IST - Partial Differential Equations and their Applications to Image Processing (2024)

Speakers and Syllabus

 Syllabus:(Each speaker is required to deliver minimum 6 lectures).

Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Ananta K. Majee,
IIT Delhi

 

6

 Classical PDEs: Classification of second order PDEs, Parabolic, Hyperbolic and Elliptic PDEs, Heat Equation, Wave equation, Telegraph Equation, Diffusion equations. Maximum principle, fundamental solution,
Fixed point theorem, existence and uniqueness of weak solution.

T. Muthukumar,
IIT Kanpur

 

6

 Variational Approach for PDEs: Quick review of distributions, mainly the concept of weak derivative, Fourier transform and convolution.
Sobolev spaces, mainly H^1 space and important inequalities, imbedding
and Trace theorems.Variational approach to elliptic PDEs, existence, uniqueness, regularity results and eigenvalue problem.

 

Rajendra K.Ray,
IIT Mandi

  6

 Finite Difference Methods for PDEs: Analysis (consistency, convergence, stability, and error estimate) of finite difference schemes for Heat equation (1D and 2D), Wave equation (1D and 2D), Laplace equation (1D and 2D), Convection-diffusion equation and Telegraph equation.
Introduction to digital image processing and PDE-based mathematical
models for image restoration. Introduction to MATLAB for image processing.

 

Subit K.Jain,
NIT Hamirpur

  6

 PDE-based Mathematical Models for Image Restoration:
Different type of noises, different types of images, different image quality measurement parameters, Basic diffusion models for image restoration, Basic variational models for image restoration. Telegraph diffusion models
and coupled PDEs based models for image restoration.

 References:
    1. L. C. Evans. Partial Differential Equations, AMS.
    2. J. C. Strikwerda. Finite difference schemes and PDEs, SIAM.
    3. G. Aubert and P. Kornprobst. Mathematical Problems in Image Processing: PDEs and the Calculus of Variations, Springer
(Lecture notes from the speakers, if available)

 

 

Time Table

 

Time-Table (with names of speakers and course associates/tutors):

 

 

Day

Date

Lecture 1

(9.30–11.00)

Tea
(11.05
to
11.25)

Lecture2

(11.30–1.00)

Lunch
(1.05
to
2.25)

Tutorial

(2.30–3.30)

Tea
(3.35
to
3.55)

Tutorial
(4.00-5.00)
 

 

 

(name of the speaker)

 

(name of the speaker)

 

(name of the speaker+tutors)

 

(name of the speaker+tutors)
 

Mon

03/06/2024

AM

 

AM

 

AM,KM,MK

 

AM,KM,MK
 

Tues

04/06/2024

AM

 

AM

 

AM,KM,MK

 

AM,KM,MK
 

Wed

05/06/2024

AM

 

AM

 

AM,KM,MK

 

AM,KM,MK
 

Thu

06/06/2024

TM

 

TM

 

TM,KM,MK

 

TM,KM,MK
 

Fri

07/06/2024

TM

 

TM

 

TM,KM,MK

 

TM,KM,MK
 

Sat

08/06/2024

TM

 

TM

 

TM,AP,MK

 

TM,AP,MK

SUNDAY:OFF
 

Mon

10/06/2024

RR

 

RR

 

RR,AP,MK

 

RR,AP,MK
 

Tues

11/06/2024

RR

 

RR

 

RR,AP,KM

 

RR,AP,KM
 

Wed

12/06/2024

SJ

 

RR

 

RR,KM,AP

 

RR,KM,AP
 

Thu

13/06/2024

SJ

 

RR

 

SJ,RR,AP

 

SJ,RR,AP
 

Fri

14/06/2024

SJ

 

SJ

 

SJ,RR,AP

 

SJ,RR,AP
 

Sat

15/06/2024

SJ

 

SJ

 

SJ,RR,AP

 

SJ,RR,AP

AM: Ananta K. Majee
TM: T. Muthukumar
RR: Rajendra K. Ray
SJ: Subit K. Jain
AP: Ashwani Punia
MK: Manish Kumar
KM: Kajal Mittal

Tutorial Assistants:

S. No.

Name

Affiliation

1

Ashwani Punia

IIT Mandi

2

Manish Kumar

IIT Mandi

3.

Kajal Mittal

IIT Mandi
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