Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

Hepatic capillariasis in rats: a new model for testing antifibrotic drugs

Rats infected with the helminth Capillaria hepatica regularly develop septal hepatic fibrosis that may progress to cirrhosis in a relatively short time. Because of such characteristics, this experimental model was selected for testing drugs exhibiting antifibrosis potential, such as pentoxifylline, gadolinium chloride and vitamin A. Hepatic fibrosis was qualitatively and quantitatively evaluated in liver samples obtained by partial hepatectomy and at autopsy. The material was submitted to histological, biochemical and morphometric methods. A statistically significant reduction of fibrosis was obtained with pentoxifylline when administered intraperitoneally rather than intravenously. Gadolinium chloride showed moderate activity when administered prophylactically (before fibrosis had started), but showed a poor effect when fibrosis was well advanced. No modification of fibrosis was seen after vitamin A administration. Hydroxyproline content was correlated with morphometric measurements. The model appears to be adequate, since few animals die of the infection, fibrosis develops regularly in all animals, and the effects of different antifibrotic drugs and administration protocols can be easily detected.

Puunjalostuskonsernin tehtaiden käyttäjäkunnossapidon nykytilanteen selvitys- ja kehitystyö

Tässä diplomityössä selvitettiin kohdeorganisaation tehtaiden käyttäjäkunnossapidon nykytilannetta ja kehityskohteita konelinjoittain. Käyttäjäkunnossapito otettiin käyttöön vain vähän aikaa sitten entisen vuorohuollon tilalle. Tutkimus toteutettiin haastattelututkimuksena ja tietoa kerättiin kyselylomakkeiden avulla. Kyselyn otanta oli 200 henkilöä, joista 89,5 % vastasi kyselyyn. Haastateltavia oli seitsemästä eri henkilöryhmästä. Haastateltavat henkilöryhmät olivat käyttäjäkunnossapidon kanssa päivittäin työskenteleviä ryhmiä. Tuloksia analysoitiin konelinjoittain, tehtastasolla ja henkilöryhmittäin. Analysoinnissa käytettiin apuna tehtaan järjestelmistä löytyviä tilastoja ja kyselyn teettämisen jälkeisiä keskusteluja. Suurin haaste käyttäjäkunnossapidon nykytilanteessa oli kunnossapito-osaamisen säilyttäminen, sillä käyttäjäkunnossapitäjien työ on suurimmaksi osaksi tuotantotyötä. Käyttäjäkunnossapitäjien osaamistasot vaihtelivat suuresti. Joidenkin konelinjojen käyttäjäkunnossapitäjillä osaamistasot eivät olleet vielä työn vaatimalla tasolla. Toimintamallin käytännön toteutuksessa oli parannettavaa useilla konelinjoilla. Käyttäjäkunnossapito ei ole pystynyt tekemään kunnossapitoa yhtä suuressa mittakaavassa kuin vuorohuolto. Jatkotoimenpiteinä ehdotettiin käyttäjäkunnossapitäjien kunnossapitotyön määrän lisäämistä tarkastuskierrosten ja ennakkohuoltojen muodossa, sekä linjakunnossapidon ja käyttäjäkunnossapidon yhteistyömallin kehittämistä.

Air pollution and neonatal deaths in São Paulo, Brazil

Air pollution has been associated with health effects on different age groups. The present study was designed to assess the impact of daily changes in air pollutants (NO2, SO2, CO, O3, and particle matter (PM10)) on total number of daily neonatal deaths (those that occur between the first and the 28th days of life) in São Paulo, from January 1998 to December 2000, since adverse outcomes such as neonatal deaths associated with air pollution in Brazil have not been evaluated before. Generalized additive Poisson regression models were used and nonparametric smooth functions (loess) were adopted to control long-term trend, temperature, humidity, and short-term trends. A linear term was used for holidays. The association between air pollutants and neonatal deaths showed a short time lag. Interquartile range increases in PM10 (23.3 µg/m³) and SO2 (9.2 µg/m³) were associated with increases of 4% (95% CI, 2-6) and 6% (95% CI, 4-8), respectively. Instead of adopting a two-pollutant model we created an index to represent PM10 and SO2 effects. For an interquartile range increase in the index an increase of 6.3% (95% CI, 6.1-6.5) in neonatal deaths was observed. These results agree with previous studies performed by our group showing the deleterious effects of air pollutants during the perinatal period. The method reported here represents an alternative approach to analyze the relationship between highly correlated pollutants and public health problems, reinforcing the idea of the synergic effects of air pollutants in public health.

Phenotypic and genotypic variant of MDR-Mycobacterium tuberculosis multiple isolates in the same tuberculosis episode, Rio de Janeiro, Brazil

Assuming that the IS6110-restriction fragment length polymorphism (RFLP) changes at a constant rate of 3.2 years, this methodology was applied to demonstrate, for the first time, variant patterns of Mycobacterium tuberculosis (MTB) in multiple isolates obtained at short time intervals from sputum and blood of an HIV+ patient with multiple admissions to the Emergency Room and to the multidrug-resistant tuberculosis (MDR-TB) Reference Center of a secondary-care hospital in Rio de Janeiro, Brazil. In sputum, the IS6110-RFLP appeared in isolates with two variant patterns with 10 and 13 IS6110 copies. However, blood presented only the pattern corresponding to 10 copies, suggesting compartmentalization. With regard to the exact match of 10 of 13 bands, this may be a subpopulation with the same clonal origin and this may be related to the IS6110 transposition. A susceptibility test demonstrated an MDR profile (INH R, RIF R, SM R, and EMB R), with the sputum isolate also exhibiting EMB S (R = resistant; S = sensitive). A gene mutation confirmed resistance only to streptomycin. There was agreement between the results of the phenotypic test and the clinical response to MDR-TB treatment, suggesting serious implications with regard to treatment administration based exclusively on molecular methods, and calling attention to the fact that more effective control strategies against the emergence of MDR strains must be implemented by the TB control program to prevent transmission of MDR-MTB strains at health facilities in areas highly endemic for TB.

Reproducibility of heart rate variability parameters measured in healthy subjects at rest and after a postural change maneuver

Heart rate variability (HRV) provides important information about cardiac autonomic modulation. Since it is a noninvasive and inexpensive method, HRV has been used to evaluate several parameters of cardiovascular health. However, the internal reproducibility of this method has been challenged in some studies. Our aim was to determine the intra-individual reproducibility of HRV parameters in short-term recordings obtained in supine and orthostatic positions. Electrocardiographic (ECG) recordings were obtained from 30 healthy subjects (20-49 years, 14 men) using a digital apparatus (sampling ratio = 250 Hz). ECG was recorded for 10 min in the supine position and for 10 min in the orthostatic position. The procedure was repeated 2-3 h later. Time and frequency domain analyses were performed. Frequency domain included low (LF, 0.04-0.15 Hz) and high frequency (HF, 0.15-0.4 Hz) bands. Power spectral analysis was performed by the autoregressive method and model order was set at 16. Intra-subject agreement was assessed by linear regression analysis, test of difference in variances and limits of agreement. Most HRV measures (pNN50, RMSSD, LF, HF, and LF/HF ratio) were reproducible independent of body position. Better correlation indexes (r > 0.6) were obtained in the orthostatic position. Bland-Altman plots revealed that most values were inside the agreement limits, indicating concordance between measures. Only SDNN and NNv in the supine position were not reproducible. Our results showed reproducibility of HRV parameters when recorded in the same individual with a short time between two exams. The increased sympathetic activity occurring in the orthostatic position probably facilitates reproducibility of the HRV indexes.

Alternative chromatographic system for the quality control of lipophilic technetium-99m radiopharmaceuticals such as [99mTc(MIBI)6]+

Knowledge of the radiochemical purity of radiopharmaceuticals is mandatory and can be evaluated by several methods and techniques. Planar chromatography is the technique normally employed in nuclear medicine since it is simple, rapid and usually of low cost. There is no standard system for the chromatographic technique, but price, separation efficiency and short time for execution must be considered. We have studied an alternative system using common chromatographic stationary phase and alcohol or alcohol:chloroform mixtures as the mobile phase, using the lipophilic radiopharmaceutical [99mTc(MIBI)6]+ as a model. Whatman 1 modified phase paper and absolute ethanol, Whatman 1 paper and methanol:chloroform (25:75), Whatman 3MM paper and ethanol:chloroform (25:75), and the more expensive ITLC-SG and 1-propanol:chloroform (10:90) were suitable systems for the direct determination of radiochemical purity of [99mTc(MIBI)6]+ since impurities such as99mTc-reduced-hydrolyzed (RH),99mTcO4- and [99mTc(cysteine)2]-complex were completely separated from the radiopharmaceutical, which moved toward the front of chromatographic systems while impurities were retained at the origin. The time required for analysis was 4 to 15 min, which is appropriate for nuclear medicine routines.

Origanum vulgare L. essential oil as inhibitor of potentially toxigenic Aspergilli

Origanum vulgare L. essential oil has been known as an interesting source of antimicrobial compounds to be applied in food conservation. In this study, the effect of O. vulgare essential on the growth of A. flavus, A. parasiticus, A. fumigatus, A. terreus and A. ochraceus was assessed. The essential oil had a significant inhibitory effect on all assayed fungi. MIC was 0.6 µL.mL-1 for all fungi, while MFC was in the range of 1.25-2.5 µL.mL-1. The radial mycelial growth of A. flavus and A. parasiticus was strongly inhibited over 14 days at 0.6, 1.25 and 2.5 µL.mL-1 of oil in solid medium. The mycelial mass of all fungi was inhibited over 90% at 0.6 and 0.3 µL.mL-1 in liquid medium, while it was 100% at 1.25 µL.mL-1. The oil in a range of concentrations (0.6 to 2.5 µL.mL-1) was effective in inhibiting the viability and spores germination in a short time of exposure. The main morphological changes caused by the essential oil in A. parasiticus observed under light microscopy were absence of conidiation, leakage of cytoplasm, loss of pigmentation, and disrupted cell structure. These results demonstrated that O. vulgare essential oil produced a significant fungitoxic effect supporting its possible rational use as anti-mould compound in food conservation.

Effect of wheat flour protein variations on sensory attributes, texture and staling of Taftoon bread

The quality of flat breads depends in part on the textural properties of breads during storage. These properties are largely affected by flour protein quality and quantity. The present study aimed to examine differences between sensory properties, textural and staling of Tandoori breads made from flours of different quality and different quantities of protein. This was implemented by using three flours with 9.4, 11.5 and 13.5% protein contents and different protein qualities shown by Zeleney sedimentation volume 16.25, 22.75 and 23.25 mL respectively. Bread strips were submitted to uniaxial compression between two parallel plates on an Instron Universal Testing machine, and firmness of the breads was determined. Results indicated the differences in the sensory attributes of breads produced by flours of different protein content and quality, demonstrating that high protein high quality flours are not able to sheet and expand under the high temperature - short time conditions employed in Taftoon bread production and are therefore not suitable for this kind of bread. Results showed that flour with 11.5% protein content, produced bread with better sensory characteristics and acceptable storage time.

BotCloud Detection System

Leveraging cloud services, companies and organizations can significantly improve their efficiency, as well as building novel business opportunities. Cloud computing offers various advantages to companies while having some risks for them too. Advantages offered by service providers are mostly about efficiency and reliability while risks of cloud computing are mostly about security problems. Problems with security of the cloud still demand significant attention in order to tackle the potential problems. Security problems in the cloud as security problems in any area of computing, can not be fully tackled. However creating novel and new solutions can be used by service providers to mitigate the potential threats to a large extent. Looking at the security problem from a very high perspective, there are two focus directions. Security problems that threaten service user’s security and privacy are at one side. On the other hand, security problems that threaten service provider’s security and privacy are on the other side. Both kinds of threats should mostly be detected and mitigated by service providers. Looking a bit closer to the problem, mitigating security problems that target providers can protect both service provider and the user. However, the focus of research community mostly is to provide solutions to protect cloud users. A significant research effort has been put in protecting cloud tenants against external attacks. However, attacks that are originated from elastic, on-demand and legitimate cloud resources should still be considered seriously. The cloud-based botnet or botcloud is one of the prevalent cases of cloud resource misuses. Unfortunately, some of the cloud’s essential characteristics enable criminals to form reliable and low cost botclouds in a short time. In this paper, we present a system that helps to detect distributed infected Virtual Machines (VMs) acting as elements of botclouds. Based on a set of botnet related system level symptoms, our system groups VMs. Grouping VMs helps to separate infected VMs from others and narrows down the target group under inspection. Our system takes advantages of Virtual Machine Introspection (VMI) and data mining techniques.

Carponate precipitation with carbon dioxide gas

The aim of this thesis research work focused on the carbonate precipitation of magnesium using magnesium hydroxide Mg(OH)2 and carbon dioxide (CO2) gas at ambient temperature and pressure. The rate of dissolution of Mg(OH)2 and precipitation kinetics were investigated under different operating conditions. The conductivity and pH of the solution were inline monitored by a Consort meter and the solid samples gotten from the precipitation reaction were analysed by a laser diffraction analyzer Malvern Mastersizer to obtain particle size distributions (PSD) of crystal samples. Also the Mg2+ concentration profiles were determined from the liquid phase of the precipitate by ion chromatography (IC) analysis. Crystal morphology of the obtained precipitates were also investigated and discussed in this work. For the carbonation reaction of magnesium hydroxide in the present work, it was found that magnesium carbonate trihydrate (nesquehonite) was the main product and its formation occurred at a pH of around 7-8. The stirrer speed has a significant effect on the dissolution rate of Mg(OH)2. The highest obtained Mg2+ concentration level was 0.424 mol L-l for the 470 rpm and 0.387 mol L-1 for the 560 rpm which corresponded to the processing time of 45 mins and 40 mins respectively. The particle size distribution shows that the average particle size keeps increasing during the reaction as the CO2 is been fed to the system. The carbonation process is kinetically favored and simple as nesquehonite formation occurs in a very short time. It is a thermodynamically and chemically stable solid product, which allows for a long-term storage of CO2. Since the carbonation reaction is a complex system which includes dissolution of magnesium hydroxide particles, absorption of CO2, chemical reaction and crystallization, the dissolution of magnesium hydroxide was studied in hydrochloric acid (HCl) solvent with and without nitrogen (N2) inert gas. It was found on the dissolution part that the impeller speed had effect on the dissolution rate. The higher the impeller speed the higher the pH of the solution, although for the highest speed of 650rpm it was not the case. Therefore, it was concluded that the optimum speed of the stirrer was 560rpm. The influence of inert gas N2 on the dissolution rate of Mg(OH)2 particles could be seen based on measured pH, electric conductivity and Mg2+ concentration curves.

Daniel Shannon fonds, 1816-1822

Lt. Daniel Shannon fl. 1777-1822, was the only son of Susan Drake, granddaughter of Rev. Thomas Drake, eldest brother of Sir Francis Drake, and Captain Daniel Shannon of the Royal Navy. He married Elizabeth Garvey, daughter of Alexander Garvey and Catharine Borden of New Jersey. Lt. Shannon was a Regular in the British Army and on February 12, 1777 he joined the Royal Standard, 5th New Jersey Volunteers. After being arrested and sentenced to hang for spying he was pardoned through the efforts of his mother Susan Drake Shannon who pleaded his case with the Governor. He served under General Cornwallis at the surrender in Virginia in 1781. In 1783 he moved to New Brunswick, Canada where he was reduced to a half-pay ensign in the 2nd Regiment of the Lincoln Militia. He was granted 500 acres of land on the St. Johns River, and on April 1, 1786 his daughter Catharine was born there. The family returned to the United States, residing in Pennsylvania, for a short time. In 1800 Lt. Shannon, with his mother and family, returned to Canada and settled in Stamford Township where he bought 200 acres of land on the Niagara River near the whirlpool. He later served in the Secret Service during the War of 1812 and was stationed at a lookout point on the Niagara River below the falls. In 1806 Shannon’s daughter, Catharine, married Thomas Lundy, fourth son of William Lundy of Stamford Township.

The Welland Canals Foundation, Honourable William Hamilton Merritt and the St. Catharines Historical Society and Museum, 1971-1990, n.d.

‘The Father of Canadian Transportation’ is a term commonly associated with William Hamilton Merritt. Although he is most known for being one of the driving forces behind the building of the first Welland Canal, he was many things throughout his life; a soldier, merchant, promoter, entrepreneur and politician to name a few. Born on July 3, 1793 at Bedford, Westchester County, N.Y. to Thomas Merritt and Mary Hamilton, Merritt’s family relocated to Canada shortly after in 1796. The move came after Merritt’s father petitioned John Graves Simcoe for land in Upper Canada after serving under him in the Queen’s Rangers during the American Revolution. The family quickly settled into their life at Twelve Mile Creek in St. Catharines. Merritt’s father became sheriff of Lincoln County in 1803 while Merritt began his education in mathematics and surveying. After some brief travel and further education Merritt returned to Lincoln County, in 1809 to help farm his father’s land and open a general store. While a farmer and merchant, Merritt turned his attention to military endeavours. A short time after being commissioned as a Lieutenant in the Lincoln militia, the War of 1812 broke out. Fulfilling his duty, Merritt fought in the Battle of Queenston Heights in October of 1812, and numerous small battles until the Battle of Lundy’s Lane in July 1814. It was here that Merritt was captured and held in Cheshire, Massachusetts until the war ended. Arriving back in the St. Catharines area upon his release, Merritt returned to being a merchant, as well as becoming a surveyor and mill owner. Some historians hypothesize that the need to draw water to his mill was how the idea of the Welland Canals was born. Beginning with a plan to connect the Welland River with the Twelve mile creek quickly developed into a connection between the Lakes Erie and Ontario. Its main purpose was to improve the St. Lawrence transportation system and provide a convenient way to transport goods without having to go through the Niagara Falls portage. The plan was set in motion in 1818, but most living in Queenston and Niagara were not happy with it as it would drive business away from them. Along with the opposition came financial and political restraints. Despite these factors Merritt pushed on and the Welland Canal Company was chartered by the Upper Canadian Assembly on January 19, 1824. The first sod was turned on November 30, 1824 almost a year after the initial chartering. Many difficulties arose during the building of the canal including financial, physical, and geographic restrictions. Despite the difficulties two schooners passed through the canal on November 30, 1829. Throughout the next four years continual work was done on the canal as it expended and was modified to better accommodate large ships. After his canal was underway Merritt took a more active role in the political arena, where he served in various positions throughout Upper Canada. In 1851, Merritt withdrew from the Executive Council for numerous reasons, one of which being that pubic interest had diverted from the canals to railways. Merritt tried his hand at other public works outside transportation and trade. He looked into building a lunatic asylum, worked on behalf of War of 1812 veterans, aided in building Brock’s monument, established schools, aided refugee slaves from the U.S. and tried to establish a National Archives among many other feats. He was described by some as having “policy too liberal – conceptions too vast – views too comprehensive to be comprehensible by all”, but he still made a great difference in the society in which he lived. After his great contributions, Merritt died aboard a ship in the Cornwall canal on July 5, 1862. Dictionary of Canadian Biography Online http://www.biographi.ca/EN/ShowBio.asp?BioId=38719 retrieved October 2006 Today numerous groups carry on the legacy of Merritt and the canals both in the past and present. One such group is the Welland Canals Foundation. They describe themselves as: “. . . a volunteer organization which strives to promote the importance of the present and past Welland Canals, and to preserve their history and heritage. The Foundation began in 1980 and carries on events like William Hamilton Merritt Day. The group has strongly supported the Welland Canals Parkway initiative and numerous other activities”. The Welland Canals Foundation does not work alone. They have help from other local groups such as the St. Catharines Historical Society. The Society’s main objective is to increase knowledge and appreciation of the historical aspects of St. Catharines and vicinity, such as the Welland Canals. http://www.niagara.com/~dmdorey/hssc/dec2000.html - retrieved Oct. 2006 http://www.niagara.com/~dmdorey/hssc/feb2000.html - retrieved Oct. 2006

Interlake Tissue Mills Fire Slides

The Interlake Tissue Mills storage location was at the intersection of Glendale and Merritt Street in Merritton. In the 1850s, the Beaver Cotton Mills (later Merritton Cotton Mills) was built. It was a frame building that burned down in 1881. A sandstone structure replaced the previous building. In 1906, the cotton mill closed and in 1912, the Independent Rubber Company took over the building. The mill was doubled in size. The rubber company remained there for ten years and then the building remained vacant until 1935. Interlake Tissue Mills acquired the building for storage purposes. A fire razed the larger of the plant’s buildings on Memorial Day weekend in 1961. After the fire, Domtar used the smaller building for storage for a short time. This is currently the site of the Keg Restaurant.

Le rendu en demi-ton avec sensibilité à la structure

Dans ce mémoire nous allons présenter une méthode de diffusion d’erreur originale qui peut reconstruire des images en demi-ton qui plaisent à l’œil. Cette méthode préserve des détails fins et des structures visuellement identifiables présentes dans l’image originale. Nous allons tout d’abord présenter et analyser quelques travaux précédents afin de montrer certains problèmes principaux du rendu en demi-ton, et nous allons expliquer pourquoi nous avons décidé d’utiliser un algorithme de diffusion d’erreur pour résoudre ces problèmes. Puis nous allons présenter la méthode proposée qui est conceptuellement simple et efficace. L’image originale est analysée, et son contenu fréquentiel est détecté. Les composantes principales du contenu fréquentiel (la fréquence, l’orientation et le contraste) sont utilisées comme des indices dans un tableau de recherche afin de modifier la méthode de diffusion d’erreur standard. Le tableau de recherche est établi dans un étape de pré-calcul et la modification est composée par la modulation de seuil et la variation des coefficients de diffusion. Ensuite le système en entier est calibré de façon à ce que ces images reconstruites soient visuellement proches d’images originales (des aplats d’intensité constante, des aplats contenant des ondes sinusoïdales avec des fréquences, des orientations et des constrastes différents). Finalement nous allons comparer et analyser des résultats obtenus par la méthode proposée et des travaux précédents, et démontrer que la méthode proposée est capable de reconstruire des images en demi-ton de haute qualité (qui préservent des structures) avec un traitement de temps très faible.