/lecture_optimization

Primary LanguageJupyter Notebook

Author

Hello, I'm Yoseob Han who is postdoctoral researcher in Harvard medical school and Massachusetts general hospital.

I am running YouTube channel to address deep learning, signal processing, and optimization. You can easily learn above topics through practice, and all the source codes are uploaded HERE.

I am also preparing a simple parallel computing course using CUDA.

In addition, I have a plan to make a lecture according to an advanced medical imaging processing related to computed tomography (CT) and magnetic resonance imaging (MRI), and will upload the lecture in a new repository.

Since all the lectures were written by myself, there may be erroneous explanations. If you find wrong parts, please let me know.

If you like the lectures, please click on the star and follow GitHub, and subscribe to my YouTube.

Optimization by example

Here, I will explain the basic concept of the optimization and address how to solve the real world problems like vision- and medical-imaging tasks using the optimization methods.

Contents

1. Inverse problem

We learn a concept of the inverse problem and explain how to solve the inverse problems depending on a system condition.

2. Optimiziation problem

We learn a concept of the optimization problem to solve the inverse problem.

3. Gradient descent method

We learn a gradient descent method and implement the gradient descent method to solve the inversion problem of 1D toy-example.

3-1. Gradient descent method for 2D matrix multiplication

We implement the gradient descent method to solve the inversion problem of 2D matrix multiplication.

3-2. Gradient descent method for natural image processing

We implement the gradient descent method to deblur the blurred image by the known 2D Gaussain kernel.

3-3. Gradient descent method for medical image processing

We implement the gradient descent method to reconstruct computed tomography (CT) image using Radon transform.

4. Newton's method

We learn a newton's method and implement the newton's method which is one of the optimization methods.

4-1. Newton's method for natural image processing

We implement the newton's method to deblur the blurred image by the known 2D Gaussain kernel.

4-2. Newton's method for medical image processing

We implement the newton's method to reconstruct computed tomography (CT) image using Radon transform.

5. Conjugate gradient method

We learn a conjugate graident method and implement the conjugate graident method to solve linear equations.

5-1. Conjugate gradient method for natural image processing

We implement the conjugate gradient method to deblur the blurred image by the known 2D Gaussain kernel.

5-2. Conjugate gradient method for medical image processing

We implement the conjugate gradient method to reconstruct computed tomography (CT) image using Radon transform.

6. Performance evaluation

We summarize the optimization methods such as a gradient descent method, a newton's method, and a conjugate gradient method.

6-1. Performance evaluation for natural image processing

We summarize the deblurring performace from optimization methods.

6-2. Performance evaluation for medical image processing

We summarize the CT reconstruction performace from optimization methods.