ISSN (Online): 2348 – 3539

**Satellite Image Enhancement using Fast Discrete Curvelet Transform **

**1**

## Mohammed Abdulwahhab Ahmed,

**2**

## E. Sreenivasa Reddy

University College of Engineering and Technology, Acharya Nagarjuna University, Guntur.

**Abstract: **Satellite images are used in many applications such as geosciences studies, astronomy, and geographical
information systems. One of the most important quality factors in satellite images comes from its contrast. Contrast
enhancement is frequently referred to as one of the most important issues in image processing. Contrast is created by the
difference in luminance reflected from two adjacent surfaces. In visual perception, contrast is determined by the difference
in the color and brightness of an object with other objects. Our visual system is more sensitive to contrast than absolute
luminance; therefore, we can perceive the world similarly regardless of the considerable changes in illumination conditions.
If the contrast of an image is highly concentrated on a specific range, the information may be lost in those areas which are
excessively and uniformly concentrated. The problem is to optimize the contrast of an image in order to represent all the
information in the input image. A new satellite image contrast and resolution enhancement technique based on the discrete
curvelet transform (DCT) with singular value decomposition on tophat transform has been proposed. In this work the
technique decomposes the input eight sub bands by using discrete curvelet transform (DCT) and estimates the singular value
matrix of the low–low sub band image, and, then, it reconstructs the enhanced image by applying inverse DCT. The
technique is compared with DWT using SVD on Morphological Process on Colour Images and Gray Scale Images. This
method will give better qualitative and quantitative results on Root Mean Square Error and Peak-Signal Noise Ratio.

**Keywords: ** RGB Component, FDCT,TOPAHT, Structure Element.

**Reference** to this paper should be made as follows: 1Mohammed Abdulwahhab Ahmed,2E. Sreenivasa Reddy (2016)
„Satellite Image Enhancement using Fast Discrete Curvelet Transform ‟, *International Journal of Inventions in Computer *
*Science and Engineering*, Volume 2 Issue 5 May 201 .

**1 Introduction **

In the modern information system, digital images have been widely used in a growing number of applications. The effort on edge enhancement has been focused mostly on improving the visual perception of images that are unclear because of blur. In general, the popular edge enhancement filtering is carried out with the help of traditional filters [1, 2 and 3]. But these filters do have some problems, Noise removal and preservation of useful us information are important aspects of image enhancement. A wide variety of methods have been proposed to solve the edge preserving and noise removal problem. Recently, researchers have focused their attention on nonlinear smoothing techniques in the spatial domain. Most of these techniques are local smoothing filters, which replace the center pixel of the neighborhood by an average of selected neighbor pixels. Mainly focusing on the clarity of the image and the number of computations done for enhancing the image, we developed a novel approach. The basic aim of edge enhancement is to modify the appearance of an image to make it visually more attractive or to improve the visibility of certain features specially the satellite images. The edge enhancement technique enhances all high spatial frequency detail in an image, including edges, lines and points of high gradients. In this approach, the details of edges in an image can be obtained by subtracting a smoothed image from the original [4]. This subtractive smoothing method has been used as the simplest way to obtain high spatial frequency image and this method of edge enhancement makes the image brighter and real edges are detected. In spite of all

these efforts, none of the proposed operators are fully satisfactory in real world applications. They do not lead to satisfactory results when used as a means of identifying locations at which to apply image sharpening. In this paper, the enhancement is applied through a framework of threshold decomposition. This has two advantages: it reduces the edge detection to a simple binary process; and it makes the estimation of edge direction straightforward. Edge detection and direction estimation may be carried out by identifying simple patterns, which are closely related to the Prewitt operators. Another method was proposed lately on satellite image enhancement which proposed an additional step by enhancing the brightness of the image before working on edge detection on Wavelet Sub bands. However, the process shows no statistical results in the research. Therefore, the quality evaluation was still un- identical in order to compare the results. In this study we proposed a novel approach satellite image sharpening on Discrete Curve let transform, we developed new algorithms in intensity evaluation and compare its quality with its original version on SVD and Morphological TOPAHT Transform. The processes were composed of image brightness, edge detection and the standard deviation of the image intensity performed by the Peak Signal to Noise Ratio (PSNR).

**II. Satellite Image Enhancement **

human viewers and providing `better' input for other automated image processing techniques.

**Fig 1 Satellite Image **

The principal objective of image enhancement is to modify attributes of an image to make it more suitable for a given task and a specific observer. During this process, one or more attributes of the image are modified. The choice of attributes and the way they are modified are specific to a given task. Moreover, observer-specific factors, such as the human visual system and the observer's experience, will introduce a great deal of subjectivity into the choice of image enhancement methods. There exist many techniques that can enhance a digital image without spoiling it.

**A.FDCT (Fast Discrete Curve Let Transform) **

Actually the ridgelet transform is the core spirite of the curvelet transform. An anisotropic geometric wavelet transform, named ridgelet transform, was proposed by Candes and Donoho. The ridgelet transform is optimal at representing straight-line singularities. Unfortunately, global straight-line singularities are rarely observed in ral applications. To analyze local line or curve singularities, a natural idea is to consider a partition of the image, and then to apply the ridgelet transform to the obtained sub-images. Apart from the blocking effect, however, the application of this so-called first generation curvelet transform is limited because the geometry of ridgelets is itself unclear, as they are not ture ridge functions in digital images. The second-generation curvelet transform has been shown to be a very efficient tool for many different applications in image processing. The overview of the curvelet transform is shown below for four step:

**Fig 2 Block Diagram of Curvelet Transform **

There are some connection between Curvelet and Wavelet this part. The sub-band decomposition can be approximated using the well known wavelet transform:

Using wavelet transform, f is decomposed into S0, D1, D2, D3, etc.

P0 f is partially constructed from S0 and D1, and may include also D2 and D3.

s f is constructed from D2s and D2s+1.

P0 f is “smooth” (low-pass), and can be efficiently represented using wavelet base.

But it is confuse that the discontinuity curves effect the high-pass layers s f.

**B. Singular Valued Decomposition (Svd) **

SVD methods deal with solving difficult linear-least squares problems such as the terms in documents case and here colours in images. They are based on the following theorem of Linear Algebra. Each image can be represented by a matrix which contains the pixel intensity values. In general, for any image matrix A, the SVD can be defined as:

Where U and V are orthogonal square matrices and ΣA

matrix contains the sorted singular values on its main diagonal. ΣA contains the intensity information of the given image which means that the maximum singular value of ΣA contributes more than the other singular values.

**C. Tophat Transform **

The Filtering Mode buttons select whether to keep pixels that are Bright or dark compared to their surroundings. The Neighbourhood Radius slider adjusts the size of the interior region used in the top hat comparison (the outer or annular region is one or two pixels wide). The Threshold slider controls the difference between the brightest or darkest pixel value in the interior and surrounding regions that must be exceeded for the pixel to be retained, to produce the resulting Filtered Image shown on the right. It is actually the basic operation of binary morphology since almost all the other binary morphological operators can be derived from it.

**Fig 3 Filtering process **

**D. Morphology Multi Structuring Element **

Morphology is a technique of image processing based on shapes. The value of each pixel in the output image is based on a comparison of the corresponding pixel in the input image with its neighbours. By choosing the size and shape of the neighbourhood, you can construct a morphological operation that is sensitive to specific shapes in the input image. In mathematical morphology, a structuring element is a shape, used to probe or interact with a given image, with the purpose of drawing conclusions on how this shape fits or misses the shapes in the image. It is typically used in morphological operations, such as dilation, erosion, opening, and closing.

**E. Inverse Curvelet Transform **

There is also procedural definition of the reconstruction algorithm. Basicly, inverse the procedure of curvelet transform with some mathematic revising:

**Ridgelet Synthesis **

Each „square‟ is reconstructed from the orthonormal ridgelet system. Summation all the Ridgelet coefficinets with basis:

**Renormalization **

Each ‟square‟ resulting in the previous stage is renormalized to its own proper square.

**Smooth Integration **

We reverse the windowing dissection to each of the windows reconstructed in the previous stage of the algorithm.

**Subband Recomposition **

We undo the bank of subband filters, using the reproducing formula to summation all the subbands:

**III.Result Analysis **

**A. Discrete Wavelet Transform **

Point: it affects only a limited number of coefficients. Hence the WT handles points discontinuities well. Curve:

Discontinuities across a simple curve affect all the wavelets coefficients on the curve.Hence the WT doesn‟t handle curves discontinuities well.

**Fig 4 Image Enhancement using Discrete Wavelet **
**Transform **

**B.Discrete Curvelet Transform **

Curvelets are designed to handle curves using only a small number of coefficients. Hence the Curvelet handles curve discontinuities well.

**Fig 5 Image Enhancement using Discrete Curvelet **
**Transform **

**C. Quality Measurement **

image, if any of the pixels is set to 0, the output pixel is set to 0. After Morphological Process is used to sharpen these detected edges. Peak signal to noise ratio (PSNR) and root mean square error (RMSE) have been implemented in order to obtain quality results. PSNR can be obtained by using the following formula:

RMSE is representing input image I1 and proposed enhanced image I2 which can be obtained by the following formula:

**Table 1 MSE values of FDCT and DWT **

**Fig 6 MSE values of FDCT and DWT **
** **

**Table 2 PSNR values of FDCT and DWT **

**Fig 7 PSNR values of FDCT and DWT **

**IV. Conclusion **

In Our Project We implemented on FDCT using SVD Process on Image TOPAHT Structuring FIlter This was done by accurately detecting the positions of the edges through on FDCT Subbands. The detected edges were then sharpened by applying smoothing and wrapping filter. By utilizing the multi-structure element edges, the scheme was capable to effectively sharpening and detecting fine details. The visual examples shown above, have demonstrated that the FDCT (Fast Discrete Curve let Transform) method was significantly better than many other well-known sharpener-type filters in respect of edge and fine detail restoration The PSNR improvement compared with DWT, FDCT technique is high.

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