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NOISE ESTIMATION AND MULTIRESOLUTION RECONSTRUCTION FOR DENTAL PANORAMIC X-RAY IMAGESUniversity of Applied Sciencesfh-campus wien, AustriaAuthor:Peter Michael GöbelThesis Supervisors:Dipl.-Ing. Gerhard EngelmannDr. Med. Univ. Michael TruppeAbstractThis thesis presents a new approach to the reconstruction of dental panoramicx-ray images with experimental results. The reduction of the x-ray dose that offershigher safety for the patient reduces diagnostic image quality. Inverse filtering of-ten fails due to insufficient knowledge about the noise, which varies depending onthe location. In order to overcome the aforementioned obstacles, the method pro-posed in this thesis firstly develops a semi-empirical scatter-glare model of thephoton projection process and applies it to the auto computation of an appropriatenoise-estimate. Secondly, the energy of the noise-estimate is then subtracted fromthat of the diagnostic image in the different resolution levels of a MultiresolutionDecomposition. Experiments show that the method outperforms state-of-the-artdenoising in terms of better modulation transfer function and signal to noise ratio.1IntroductionMedical images commonly require the enhancement of relevant details and suppression of unwanted artifacts, such as noise and other distortions. Re-construction methods, such as proposed by this thesis, are trying to meet these contradictory requirements.In recent years panoramic radiography (i.e. ortho-pantomographic x-ray) developed to one of the major complementary examinations in dentistry. A typical system is having x-ray source and detector in opposition; and is ro-tating around the patients head. During that rotation, the focal area of the x-ray beam describes a planar curve, which is standardized for the human teeth and jaws. Even though the dosage of radiation is small compared to other investigations, people are still inflicted by dental anxieties, fears, and phobias against x-ray examinations. Since dental radiographs are taken periodically, and more often than any radiographs, a higher public aware-ness to the risks associated with the exposure to ionizing radiation is notice-able. Therefore, reducing the dose as well as providing sufficient information concerning the procedure are strategies to overcome these obstacles. As a drawback (see Figure 1, right image), the reduction of the x-ray dose inflicts loss of diagnostic image quality by mainly an increase of scatter noise.Figure 1: Shows a comparison of the effects caused by reducing the radiographic dose. The left image shows an ordinary standard radio-graph stemming from the x-ray of a human dummy head. In the right image, the same head is shown, but acquired with reduced dose. Thus, one can see clearly degradation effects appearing more in the right image compared to the left one.2The effects that contribute mostly to the deterioration (degradation) of im-age quality are identified by the analysis of this thesis as:the systematic non-homogeneous illumination caused by the x-ray source and its collimationthe psychophysical contrast adjustment by the human visual system for the human eye according to the highlight levels of the surrounding(background) illuminationthe impact of the photon scatter noise statistics1.1The Research QuestionHence, the research question of the herein proposed approach aims in: “Finding a solution to achieve high diagnostic image quality in concurrence to the reduction of the radiographic dose.” An answer is given by this thesis in yielding a solution to aforementioned issues with:the compensation of background influences by introducing the transmit-tance rather than using the original panoramic imageapplying a polynomial correction method yielding a correction matrix for the avoidance of low frequency, big contrast differencesintroducing a new multiresolution denoising approach, which is preserving diagnostic detail rather than blurring the image like other methods do 1.2State of the artStatistical models for images are described by Smith [S97]; the estimation of noise characteristics is left open by many authors, Olsen [O93] showed a comparative study between six methods. Portilla et al. [PS03] presented a modeling approach for noise by Gaussian scale mixtures. The adaptation to unknown noise variance with a locally adaptive Wiener filter was done by Lee [L80] using the spatial image domain, but the method cannot detect weak details and it leaves noise in the vicinity of edges and lines. Since Fou-rier space based filtering becomes very inefficient when images are allowed to have local discontinuities, the most popular method for image denoising became multiscale filtering, utilizing the Besov space with the wavelet trans-form (WT) [UAL03]. Figueiredo [FN01] generalized the process of how sig-nals can be manipulated by applying the WT. Processing consists in manipu-lating the WT coefficients, rather than the signal samples themselves. An underlying basic idea is that the transformed deterministic image content is represented by a set of a few stronger wavelet coefficients, whereas the3noise is distributed across all coefficients at weak intensity. If this noise level is used as a threshold value for a shifting of all coefficients toward zero, the image gets denoised after transforming back the new coefficients.All of aforementioned methods have problems distinguishing between the noise’s variance and the variance caused by the informative image content. Since the image contrast in x-ray is very low, diagnostic information be-comes blurred what is not acceptable to the medical diagnosis purpose.2Root of the MatterSupported by an idea, originated by Blind Source Separation (BSS)1, an image model is formed that utilizes a background image, which is a pano-ramic x-ray without patient; a Monte Carlo simulation of the x-ray source including a modeling of the photon x-ray scatter by patients matter; and also the diagnostic x-ray image. A transmittance image, calculated as the fraction of the diagnostic image and the background image corrects the in-homogeneous x-ray illumination and is used instead the usual diagnostic image. The fraction functional between two polynomials of degree 2 and 17, both fitted to the vertical gray profile of the transmittance image, is yielding a correction matrix for the avoidance of low frequency and big contrast dif-ferences, according to properties dictated by the human vision system for better perception. The Monte Carlo simulation of the photon x-ray scatter yields a scatter glare distribution, which is used together with the likelihoods of the diagnostic image for scatter backprojection to achieve a Bayesian estimate of the image noise contribution. Then, the noise is modeled by the finite realization of a mixture of infinite Gaussian noise fields [PS03], having zero mean and varying variance, yielding the scatter glare noise estimate. The polynomial corrected transmittance image is then denoised by a new denoising approach, utilizing Plancherel’s Theorem for the subtraction of the scatter glare noise estimate’s energy from that of the transmittance image using the wavelet domain. The compaction property of the WT enables build-ing the difference of two random signals2, thus, in particular between their signal power values, using the wavelet coefficients of both signals. Applying the inverse WT yields the reconstruction, ready for contrast enhancement.1 BSS is in general the separation of a set of n statistically independent signals from a set of m observed signals with only little or no information about the signals.2 i.e. subtracting the noise from the original image453 Summary of ResultsThe method proposed by this thesis, firstly optimizes the diagnostic image and secondly subtracts the appropriately auto-calculated noise estimate. Other than as with classical filtering 3, or adaptive filtering 4, or also classical wavelet denoising with using coefficient thresholding, in parallel, fine image details are preserved although the noise level is substantially decreased. Hence, it becomes possible to apply contrast enhancement without amplifi-cation of the noise contribution. Figure 2 demonstrates the success of the proposed method in comparison with classical wavelet denoising. The new method performs with the better preservation of high frequency information and removes the noise in areas of low edge count more than in areas with detail (see Figure 2, and compare the right picture with the middle one). Thus the method is capable distinguishing between noise variance and diag-nostic image structure. Although some methods have been already discov-ered by others – however – the way in combining them, extending and filling gaps by means of new concepts appears to be new.3that naively assumes the noise contribution mainly located at higher frequencies 4 e.g. Wiener Filtering, which adopts to local image variance, it has problems in distinguishing between the noises variance and the variance caused by the informative image contentFigure 2: A Comparison of the denoising method by means of MTF with a line pair gauge phantom: it is shown at the left the original noisy image; at the middle the clas-sical denoised image (by soft thresholding); and at the right the result of the new me-thod, proposed by this thesis. Within every picture slide the graphs are showing the pattern responses for 2.5, 2.8, 3.1, 5.0, 5.8, and 6.3 lines per mm. The magnified quarters are showing a magnified version of the line pairs of 2.5 lines per mm. As the image content in the middle gets blurred, the new method shows (at the right) the noise removed by preserving diagnostic information. Thus, in particular, the achieved MTFs are – at the original left 53% – at the middle 21% – and finally at the right 44%.4Conclusions and OutlookIt was shown by this thesis that even though solutions exist since several years, a renewal of the analysis of an imaging system may yield a more appropriate method, which outperforms those being state-of-the-art. De-noising is one of the fields in research with an emerging output of publica-tions per year. Nevertheless, the proposed method in this thesis shows much better performance in terms of reconstructed image quality with less blurring and in terms of calculation complexity. Hence, the method may be utilized for the clinical practice. Hereafter, a clinical study will be carried out by applying the method to a group of patients. Parts of the work were pre-sented in the year 2005 at four international conferences [HACI, SSP, ECCT, DAGM], and have aroused considerable scientific and commercial interest. Image restoration as presented by this thesis is very close related to other issues arising in the field of medical image compression. The basic motiva-tion in medical imaging beyond to manipulate visual diagnostic information is transfer and archiving. Trends in medical imaging are developing increas-ingly digital; meanwhile the amount of images captured per year is in the range of hundred petabytes and still on the rise. Compression is done either by lossless or lossy methods; in particular the JPEG2000 standard offers both methods by setting parameters. The allowable compression rate is di-rectly coupled to particular diagnostic demands, especially in the case of lossy compression. Depending on the particular compression rate several artifacts emerge within the image after reconstruction. The image noise has a crucial influence on the compression efficiency, since noise - as a signal - is per definition not compressible. In current clinical practice lossy schemes are not often being used, because of legal questions and regularity policies. New clinical testing can develop reasonable policies and acceptable stan-dards for the use of lossy schemes.However, a number of questions arise which are worth for exploration on:How much influence does noise have on the compression performance?Does one achieve more realistic simulation results, if Monte Carlo noise modeling can be applied for the generation of simulation images?Is it possible to find an objective image quality measurement score, which satisfies the requirements of both, clinical practice and legal rights? What criterion determines how an image can be compressed more ag-gressively?6In fact, there is still a need to develop objective quality measures, which can prove lossy compression or denoising to be applicable. Measures, stemming from spatial autocorrelation, may cope better with the classification of arti-facts, whether important or not, that change the diagnostic content. Thus, it is important to apply an appropriate metric to objectively measure whether artifacts are acceptable or not. The development of such a metric will be one focus of my future scientific work.5Bibliography[FN01] M.A.T. Figueiredo and R.D. Nowak. Wavelet-based image estima-tion: An empirical Bayes’ approach using Jeffreys' noninformativeprior. IEEE Trans. on Image Proc., 10(9):1322-1331, Sep. 2001. [L80] J.S. Lee. Digital image enhancement and noise filtering by use of local statistics. IEEE Trans. Patt. Anal., 1:165-168, 1980.[PS03] J. Portilla, P.E. Simoncelli. Image restoration using Gaussian scale mixturesin the wavelet domain. 9th IEEE Conference on ImageProcessing, Barcelona, Spain, Sep., 2003.[O93] S.I. Olsen. Noise variance estimation in images. In In 8 th Scandi-navian Conference on Image Analysis, Norway, 1993.[S97] S.W. Smith. The Scientist and Engineer's Guide to Digital Signal Processing. California Technical Publishing, 1997.[UAL03] J.M. Unser, A. Aldroubi, and A. Laine, Wavelets in medical imaging.IEEE Trans. on Medical Imaging., 22(3):285-288, March 2003. [HACI] P. M. Goebel , A. N. Belbachir, An Application Analysis Approach for Noise Estimation in Panoramic X-ray Images, 5th Conf. of theKÉPAF, HACIPPR05, OCG Bd.192, May, 2005, Veszprem, H [SSP] P. M. Goebel, A. N. Belbachir, M. Truppe, Noise Estimation in Panoramic X-ray Images: An Application Analysis Approach, IEEEWorkshop on Statistical Signal Processing, July, 2005 Bordeaux, F [ECCT] P. M. Goebel, A. N. Belbachir, M. Truppe, Background Removal in Dental Panoramic X-ray Images by the A-Trous MultiresolutionTransform, 17th IEEE Conf. Circuit Theory and Design., ECCTD05,Sep., 2005, Cork, IE[DAGM] P. M. Goebel, A. N. Belbachir, M. Truppe, Blind Background Sub-traction in Dental Panoramic X-ray Images: An Application Ap-proach. 27th Conf. of the DAGM 2005, Sep., 2005, Vienna, A7。