A total variation-undecimated wavelet approach to chest radiograph image enhancement

total variation denoising deblurring of optimization the total variation of as a penalty function. The observed noisy linearrepresentation:


Total Variation of an Image
We noted earlier that, the choice of the parameter λ is key to the success of this M in u λT z (u) + 1 2 Ω |h * u − z| 2 dx the definition becomes simpler if f is a differentiable function defined on a bounded open domain ⊂ R (x) < ∞. This space can easily be shown to be a Banach space, and is endowed with the norm ||f || The TV method for image denoising has been implemented for several CAD systems [19,20].
This hybrid approach used here represents a noisy image in a simplified form by (1). The reconstruction of u(x) reduces to the optimization problem of minimizing the function (see for example [17]). Here, the parameter λ > 0 and R(u) is the regularization functional defined on the domain . The disadvantage of this method is that despite removing noise adequately, it removes essential details from the image [12]. Since the efficiency of the method is controlled by the choice of the regularization functional, this is usually costly in medical imaging. It has been shown that the use of the total variation of the image function below amerolates this problem.
This has been shown to lead to sharper reconstruction of the original image by both removing the imbedded noise and better preservation of its edges [21]. An important attribute of the TV minimization scheme is that it takes the geometric information of the original images to account, and this helps to preserve and sharpen the edges significantly [21]. method. To eliminate the problems presented by trying to figure out the right choice of this parameter, the wavelet total variation scheme is proposed. This method represents the components of the func tion by orthogonal wavelet basis. The wavelet coefficients are then selected to achieve the goals of denoising and enhancement. To achieve our goal, we extend the Rudin-Osher-Fatemi model to denoising with a blurring convolution operator. This leads to the following optimization problem:

The Total Variation Technique
Dividing by t and letting t → ∞ → leads to T Proposition 1 [16] Let K = {p ∈ L 2 L is considered as a functional over the Hilbert space where h is the convolution operator. In order to detect the edges of nodules from the sorrounding anatomical noise, we apply a Sobel type convolution kernel. This helps to accentuate the edges of the the nodule in the CR image [22].

Undecimated Wavelets Contrast Enhancement and Nodules Detection
Conventional methods of image enhancement such as histogram equalization and gamma adjustment have limited versatility leading to loss of important image features [23]. This is highly fatal in medical imaging applications such as lung cancer detection using chest CRs. Wavelets have become a method of choice for several image processing applications such as denoising and image enhancement since they have the capability of making available spatial frequency information. This property makes it easier to distinguish between noise and real image data.

Undecimated Wavelet Based Transform Decomposition
We propose a method to automatically extract image texture parameters that can assist It can be shown that the solution of the optimization problem above is equivalent to the solution of the associated Euler-Lagrange partial differential equation of the form [9]: since the optimization problem is strictly convex, it has a unique solution. The TV minimization is then combined with the undecimated wavelet image enhancement approach explained in the next section.
Wavelet based methods usually outperform traditional methods in improving the edge for the generation of the enhanced energy features. The UDWT produces an exact translational invariance, as well as overcomplete one to one relationship between all colocated coefficients at all scales as against the DWT which is a spatial frequency transform that has been used extensively for texture analysis. A wavelet family such as Bi-orthogonal spline wavelets which provide excellent image scale separation is used. Such wavelets also provide excellent image reconstruction makes it more suitable. Compared with the normal chest X-rays, there are a number of small opacities in the lung anatomical structures, that cause the differences of texture features in CRs with cancer nodules. The nodules are distinguished by using texture features derived from the CRs of lung fields after a series of wavelet transformation.
features in an image [24]. Peng et al. [25] for example, rely on shift invariant WT for contrast enhancement of radiographs. We combine the TV method with UDWT approach of [26] to improve the visual quality of CRs. To eliminate the translation variant drawback of wavelets, the undecimated wavelet transform (UDWT) is applied. Despite the colosal computational storage demands of the UDWT, it gives precise frequency localization information [27]. Even thresholding using only the UDWT improves the results for image denoising by more than 2.5dB [21,28]. The wavelet model consists of coefficients which are of large magnitudes and are associated with edges and some textures, while the small coefficients are classified as smooth background features. The UDWT is applied with two basic steps: first, the modified UDWT is applied to the medical image, then this is followed by a wavelet coefficient mapping was applied to finally enhance the medical images. The UDWT algorithm is desired to eliminate the translation variant liability of the of the standard DWT. This is achieved by ignoring the downsampling operation of the DWT, leading to the same length for the approximating coefficients and detail coefficients at each level, as the original signal. The resulting gain in image quality far outweighs the storage liabilities for the method on modern computers with vast storage capabilities.
where M k and N k represent the size of sub-band images of the kth scale. The four sub-band images of the kth scale are of equal size as M k and N K and x(i, j) (i = 1 to M K ) and j = 1 to N k respectively. is the gray value of pixel (i, j) of the image. The final feature vector contains 44 energy features of wavelet coefficients calculated in sub-bands at successive scales.
The major characteristics to apply is to obtain features which portray scale dependent properties of the CRs. A feature from each subimage is extracted separately, and a non linear function of the coefficients is computed using the fact that the coefficients of the subimage sum to zero. Other studies use alternative measures such as entropy as well as more than one feature. The level 2 wavelet coefficients for a chest radiograph image are calculate in Figure 2.

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ISSN Using the pyramid decomposition of the two dimensional wavelet decomposition, after decomposition for the first scale, the original image is divided into four subbands, which is expressed by combinations of low and high frequencies. The major texture energy based features are calculated on the 11th scale of four sub bands for each scale. Energy level calculation on l = 1 to 4 and k = 1 to 11 respectively is calculated [15] by:

Specif icity = T RU E N EGAT IV ES
The total variation method is applied to denoised and enhanced CR image shown in Figure 3. Table 1 shows the various sensitivity, specificity, and accuracy of the undecimated total variation method compared to a total variation only approach.
A database of a set of 247 Chest X-ray images obtained from Standard Public Database, the Japanese Society of Radiological Technology (JSRT) is used to test our algorithm. The set includes posterior and anterior chest films measuring 34.6 cm by 34.6 cm (14 by 14 inches) were collected from 14 medical institutions by using screen-film systems over a period of 3 years. All nodules were confirmed by CT, and the locations of the nodules were confirmed by three chest radiologists who were in complete agreement. The images were digitized using an LD-4500 or an LD-5500 laser film digitizer (Konica, Tokyo, Japan), with a resolution 0.175 m pixels in size and a matrix of 2048x2048, and 4096 or 12-bit gray scale levels corresponding to a 3.5 optical density range. A total of 154 images are confirmed to contain lung nodules and 93 images without lung nodules. One hundred of the 154 contain nodules which were confirmed as malignant and 54 are benign [29]. The CRs were extracted and classified with the WEKA tool, and the Support Vector Machine (SVM) was used and 80% of all the nodules and normal cases of 247 CRs were used in the training set and 20% as the testing set which yielded an average of 71.9% in sensitivity. The CRs which contain the nodules were grouped according to the degree of dificulty of detection. The results are compared with previous studies [30][31][32][33][34] for performance evaluation. he accuracy of this method is demonstrated in the form of sensitivity, specificity, and accuracy for the total variation enhanced CRs in computer aided design systems.  Wavelets help solid regions of interest to be extracted with accuracy due to its improved noise level during its pre-processing. It is helpful to improve edge detection since pure pixel based algorithms are prone to noise, using biorthogonal spline based wavelet filters. The wavelet transform perform similar analysis as the human visual system in hierarchical edge detection at multiple levels of resolution [39,40], and processes an image in a multiscale manner.

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ISSN: 1693-6930 Texture features always represent the characteristics of CRs and can be used in We derive the mean and the variance of the energy, distribution of the transform coefficients for each subband at each decomposition level are used to construct the feature set. Normally, pathological changes reflecting in the texture analysis of CRs occur qualitatively and quantitatively. Unfortunately there are no unique ways in accessing texture from medical images since there are different modalities in medical images.
We use the undecimated wavelet based texture analysis with wavelets filters. In wavelet transformation, the energy is distributed in different wavelet coefficients with detail components containing high degree of local relevance. The analysis explores different wavelets families in the over-complete wavelet transform as the UWTA [36,37]. By removing the downsampling step of the FWT, a translation invariant, overcomplete wavelet decomposition of an CRs image is obtained. Using such a representation when extracting features for texture analysis has the advantages of greater spatial resolution, more robustness against translation, and allowing greater confidence when extracting statistical features of larger number coefficients [38].
We quantify the characteristics of nodules by mathematical feature descriptors, to give diagnostic indicators and then further classification decides whether nodules detected show signs of malignancy in the CRs image. The feature extraction in our work is based on undecimated wavelet texture analysis (UWTA). The undecimated wavelet transformation involves, filtering with-out subsampling, so unlike the DWT, the UDWT does not incorporate the down sampling opera-tions. Thus, the approximation coefficients (low-frequency coefficients) and detailed coefficients (high-frequency coefficients) at each level are of the same length as the original signal. Based on the UDWT, fourteen texture features of pulmonary nodules on digital CRs were extracted in every sub-image.
classifying CRs into two categories: nodules or non-nodules. There are wellknown methodologies and approaches for texture feature extraction which support identifications below the threshold of human visual perception. Wavelets-based methods possess the superior qualities in discrimination algorithms where preservation is a major concern in the various resolutions [35].
Feature extraction is carried out after the segmentation algorithm of the lung region. Theaccuracy in the segmentation algorithm supports the reliability of feature extraction algorithm and the classification algorithm. The features generated convey meaningful information which are subjected to the classification algorithm to determine whether a nodule is detected or not. The characteristics of the detected nodules is used in discriminating malignant from benign nodules. Most nodule infested CRs have a number of small opacities, resulting in the differences of texture features between the normal and the abnormal CRs. The diagnosis of cancer nodules is improved by using texture features derived from CRs of lung fields after a series of wavelet transformations.

Wavelet Based Feature Extraction and Feature Analysis in Digital Chest Radiographs
10 I 2 (m,n) peak M SE P SN R = 10log (10) where I (m,n) (m,n) and is usually 255 for pixels represented using 8 bits per sample, and M SE is the mean square error. The PSNR we obtained is 42.8dB. This confirms the validity and efficiency of our method.

Image Quality Analysis
peak is the peak pixel value in the image I We use the peak signal to noise ratio (PSNR) to evaluate the performance of our algorithm, where TELKOMNIKA Vol. 17