Fawaz Hjouj | Khalifa University (original) (raw)
Papers by Fawaz Hjouj
IEEE Access
Characterizing heterogeneity in reservoir rocks at the pore scale is crucial to understand the fl... more Characterizing heterogeneity in reservoir rocks at the pore scale is crucial to understand the flow patterns better, and estimate reservoir petrophysical properties such as porosity and permeability. This study introduces multifractals as descriptors for rock samples' heterogeneity at the pore scale. We analyzed twenty rock samples from sandstone and carbonate reservoirs using their 3D X-ray micro-computed tomography images. In addition, we simulated porosity and permeability properties and examined their correlation with multifractal parameters. The results show that the capacity dimension D 0 and the information dimension D 1 correlate with porosity and permeability simulated from images, respectively. Finally, we calculated several multifractal parameters such as the width of the spectrum, the asymmetry degree of the spectrum in the horizontal direction and the value of the vertical difference between the two branches of the spectrum. Results illustrate the ability of multifractal parameters to classify groups of rock samples according to their degree of heterogeneity.
Proceedings of the 2022 5th International Conference on Digital Medicine and Image Processing
IEEE Access
Let F represent a digitized version of an image f (x, y). Assume that the image fits inside a rec... more Let F represent a digitized version of an image f (x, y). Assume that the image fits inside a rectangular region and this region is subdivided into M × N squares. We call these squares the shifted box functions. Thus f (x, y) is approximated by M × N matrix F. This paper proofs that F can be recovered exactly and uniquely from the Radon transform of f using only one selected view angle with a well selected family of MN lines. The paper also proposes a precise method for computing the Radon transform of an image. The approach can be categorized as an algebraic reconstruction, but it is merely a theoretical contribution for the field of limited data tomography. INDEX TERMS Algebraic reconstruction, radon transform, tomography, limited data tomography.
83rd EAGE Annual Conference & Exhibition
IEEE Access
In this paper, we present methods for identifying an image from a given set of Radon projections.... more In this paper, we present methods for identifying an image from a given set of Radon projections. Given a suitably regular 2-D or 3-D function, we form a new function from using a linear transformation. We show how the Radon projections of and can be used to determine the transformation. The proposed algorithms introduce three major contributions, (1) Improvements on the 2-D setting using the moments of the Radon projections with only two orthogonal projections. (2) A natural extension of the 2-D setting to work with the 3-D setting. In particular, reducing the 3-D problem to a 2-D problem so that we can recover a translation, a scaling, or a rotation transformation of a 3-D object in the Radon domain. (3) An efficient method of recovering a rotation of a 3-D image around an arbitrary axis and an angle of rotation.
The Open Chemical Engineering Journal
Background: This paper is an improvement of a previous work on the problem recovering a function ... more Background: This paper is an improvement of a previous work on the problem recovering a function or probability density function from a finite number of its geometric moments, [1]. The previous worked solved the problem with the help of the B-Spline theory which is a great approach as long as the resulting linear system is not very large. In this work, two solution algorithms based on the approximate representation of the target probability distribution function via an orthogonal expansion are provided. One primary application of this theory is the reconstruction of the Particle Size Distribution (PSD), occurring in chemical engineering applications. Another application of this theory is the reconstruction of the Radon transform of an image at an unknown angle using the moments of the transform at known angles which leads to the reconstruction of the image form limited data. Objective: The aim is to recover a probability density function from a finite number of its geometric moments...
Determining the internal structure of an object without having to cut it, or viewing a section of... more Determining the internal structure of an object without having to cut it, or viewing a section of a body without interference from other regions, have long been goals of radiologists and engineers. These goals have been achieved through computed tomography (CT) and other technologies that are used in every hospital. This Module on CT should help readers appreciate this technology and the underlying mathematics.
Journal of Mathematical Sciences & Computer Applications, 2017
We consider the two-dimensional parallel beam Tomography problem in which both the object being i... more We consider the two-dimensional parallel beam Tomography problem in which both the object being imaged and the projection directions are unknown. The angles of projections need not to be uniformly distributed. Our solution combines two known approaches: the Geometric Moment and the Graph Laplacian. After sorting the projections using the Graph Laplacian method we create a one to one moment function of the angles. We then solve for each angle uniquely.
Journal of Mathematical Sciences & Computer Applications, 2017
We give an algorithm for reconstructing a density function f in the plane from limited number of ... more We give an algorithm for reconstructing a density function f in the plane from limited number of Radon projections on a range of angles −𝝋∗
Journal of Mathematical Sciences & Computer Applications, 2017
Given a regular binary function f on R2 with compact support D, we use translation to form a new ... more Given a regular binary function f on R2 with compact support D, we use translation to form a new binary function g from f so that the image representation of g (x, y) is made up of non-overlapping copies of D. Thus, g is made up of discrete entities that are surrounded by regions of space. We devise a procedure that can determine the translation parameters using a minimum number of Radon projections g of g . This model is a mathematical abstraction of an application of the Radon transform in Spectroscopy.Keywords: Radon transforms, transformation of an image, Back projection.
IEEE Access
Characterizing heterogeneity in reservoir rocks at the pore scale is crucial to understand the fl... more Characterizing heterogeneity in reservoir rocks at the pore scale is crucial to understand the flow patterns better, and estimate reservoir petrophysical properties such as porosity and permeability. This study introduces multifractals as descriptors for rock samples' heterogeneity at the pore scale. We analyzed twenty rock samples from sandstone and carbonate reservoirs using their 3D X-ray micro-computed tomography images. In addition, we simulated porosity and permeability properties and examined their correlation with multifractal parameters. The results show that the capacity dimension D 0 and the information dimension D 1 correlate with porosity and permeability simulated from images, respectively. Finally, we calculated several multifractal parameters such as the width of the spectrum, the asymmetry degree of the spectrum in the horizontal direction and the value of the vertical difference between the two branches of the spectrum. Results illustrate the ability of multifractal parameters to classify groups of rock samples according to their degree of heterogeneity.
2021 4th International Conference on Digital Medicine and Image Processing, 2021
In this paper, we review the problem of identifying a Linear Transformation applied on an image. ... more In this paper, we review the problem of identifying a Linear Transformation applied on an image. Three major parts are presented, all involved the use of Radon Transform: First, recovering a sequence of basic transformations on an image; namely, reflection, rotation, dilation, and translation. Second, recovering a transformation on reference Image and an inspected image, where is obtained from by a general Linear Transformation. In doing so, we review our Analysis using the Singular Value Decomposition of the Transformation's Matrix. Third, we present an alternative efficient method of obtaining a matrix of transformation by testing a well-defined class of potential matrices using only the two projections of the inspected image.
Proceedings of the 2019 2nd International Conference on Digital Medicine and Image Processing, 2019
We consider the two-dimensional parallel beam Tomography problem in which both the object being i... more We consider the two-dimensional parallel beam Tomography problem in which both the object being imaged and the projection directions are unknown. Specifically: Given unsorted set of Radon projections that correspond to angles φj=0°, 1°, ..., 179°. Our main goal is to determine (align) the projections with their angles. We introduce a type of Local Radon Transform from which we propose a distance formula between any two Radon projections. We solve the problem by combining the second order Geometric Moments of these projections together with this measure of distance. We validate our framework on synthetic images and real images.
Proceedings of the 2019 2nd International Conference on Digital Medicine and Image Processing, 2019
We present a novel original method for estimating and recovering a general geometric transformati... more We present a novel original method for estimating and recovering a general geometric transformation which is applied to an image. Our main tool is the Radon Transform; we develop analysis to address the behavior of this transform under a Linear Transformation in terms of the singular value decomposition of the Transformation's matrix. We derive a mathematical exact solution to this problem. We then implement our analysis and validate the work on synthetic images as well as real images. In so doing, we developed efficient numerical tools for carrying out such analysis.
The Open Chemical Engineering Journal, 2020
Background: This paper reviews the Particle Size Distribution (PSD) problem in detail. Mathematic... more Background: This paper reviews the Particle Size Distribution (PSD) problem in detail. Mathematically, the problem faced while recovering a function from a finite number of its geometric moments has been discussed with the help of the Spline Theory. Undoubtedly, the splines play a major role in the theory of interpolation and approximation in many fields of pure and applied sciences. B-Splines form a practical basis for the piecewise polynomials of the desired degree. A high degree of accuracy has been obtained in recovering a function within the first ten to fifteen geometric moments. The proposed approximation formula has been tested on several types of synthetic functions. This work highlights some advantages, such as the use of a practical basis for the approximating space, the exactness of computing the moments of these basis functions and the reduction of the size along with an appropriate transformation of the resulting linear system for stability. Objective: The aim is to re...
International Journal of Modelling and Simulation, 2019
ABSTRACT Developing a better characterization of fluid flow properties in carbonate reservoirs is... more ABSTRACT Developing a better characterization of fluid flow properties in carbonate reservoirs is a critical step for enhanced oil recovery applications in the oil industry. Indeed, carbonate reservoirs rocks are in general highly heterogeneous with variability revealed from submicron to centimeters. In several studies, Digital Rock Physics (DRP) was implemented as a technique which aims to help characterizing rock properties behavior at pore scale. This approach uses 3D X-ray micro tomography images to characterize pore network and also simulate rock properties from these images. Even though DRP is able to predict realistic rock properties in sandstone reservoirs it is still suffering from a lack of clear workflow in carbonate rocks. The main challenge is the upscaling of simulated properties from fine to coarse. In this paper, we propose a new upscaling method to characterize absolute permeability in carbonate core plugs samples using textures of Micro-Computed Tomography images. We propose to classify 3D micro-CT images of rock samples in terms of textures and predict the overall rock permeability. Finally, we discuss the advantages and limitations of this new approach. Overall the present work proposes an efficient and faster alternative DRP workflow for upscaling from pore-scale to core-scale.
Journal of Mathematical Sciences & Computer Applications, 2010
Proceedings of the 2019 2nd International Conference on Digital Medicine and Image Processing
Computed tomography (CT) scanners and CT exams increase continuously. The researchers aim to mini... more Computed tomography (CT) scanners and CT exams increase continuously. The researchers aim to minimize the ionizing radiation dose by introducing new CT protocols, providing diagnostic CT images with a lower radiation dose to patients. However, such studies encounter difficulties, when the radiation dose is lowered, the quality of images becomes less and sometimes not diagnostic. In this study, the researcher aims to provide a low dose brain CT protocol, in order to then determine if the images match the quality criteria of Brain CT; and determine the diagnostic appearance of the images. Then, the researcher will compare the results obtained from the Brain CT, as well as the brain post-processing algorithm to determine which one provides a better diagnostic image, and a better match for the quality criteria of Brain CT, by the Numerical criterion (1: weak, 2: moderate, 3:perfect) which is used by expert medical imaging technologists, On a sample of 35 patients; the first brain CT was conducted by 22 milli-gray (mGy) volume computed tomography dose index (CTDIvol); the resulting image was noisy, with a poor match for quality criteria, then CTDIvol was raised to 25 mGy, then to 30 mGy, and finally to 33.8 mGy. At this point, the image was acceptable to complete the study. Four radiologists have been engaged to determine if the image provides diagnostic appearance, then six expert medical imaging technologists were involved to determine the quality criteria. These steps were followed for the Brain CT before and after applying the post-processing algorithm. Then the results were compared with the reference study of brain CT. The results for low dose brain CT were diagnostic and matching the quality criteria for brain CT. After applying the brain post-processing algorithm the image's diagnostic appearance was disturbed, the suggested protocol by the study provided a 47% dose reduction, from the standard protocol which uses 63 mGy. The problem of signal reduction is solved by using iDose4, which improves the signal to noise ratio (SNR).
IEEE Transactions on Image Processing, 2000
In this paper, we present a method for identification of binary objects from a given set of radon... more In this paper, we present a method for identification of binary objects from a given set of radon projections. Given a suitably regular 2-D function f, we form a new function g from f by using the operations of reflection, scaling, translation, and rotation. We show how the radon projections of g are related to those of f and devise a procedure that can be used to determine the parameters from the radon projections of f and g. We illustrate this process using a family of block images that include common 7 x 5 pixel representations for the letters A, B,....., Z.
IEEE Access
Characterizing heterogeneity in reservoir rocks at the pore scale is crucial to understand the fl... more Characterizing heterogeneity in reservoir rocks at the pore scale is crucial to understand the flow patterns better, and estimate reservoir petrophysical properties such as porosity and permeability. This study introduces multifractals as descriptors for rock samples' heterogeneity at the pore scale. We analyzed twenty rock samples from sandstone and carbonate reservoirs using their 3D X-ray micro-computed tomography images. In addition, we simulated porosity and permeability properties and examined their correlation with multifractal parameters. The results show that the capacity dimension D 0 and the information dimension D 1 correlate with porosity and permeability simulated from images, respectively. Finally, we calculated several multifractal parameters such as the width of the spectrum, the asymmetry degree of the spectrum in the horizontal direction and the value of the vertical difference between the two branches of the spectrum. Results illustrate the ability of multifractal parameters to classify groups of rock samples according to their degree of heterogeneity.
Proceedings of the 2022 5th International Conference on Digital Medicine and Image Processing
IEEE Access
Let F represent a digitized version of an image f (x, y). Assume that the image fits inside a rec... more Let F represent a digitized version of an image f (x, y). Assume that the image fits inside a rectangular region and this region is subdivided into M × N squares. We call these squares the shifted box functions. Thus f (x, y) is approximated by M × N matrix F. This paper proofs that F can be recovered exactly and uniquely from the Radon transform of f using only one selected view angle with a well selected family of MN lines. The paper also proposes a precise method for computing the Radon transform of an image. The approach can be categorized as an algebraic reconstruction, but it is merely a theoretical contribution for the field of limited data tomography. INDEX TERMS Algebraic reconstruction, radon transform, tomography, limited data tomography.
83rd EAGE Annual Conference & Exhibition
IEEE Access
In this paper, we present methods for identifying an image from a given set of Radon projections.... more In this paper, we present methods for identifying an image from a given set of Radon projections. Given a suitably regular 2-D or 3-D function, we form a new function from using a linear transformation. We show how the Radon projections of and can be used to determine the transformation. The proposed algorithms introduce three major contributions, (1) Improvements on the 2-D setting using the moments of the Radon projections with only two orthogonal projections. (2) A natural extension of the 2-D setting to work with the 3-D setting. In particular, reducing the 3-D problem to a 2-D problem so that we can recover a translation, a scaling, or a rotation transformation of a 3-D object in the Radon domain. (3) An efficient method of recovering a rotation of a 3-D image around an arbitrary axis and an angle of rotation.
The Open Chemical Engineering Journal
Background: This paper is an improvement of a previous work on the problem recovering a function ... more Background: This paper is an improvement of a previous work on the problem recovering a function or probability density function from a finite number of its geometric moments, [1]. The previous worked solved the problem with the help of the B-Spline theory which is a great approach as long as the resulting linear system is not very large. In this work, two solution algorithms based on the approximate representation of the target probability distribution function via an orthogonal expansion are provided. One primary application of this theory is the reconstruction of the Particle Size Distribution (PSD), occurring in chemical engineering applications. Another application of this theory is the reconstruction of the Radon transform of an image at an unknown angle using the moments of the transform at known angles which leads to the reconstruction of the image form limited data. Objective: The aim is to recover a probability density function from a finite number of its geometric moments...
Determining the internal structure of an object without having to cut it, or viewing a section of... more Determining the internal structure of an object without having to cut it, or viewing a section of a body without interference from other regions, have long been goals of radiologists and engineers. These goals have been achieved through computed tomography (CT) and other technologies that are used in every hospital. This Module on CT should help readers appreciate this technology and the underlying mathematics.
Journal of Mathematical Sciences & Computer Applications, 2017
We consider the two-dimensional parallel beam Tomography problem in which both the object being i... more We consider the two-dimensional parallel beam Tomography problem in which both the object being imaged and the projection directions are unknown. The angles of projections need not to be uniformly distributed. Our solution combines two known approaches: the Geometric Moment and the Graph Laplacian. After sorting the projections using the Graph Laplacian method we create a one to one moment function of the angles. We then solve for each angle uniquely.
Journal of Mathematical Sciences & Computer Applications, 2017
We give an algorithm for reconstructing a density function f in the plane from limited number of ... more We give an algorithm for reconstructing a density function f in the plane from limited number of Radon projections on a range of angles −𝝋∗
Journal of Mathematical Sciences & Computer Applications, 2017
Given a regular binary function f on R2 with compact support D, we use translation to form a new ... more Given a regular binary function f on R2 with compact support D, we use translation to form a new binary function g from f so that the image representation of g (x, y) is made up of non-overlapping copies of D. Thus, g is made up of discrete entities that are surrounded by regions of space. We devise a procedure that can determine the translation parameters using a minimum number of Radon projections g of g . This model is a mathematical abstraction of an application of the Radon transform in Spectroscopy.Keywords: Radon transforms, transformation of an image, Back projection.
IEEE Access
Characterizing heterogeneity in reservoir rocks at the pore scale is crucial to understand the fl... more Characterizing heterogeneity in reservoir rocks at the pore scale is crucial to understand the flow patterns better, and estimate reservoir petrophysical properties such as porosity and permeability. This study introduces multifractals as descriptors for rock samples' heterogeneity at the pore scale. We analyzed twenty rock samples from sandstone and carbonate reservoirs using their 3D X-ray micro-computed tomography images. In addition, we simulated porosity and permeability properties and examined their correlation with multifractal parameters. The results show that the capacity dimension D 0 and the information dimension D 1 correlate with porosity and permeability simulated from images, respectively. Finally, we calculated several multifractal parameters such as the width of the spectrum, the asymmetry degree of the spectrum in the horizontal direction and the value of the vertical difference between the two branches of the spectrum. Results illustrate the ability of multifractal parameters to classify groups of rock samples according to their degree of heterogeneity.
2021 4th International Conference on Digital Medicine and Image Processing, 2021
In this paper, we review the problem of identifying a Linear Transformation applied on an image. ... more In this paper, we review the problem of identifying a Linear Transformation applied on an image. Three major parts are presented, all involved the use of Radon Transform: First, recovering a sequence of basic transformations on an image; namely, reflection, rotation, dilation, and translation. Second, recovering a transformation on reference Image and an inspected image, where is obtained from by a general Linear Transformation. In doing so, we review our Analysis using the Singular Value Decomposition of the Transformation's Matrix. Third, we present an alternative efficient method of obtaining a matrix of transformation by testing a well-defined class of potential matrices using only the two projections of the inspected image.
Proceedings of the 2019 2nd International Conference on Digital Medicine and Image Processing, 2019
We consider the two-dimensional parallel beam Tomography problem in which both the object being i... more We consider the two-dimensional parallel beam Tomography problem in which both the object being imaged and the projection directions are unknown. Specifically: Given unsorted set of Radon projections that correspond to angles φj=0°, 1°, ..., 179°. Our main goal is to determine (align) the projections with their angles. We introduce a type of Local Radon Transform from which we propose a distance formula between any two Radon projections. We solve the problem by combining the second order Geometric Moments of these projections together with this measure of distance. We validate our framework on synthetic images and real images.
Proceedings of the 2019 2nd International Conference on Digital Medicine and Image Processing, 2019
We present a novel original method for estimating and recovering a general geometric transformati... more We present a novel original method for estimating and recovering a general geometric transformation which is applied to an image. Our main tool is the Radon Transform; we develop analysis to address the behavior of this transform under a Linear Transformation in terms of the singular value decomposition of the Transformation's matrix. We derive a mathematical exact solution to this problem. We then implement our analysis and validate the work on synthetic images as well as real images. In so doing, we developed efficient numerical tools for carrying out such analysis.
The Open Chemical Engineering Journal, 2020
Background: This paper reviews the Particle Size Distribution (PSD) problem in detail. Mathematic... more Background: This paper reviews the Particle Size Distribution (PSD) problem in detail. Mathematically, the problem faced while recovering a function from a finite number of its geometric moments has been discussed with the help of the Spline Theory. Undoubtedly, the splines play a major role in the theory of interpolation and approximation in many fields of pure and applied sciences. B-Splines form a practical basis for the piecewise polynomials of the desired degree. A high degree of accuracy has been obtained in recovering a function within the first ten to fifteen geometric moments. The proposed approximation formula has been tested on several types of synthetic functions. This work highlights some advantages, such as the use of a practical basis for the approximating space, the exactness of computing the moments of these basis functions and the reduction of the size along with an appropriate transformation of the resulting linear system for stability. Objective: The aim is to re...
International Journal of Modelling and Simulation, 2019
ABSTRACT Developing a better characterization of fluid flow properties in carbonate reservoirs is... more ABSTRACT Developing a better characterization of fluid flow properties in carbonate reservoirs is a critical step for enhanced oil recovery applications in the oil industry. Indeed, carbonate reservoirs rocks are in general highly heterogeneous with variability revealed from submicron to centimeters. In several studies, Digital Rock Physics (DRP) was implemented as a technique which aims to help characterizing rock properties behavior at pore scale. This approach uses 3D X-ray micro tomography images to characterize pore network and also simulate rock properties from these images. Even though DRP is able to predict realistic rock properties in sandstone reservoirs it is still suffering from a lack of clear workflow in carbonate rocks. The main challenge is the upscaling of simulated properties from fine to coarse. In this paper, we propose a new upscaling method to characterize absolute permeability in carbonate core plugs samples using textures of Micro-Computed Tomography images. We propose to classify 3D micro-CT images of rock samples in terms of textures and predict the overall rock permeability. Finally, we discuss the advantages and limitations of this new approach. Overall the present work proposes an efficient and faster alternative DRP workflow for upscaling from pore-scale to core-scale.
Journal of Mathematical Sciences & Computer Applications, 2010
Proceedings of the 2019 2nd International Conference on Digital Medicine and Image Processing
Computed tomography (CT) scanners and CT exams increase continuously. The researchers aim to mini... more Computed tomography (CT) scanners and CT exams increase continuously. The researchers aim to minimize the ionizing radiation dose by introducing new CT protocols, providing diagnostic CT images with a lower radiation dose to patients. However, such studies encounter difficulties, when the radiation dose is lowered, the quality of images becomes less and sometimes not diagnostic. In this study, the researcher aims to provide a low dose brain CT protocol, in order to then determine if the images match the quality criteria of Brain CT; and determine the diagnostic appearance of the images. Then, the researcher will compare the results obtained from the Brain CT, as well as the brain post-processing algorithm to determine which one provides a better diagnostic image, and a better match for the quality criteria of Brain CT, by the Numerical criterion (1: weak, 2: moderate, 3:perfect) which is used by expert medical imaging technologists, On a sample of 35 patients; the first brain CT was conducted by 22 milli-gray (mGy) volume computed tomography dose index (CTDIvol); the resulting image was noisy, with a poor match for quality criteria, then CTDIvol was raised to 25 mGy, then to 30 mGy, and finally to 33.8 mGy. At this point, the image was acceptable to complete the study. Four radiologists have been engaged to determine if the image provides diagnostic appearance, then six expert medical imaging technologists were involved to determine the quality criteria. These steps were followed for the Brain CT before and after applying the post-processing algorithm. Then the results were compared with the reference study of brain CT. The results for low dose brain CT were diagnostic and matching the quality criteria for brain CT. After applying the brain post-processing algorithm the image's diagnostic appearance was disturbed, the suggested protocol by the study provided a 47% dose reduction, from the standard protocol which uses 63 mGy. The problem of signal reduction is solved by using iDose4, which improves the signal to noise ratio (SNR).
IEEE Transactions on Image Processing, 2000
In this paper, we present a method for identification of binary objects from a given set of radon... more In this paper, we present a method for identification of binary objects from a given set of radon projections. Given a suitably regular 2-D function f, we form a new function g from f by using the operations of reflection, scaling, translation, and rotation. We show how the radon projections of g are related to those of f and devise a procedure that can be used to determine the parameters from the radon projections of f and g. We illustrate this process using a family of block images that include common 7 x 5 pixel representations for the letters A, B,....., Z.