir e image [12]. This
type of blurring can be distr ibution in horizontal and vertical dir ection and can be circular averaging by radius R which is evaluated by the
formula:
R= √ g2 + f2 (4)
Wher e: g is the hor izontal size blur ring dir ection and f is vertical blurr ing size dir ection and R is the radius size of

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the cir cular average blurr ing.
 Gaussian Blur
The Gaussian Blur effect is a filter that blends a specific number of pixels incr ementally , follow ing a bell- shaped curve [10]. Blurr ing is dense in the center and
feather s at the edge. Apply Gaussian Blur filter to an image when you w ant mor e contr ol over the Blur effect [1].
calculate the most likely given the observed and known . This leads to an equation for w hich can be solved iter atively accor ding to:

= (6)
Wher e
 Motion Blur
The Many types of motion blur can be distinguished all
of w hich ar e due to r elative motion between the r ecording device and the scene. This can be in the form of a translation, a r otation, a sudden change of scale, or some combinations of these. The Motion Blur effect is a filter that makes the image appear to be moving by adding blur in a specific dir ection [2]. The motion can be
contr olled by angle or dir ection (0 to 360 degr ees or –90 to +90) and/or by distance or
intensity in pixels (0 to 999), based on the softwar e used [9].
 Out of Focus Blur
When a camera images a 3-D scene onto a 2-D imaging
plane, some parts of the scene ar e in focus while other
parts ar e not [5]. If the apertur e of the camera is cir cular , the image of any point sour ce is a small disk, known as the circle of confusion (COC). The degr ee of defocus (diameter of the COC) depends on the focal length and the aper tur e number of the lens, and the
distance betw een camera and obj ect. An accurate model not only descr ibes the diameter of the COC, but also the intensity distr ibution w ithin the COC [7].
III. DEBLURRING TECHNIQUES A. Lucy - Richar dson Algor ithm Technique
The Richardson–Lucy algor ithm, also known as
Richar dson–Lucy deconvolution, is an iterative pr ocedur e for r ecovering a latent image that has been the blurr ed
by a known PSF [15].
= . (5)
Wher e: is the point spr ead function (the fraction of light coming fr om true location j that is observed at position i), is the pixel value at location j in the latent image, and is the
obser ved value at pixel location i. The statistics ar e
per formed under the assumption that ar e Poisson
distr ibuted, which is appr opriate for photon noise in the
data. The basic idea is to
= . (7)
It has been shown empir ically that if this iteration conver ges, it conver ges to the maximum likelihood solution for uj .
 Point Spr ead Function (PSF)
Point Spr ead Function (PSF) is the degr ee to which an optical system blurs (spr eads) a point of light [11]. The PSF is the inver se Four ier transform of Optical Transfer Function (OTF).in the fr equency domain ,the OTF descr ibes the r esponse of a linear , position-invariant system to an impulse.OTF is the Fourier transfer of the point (PSF) [6].
B. Inverse Filter
Inverse filter ing is one of the techniques used for image
r estoration to obtain a r ecover ed image f’(x,y) fr om the
g(x,y) image data so that f’(x,y)=f(x,y) in the ideal
situation n(x,y)=0.
h(x,y)* (x,y)=δ(x,y)or H( , ) ( , (8) C. W iener Filter De-blurring Technique
The data amount of r emote sensing images is huge.
Ther efor e, the wiener filter ing is selected for image r estoration after getting the PSF of the image system. Wiener filter ing has good per formance. It doesn’t have iterative pr ocess, and saves time than oth er methods. Wiener filter ing seeks an appr oximate estimation which has the minimum mean squar e err or with the original image. The solution of W iener filter ing
in the fr equency -domain can be simplified to (7), wher e H(u,v) is the two-dimensional Four ier tr ansform of the Gaussian fitted PSF.K is the r egular ized constant in the r estoration pr ocess.
D. Neur al Netw or k Appr oach
Neur al netw or ks is a form of multipr ocessor computer system, with simple pr ocessing elements, a high degr ee of interconnection, adaptive interaction betw een elements,

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When an element of the neur al networ k fails, it can continue without any pr oblem by their parallel natur e [13].
ANN pr ovides a r obust tool for appr oximating a tar get function given a set input output example and for the r econstruction function from a class a images. Algorithm such as the Back pr opagation and the Perceptr on use gradient - decent techniques to tune the networ k parameters to best-fit a training set of input-output examples. Her e we ar e using Back pr opagation neural networ k appr oach for image r estor ation. This appr oach is capable of learning complex non -linear functions is expected to pr oduce better structur e especially in high fr equency r egions of the image. W e used a tw o-layer Back propagation networ k w ith full connectivity.
D. Modified W iener filter
Follow ing the least-squar es pr ocedur e, a modified W iener
filter has been developed with the possibility of having an extra constraint and so impr oving its per formance.
As a first appr oach, the additional constr aint is set to be wher e Tb is a br ightness temperatur e model extracted adequately fr om a land/sea mask and e is a tolerance err or . Hence, two Lagrange multiplier s, λ1 and λ2, will be used to include the tw o constr aints so that:
J(f)=‖Qf +
(9) Differ entiating with r espect to f, setting the r esult to zer o and solving it for f gives us the following expr ession in the spatial domain:
f=( Q+ H+ H . ( g+ Tb ) (10)

At this point, the Wiener concept is used to set the value of Q. Making use of the diagonalization pr ocedur e, we get the follow ing expr ession in the fr equency domain:

K(u,v)= (11)

wher e γ ≅ 1/λ1 and β ≅ λ2/λ1 for ease of notation and Τb is the Four ier tr ansfor m of Tb . Note that if w e don’t add the second constraint, λ2 = 0, this new filter r educes to the Wiener filter .
E. BLIND DECONVOLUTION
Blind deconvolution is a deconvolut ion technique that permits r ecovery of the tar get scene fr om a single or set of "blurr ed" images in the pr esence of a poorly determined or unknown point spr ead function (PSF).
Blind deconvolution can be per formed iteratively, wher eby each iter ation impr oves the estimation of the PSF and the scene, or non-iteratively, wher e one a pplication of the algor ithm, based on exter ior infor mation, extr acts the PSF. Iter ative methods include maximum a poster ior i estimation and expectation-maximization algor ithms . A good estimate of the PSF is helpful for quicker conver gence but not necessary.
F. Edge-Pr eserving Regular ization
The r estoration image can be solved with the methods of deterministic r egular ization and maximum a poster ior i estimation (MAP), and the r esult r egular ized solution of equation is:
=ar gmin*L(g,f)+λU(f)+ (12)
In the equation, L(g,f) is the data consistency constr aint, U(f) is the r egular ization term, λ is the r egularization parameter .
For the data consistency constraints L(g,f), if the hypothetical model is random, distributed independent and zer o averaged Gaussian type, the r esulting L(g,f) is the standar d based of the

pr oposed method, the “lena” image is used. Firstly, the or iginal clear image is blurr ed and added some noise, and then our method is used to per for m the r estor ation of degradation image, lastly, the r estor ation image is compar ed with the or iginal clear image to shown the effectivness. The PSF is estimated fr om the image or image
set, allowing the deconvolution to be per formed

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G. Discr ete formulation
A discr ete convolution formulation can be der ived fr om Eq.
g =h ⨂ f +n (13)
wher e g is a column vector containing the r eal
obser vations, f is a column vector containing the unknown
TB at the desir ed r esolution, n is a column vector that includes all that might be consider ed noise, h is the matr ix
r epr esentation of the antenna r esponse function, and ⊗
indicates convolution.
Assuming that f and h ar e two dimensional periodic functions of per iods M and N adequately padded w ith zer os to avoid overlap betw een differ ent per iods, and using the lexicogr aphic notation as above:
g =H . f + n (14)
wher e f, g, and n ar e of dimension (MN) x 1 and H is of dimension MN x MN. This matrix consists on M2 partitions, each partition being size N x N and order ed according to:

(15)

Each partition Hj is constr ucted fr om the jth r ow of the extended function h by a circular shifting it to the r ight [6].

A dir ect solution of (2) is not computationally feasible as, j ust for images of a pr actical size, it will r equir e an inver sion of a too high number of simultaneous linear
-cir culant, it can be diagonalized and ther efor e the pr oblem can be considerably r educed by wor king in fr equency domain [2]. The Four ier space equivalent of (2) can be wr itten as:
G = H. F+ N (16)
wher e G, Η, F and N ar e the Four ier transforms of g, H, f and n r espectively. Using fr equency-domain based deconvolution methods the computation time is no longer a limitation since nowadays ther e ar e very pow er ful tools to per form Fast Four ier Transforms.
IV. CONCLUSION
For image blur caused by the degr adation in the imaging pr ocess of the r emote sensing images. An effective image r estoration techniqes has been pr esented in this paper . The details of the r estor ed image become clear er . The image r estoration is benefit to image inter pr etation and analysis.
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 Neha Gulati is pursuing Masters degree in Electronics andCommunication Eng ineering in Maharishi Markhandeshw aUniversity,India.

E. mail:nehalibra25@gmail.com

 Ajay Kaushik is w orking as a lecturer in Electronics and Co mmun ication Depart ment in Maharishi Markhandeshw ar University,India.

E.ma il:kaushik.a jay24@gmail.com