Deep Learning for Medical Imaging: COVID-19 Detection-MATLAB-MATHWORKS- Dr. Barath Narayanan

Barath Narayanan

Posted by Johanna Pingel, March 18, 2020

I'm pleased to publish another post from Barath Narayanan, University of Dayton Research Institute (UDRI), LinkedIn Profile. Co-author: Dr. Russell C. Hardie, University of Dayton (UD) Dr. Barath Narayanan graduated with MS and Ph.D. degree in Electrical Engineering from the University of Dayton (UD) in 2013 and 2017 respectively. He currently holds a joint appointment as a Research Scientist at UDRI's Software Systems Group and as an Adjunct Faculty for the ECE department at UD. His research interests include deep learning, machine learning, computer vision, and pattern recognition. In this blog, we are applying a Deep Learning (DL) based technique for detecting COVID-19 on Chest Radiographs using MATLAB.

 Background

 Coronavirus disease (COVID-19) is a new strain of disease in humans discovered in 2019 that has never been identified in the past. Coronavirus is a large family of viruses that causes illness in patients ranging from common cold to advanced respiratory syndromes such as Middle East Respiratory Syndrome (MERS-COV) and Severe Acute Respiratory Syndrome (SARS-COV). Many people are currently affected and are being treated across the world causing a global pandemic. In the United States alone, 160 million to 214 million people could be infected over the course of the COVID-19 epidemic (https://www.nytimes.com/2020/03/13/us/coronavirus-deaths-estimate.html). Several countries have declared a national emergency and have quarantined millions of people. Here is a detailed article on how coronavirus affects people: https://www.nytimes.com/article/coronavirus-body-symptoms.html

Detection and diagnosis tools offer a valuable second opinion to the doctors and assist them in the screening process. This type of mechanism would also assist in providing results to the doctors quickly. In this blog, we are applying a Deep Learning (DL) based technique for detecting COVID-19 on Chest Radiographs using MATLAB.

The COVID-19 dataset utilized in this blog was curated by Dr. Joseph Cohen, a postdoctoral fellow at the University of Montreal. Thanks to the article by Dr. Adrian Rosebrock for making this chest radiograph dataset reachable to researchers across the globe and for presenting the initial work using DL. Note that we solely utilize the x-ray images. You should be able to download the images from the article directly. After downloading the ZIP files from the website and extracting them to a folder called "Covid 19", we have one sub-folder per class in "dataset". Label "Covid" indicates the presence of COVID-19 in the patient and "normal" otherwise. Since, we have equal distribution (25 images) of both classes, there is no class imbalance issue here.

K-fold Validation

As you already know that there is a limited set of images available in this dataset, we split the dataset into 10-folds for analysis i.e. 10 different algorithms would be trained using different set of images from the dataset. This type of validation study would provide us a better estimate of our performance in comparison to typical hold-out validation method.

 We adopt ResNet-50 architecture in this blog as it has proven to be highly effective for various medical imaging applications [1,2].

 LINK

Vilenkin N.Ya., Bohan K.A., Maron I.A., Matveev I.V., Smolyansky M.L., Tsvetkov A.T. Task book on the course of mathematical analysis. Part I. M .: Education, 1971

LINK ORIGINAL EN LA WEB:
 http://ikfia.ysn.ru/wp-content/uploads/2018/01/Vilenkin_ch1_1971ru.pdf

LINK ALTERNATIVO
 http://www.mediafire.com/file/d3e8refve1geort/Vilenkin-TOMO1-1971.pdf/file

Naum Yakovlevich Vilenkin (October 30, 1920, Moscow - October 19, 1991)

 - Soviet mathematician, popularizer of mathematics. He is the author of well-known school textbooks in mathematics for grades 5 and 6, which have served for more than forty years. The first textbooks were published in September 1970 (co-authored with K. I. Neshkov, S. I. Shvartsburd, A. D. Semushin, A. S. Chesnokov, T. F. Nechaeva). Studied at the 7th prof. Prof. Kovalensky ”in Krivoarbatsky Lane. Then he graduated from Moscow State University (1942); Doctor of physico-mathematical sciences (1950), professor (1951). Since 1943, he worked in various universities, since 1961 - at the Moscow Correspondence Pedagogical Institute. The first works, including the dissertation, were devoted to the theory of topological groups. Developing the character theory of Pontryagin, he established a connection between the character systems of zero-dimensional compact Abelian groups, also known as Vilenkin systems, with the class of orthonormal systems of piecewise constant functions. Since the 1950s, the systems introduced by Vilenkin have been actively studied in connection with their widespread use in the field of digital signal processing. Since the mid-1950s, he worked on the study of the theory of representations of Lie groups, where he obtained a number of results related to infinite-dimensional representations constructed by I. M. Gelfand and M. A. Naimark. He is the author of the monograph Special Functions and Theory of Representation of Groups (1965, 1991), which was then (together with A. U. Klimyk) transformed into Representations of Lie groups and special functions (1991–1993, 1995). He is the author of popular science books Tales of Sets, Combinatorics, and a number of school mathematics textbooks.

A PROBLEM BOOK IN ALGEBRA -V.A. KRECHMAR

LINK: http://www.mediafire.com/file/w5wfjeizcl2omkd/ALGEBRAPROBLEM-KRECHMAR.pdf/file

Pesquisadores do Instituto Nacional de Pesquisas Espaciais (Inpe ) e Instituto Tecnológico de Aeronáutica (Ita) desenvolvem Modelo Matemático para avaliar pandemia CORONA VIRUS

LIMITES EJERCICIOS

LINK:https://www.mediafire.com/file/ix4cx3ml8wivhgj/LIMITES-CAPITULO6-Kuznetsova.pdf/file

PROBLEM BOOK IN HIGH SCHOOL MATHEMATICS PRILEPKO

LINK:http://www.mediafire.com/file/ah9mrvajgz7k5l1/Prilepko_-_Problem_Book_In_High_School_Mathematics.pdf/file

Analisis matematico en preguntas y problemas - Butuzov

LINK:http://www.mediafire.com/file/h8hqim6i4nts0g2/analisis_matematico_en_preguntas_y_problemas.pdf/file

The Mathematics of Predicting the Course of the Coronavirus-Las matemáticas para predecir el curso del coronavirus

Epidemiologists are using complex models to help policymakers get ahead of the Covid-19 pandemic. But the leap from equations to decisions is a long one.

THE BASIC MATH of a computational model is the kind of thing that seems obvious after someone explains it. Epidemiologists break up a population into “compartments,” a sorting-hat approach to what kind of imaginary people they’re studying. A basic version is an SIR model, with three teams: susceptible to infection, infected, and recovered or removed (which is to say, either alive and immune, or dead). Some models also drop in an E—SEIR—for people who are “exposed” but not yet infected.

Then the modelers make decisions about the rules of the game, based on what they think about how the disease spreads. Those are variables like how many people one infected person infects before being taken off the board by recovery or death, how long it takes one infected person to infect another (also known as the interval generation time), which demographic groups recover or die, and at what rate. Assign a best-guess number to those and more, turn a few virtual cranks, and let it run. “At the beginning, everybody is susceptible and you have a small number of infected people.

They infect the susceptible people, and you see an exponential rise in the infected,” says Helen Jenkins, an infectious disease epidemiologist at the Boston University School of Public Health. So far, so terrible. The assumption for how big any of those fractions of the population are, and how fast they move from one compartment to another, start to matter immediately. “If we discover that only 5 percent of a population have recovered and are immune, that means we’ve still got 95 percent of the population susceptible. And as we move forward, we have much bigger risk of flare-ups,” Jenkins says. “If we discover that 50 percent of the population has been infected—that lots of them were asymptomatic and we didn’t know about them—then we’re in a better position.” So the next question is: How well do people transmit the disease? That’s called the “reproductive number,” or R0, and it depends on how easily the germ jumps from person to person—whether they’re showing symptoms or not. It also matters how many people one of the infected comes into contact with, and how long they are actually contagious. (That’s why social distancing helps; it cuts the contact rate.) You might also want the “serial interval,” the amount of time it takes for an infected person to infect someone else, or the average time before a susceptible person becomes an infected one, or an infected person becomes a recovered one (or dies). That’s “reporting delay.”

 And R0 really only matters at the beginning of an outbreak, when the pathogen is new and most of the population is House Susceptible. As the population fractions change, epidemiologists switch to another number: the Effective Reproductive Number, or Rt, which is still the possible number of people infected, but can flex and change over time. Most Popular IDEAS It's Time to Face Facts, America: Masks Work CULTURE Tiger King Is Cruel and Appalling—Why Are We All Watching It? GEAR How to Make Your Own Hand Sanitizer SCIENCE The Mathematics of Predicting the Course of the Coronavirus You can see how fiddling with the numbers could generate some very complicated math very quickly. (A good modeler will also conduct sensitivity analyses, making some numbers a lot bigger and a lot smaller to see how the final result changes.) Those problems can tend to catastrophize, to present a worst-case scenario. Now, that’s actually good, because apocalyptic prophecies can galvanize people into action. Unfortunately, if that action works, it makes the model look as if it was wrong from the start. The only way these mathematical oracles can be truly valuable is to goose people into doing the work to ensure the predictions don’t come true—at which point it’s awfully difficult to take any credit.

SOURCE:https://www.wired.com/story/the-mathematics-of-predicting-the-course-of-the-coronavirus/