Automatic Detection and Correction of Defective …

1 Noname manuscript No.(will be inserted by the editor) Automatic Detection and Correction of Defective Pixels forMedical and Space ImagersEliahu Cohen Moriel Shnitser Tsvika Avraham Ofer Hadar Yocheved DotanReceived: date / Accepted: dateAbstractA novel model for image restoration is dis-cussed where the imagers are digital cameras in space,damaged from cosmic radiation, or ultrasonic medi-cal devices damaged from speckle noise. In previousworks we have suggested a simulated annealing algo-rithm based on Ising theory for the restoration of col-ored images and videos which were damaged from var-ious kinds of noise. In what follows we will discuss theaffinity between statistical physics and image process-ing and use an adjusted version of our Ising-like algo-rithm for pixel Correction in digital space cameras andnoise removal from ultra-sound images.

2 We will presentrestoration results which are achieved by the combina-tion of known algorithms such as Median and LOCO-Itogether with Ising-like models. The mean error andPSNR values of the restored images will be shown toexceed the values achieved with similar CohenDepartment of Exact Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, IsraelTel.: +972-3-6405234 Fax: +972-3-6407932E-mail: Shnitser, T. Avraham, O. HadarDepartment of Communication systems Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, IsraelTel.: +972-8-6472210 Fax: +972-8-6472883E-mail: DotanDepartment of Electrical and Computer Engineering, RuppinAcademic Center, Emek-Heffer 40250, IsraelTel.

3 : +972-9-8981376 Fax: +972-9-8981302E-mail: restoration pixel Correction Isingtheory simulated annealing space imagers medicalsonography1 IntroductionSince solution of classical equations of motion is notpossible for a macroscopic system, with a typical num-ber of 1023particles, physicists use statistical methodsfor finding the average characteristics of the system [1 3]. This problem resembles the one encountered whentrying to extract as many information as possible re-garding an image or a video signal. Here also, large andcomplex system is discussed which has specific correla-tions between its parts (pixels and frames) where someinformation is missing or corrupted (similarly to im-purities in a crystal).

4 Utilizing this similarity, we haveemployed [4, 5] our physical intuition regarding many-particles systems to the field of image processing andsuggested a model for restoration of images and videosignals damaged by external (artificial) noise. We nowuse our model for the restoration of original imagestaken from two important fields of imaging: remote dig-ital cameras in space applications and medical The ProblemsPhysical systems of many particles are described by av-erage thermodynamic potentials??. The most basic ofthem is the internal energy,U, which can be representedin its differential form by:dU=TdS pdV+ i idNi+EdP+HdM,(1) MEDIAN 2014 March 28th, 2014 Dresden, Germany 442 Eliahu Cohen et the temperature,Sis the entropy,pdescribesthe pressure andVis the volume.

5 Iis the chemical po-tential of typeiparticles andNiis their the electric and magnetic fields, polarization andMis the magnetization. Generally,the parameters above have some probabilistic distribu-tion, yet in most applications only the average valuesare used. In an adiabatic system (where the entropy isconstant), equilibrium is achieved by the condition ofminimal energy:dU= 0, d2U >0.(2)The analogy between thermodynamics and images isthe following:U, the internal energy of the image, canbe assumed to be a global parameter which should beminimized in order to get an image of high quality. Inour case, minimal energy means that images tend tobe smooth, with adjacent pixels having similar values,but not too smooth.

6 Deviations from this smoothnessare maintained by randomness (thermal noise) and bysome external knowledge we call an external field .N,the number of particles in the physical system, can beused to describe the number of pixels in the noisy the complexity of the thearea of the image, usually strictly relate , thephysical (Boltzmann) entropy, is also well-defined forimages in terms of Shannon the en-ergy density, andTdescribes the energy required to re-duce the entropy of the be thoughtof as external parameters affecting the image, , dis-tortions and noises whereEandHdenote the energychange they cause. Using this analogy, we claim thatphysical models can be applied to the problem of de-scribing images.

7 In particular, one of these models isthe Ising model which will be briefly discussed in Since this model explicitly discusses phase transi-tions from disordered (which means noisy in the caseof images and videos) to ordered phases (restored im-ages/video) we found them very useful for the imageprocessing tasks at The ProblemsThe method we use is rather general, but we will fo-cus during this work on two problems are known to beimportant but Hot Pixels in space imagersOver the last decade, digital imagers have become in-creasingly prevalent in many applications. Like all mi-croelectronic devices, imagers are prone to develop de-fects over their lifetime.

8 Previous studies [6, 7] have shownthat these defects are permanent, their number increasescontinuously over the sensors lifetime, and they even-tually manifest themselves in all captured images andreduce significantly the image quality. The most com-mon type of defect is Hot Pixel , a pixel that ap-pears as a bright dot in every image. With many im-agers located in remote, unreachable locations such asspace, Automatic Detection and Correction of defects arecrucial. Korens group developed a Bayesian techniquefor detecting and tracing defects based on a series ofimages taken by the imager [6]. Later they restored thepixels values by using the dark current information anda weighted filtering technique [7].

9 Our model will get asan input only those damaged pixels without the darkcurrent information and restore them, trying to bypassthe challenge posed by Speckle noise in medical sonographySpeckle noise appears as a multiplicative granular noisedue to the random interference of the wavelets scatteredby the microscopic fluctuations of the object surfacewithin one resolution element. The presence of specklenoise in ultrasound images reduces the resolution ofthe image and the effectiveness of image methods have been proposed to suppress itwhere the objectives of speckle reduction are to pre-serve the backscattering coefficient value in homoge-neous areas and edges between the different areas.

10 Wehave implemented a few additions in our model, suchas switching from Boltzmann to Tsallis distribution [8]and inserting a quantum annealing term [9] in order toconfront this kind of multiplicative The ModelA well-known model in the field of solid-state physics isthe Ising model [1], which assumes a simple two-bodyinteraction in a discrete system of spin-1/2 is an internal degree of freedom which cantake one of the values 1 or -1. We have performed sev-eral adaptations in order to use the model for coloredimages restoration [4], namely, adding another spatialdimension, enabling multi-valued pixels and taking careof the 12 weighted neighbors (3x3 neighborhood+4 nextnearest neighbors) of each pixel denoted here by C (SeeFig.)