9/26 디지털 영상통신 Mathematical Preliminaries Math Background Predictive Coding Huffman Coding Matrix Computation

Mathematical Preliminaries Self-Information (Shannon) Entropy (in bits, x=2) Markov Models

Self-Information(Shannon)(1) Definition x=2 : bits[unit]

For two independent events A and B, the self- information associated with the occurrence of both events, A and B. Experiment set is composed of independent events A i. Self-Information (2)

Entropy (in bits, x=2)

Markov Model (1) Definition (Ex) 1-st Markov Model

Markov Model (2) (Ex) White and Black pixel (binary image)

Math Background Joint, Conditional, and Total Probabilities ; Independence Expectation Distribution Functions Stochastic Process Random Variables Characteristics  independent, orthogonal, uncorrelated, autocorrelation Strict Sense Stationary Wide Sense Stationary

Joint, conditional, and total probabilities ; Independence

Expectation Distribution Function(1) Uniform Distribution ab

Distribution Function(2) Gaussian Distribution Laplacian Distribution

Distribution Function (3)

Stochastic Process : Function of time

Random Variables Characteristics(1) Independent Orthogonal Uncorrelated Autocorrelation Function

Random Variables Characteristics(2) Strict Sense Stationary Wide Sense Stationary

Predictive Coding (1)

Predictive Coding (2)

Predictive Coding (3) Examples

Predictive Coding (4)

Predictive Coding (5)

Predictive Coding (6)

Predictive Coding (7)

Predictive Coding (8)

Predictive Coding (9)

Predictive Coding (10)

Predictive Coding (11)

Predictive Coding (12)

Predictive Coding (13)

Predictive Coding (14)

Predictive Coding (15)

Predictive Coding (16)

Huffman Coding (1) (Ex) P(a 1 )=1/2, P(a 2 )=1/4, P(a 3 )=P(a 4 )=1/8

Huffman Coding (2) Nodes internal node external node

Huffman Coding (3) The Huffman Coding Algorithm  In an optimum code, symbols that occur more frequently (have a higher probability of occurrence) will have shorter codewords than symbols that occur less frequently.  In an optimum code, the two symbols that occur least frequently will have the same length.

Matrix Computation (1) ① ② Determinants 의 응용 Object : Find the solution of Ax=b

Matrix Computation (2) ③

Matrix Computation (3) ④ Cramer ’ s Rule : jth component of x=A -1 b 응용 : stability, Markov Process (Steady State)