ĐIỆN tử VIỄN THÔNG bài 4 lossy compression khotailieu

Multimedia Engineering Lecture 4: Lossy Compression Techniques Lecturer: Dr Đỗ Văn Tuấn Department of Electronics and Telecommunications Email: tuandv@epu.edu.vn Lecture contents Introduction Distortion measures Quantization Transform coding Introduction  Lossless compression algorithms not deliver compression ratios that are high enough Hence, most multimedia compression algorithms are lossy  In order to achieve higher rate of compression, we give up complete reconstruction and consider lossy compression technique  So we need a way to measure how good the compression technique is meaning that how close to the original data the reconstructed data is Lecture contents Introduction Distortion measures Quantization Transform coding Distortion Measures  Mean Square Error (MSE)  Signal to Noise Ratio  Peak Signal to Noise Ratio Rate-Distortion Theory  We trade-off rate (number of bits per symbol) versus distortion this is represented by a rate-distortion function R(D) Lecture contents Introduction Distortion measures Quantization Transform coding Quantization  Quantization is a heart of any scheme  The source we are compressing contains a large number of distinct output values (infinite for analog)  We compress the source output by reducing the distinct values to a smaller set via quantization  Each quantizer can be uniquely described by its partition of the input range (encoder side) and set of output values (decoder side)  Two types of quantization: Uniform quantization and non-uniform quantization Uniform Quantization Uniform Scalar Quantizers: (a) Midrise, (b) Midtread Non-uniform Quantization  Typical one is companded quantization  Companded quantization is nonlinear  As shown above, a compander consists of a compressor function G, a uniform quantizer, and an expander function G−1  The two commonly used companders are the μ-law and A-law companders 10 Lecture contents Introduction Distortion measures Quantization Transform coding 11 Transform coding  Reason for transform coding  Coding vectors is more efficient than coding scalars so we need to group blocks of consecutive samples from the source into vectors  If Y is the results of a linear transformation T of an input X such that the elements of Y are much less correlated than X, then Y can be coded more efficiently than X  With vectors of high dimensions, if most of the information in the vectors is carried in the first few components we can roughly quantize the remaining elements  The more decorrelated the elements are, the more we can compress the less important elements without affecting the important ones 12 Discrete Cosine Transform  The DCT is a wildly used transform technique  Spatial frequency: indicates how many times pixel values change across an image block  The DCT formalizes this notion in terms of how much the image contents change in correspondence to the number of cycles of a cosine wave per block  The DCT decomposes the original signal into its DC and AC components  The inverse DCT (Called IDCT) reconstructs the original signal 13 Discrete Cosine Transform  Given an input function f(i,j) over two integer variables i and j (a piece of an image), the 2D DCT transforms it into a new function F(u, v), with integer u and v running over the same range as i and j The general definition of the transform is:  Where i , u = 0, 1, ,M − 1; j , v = 0, 1, ,N − and the constants C(u), C(v) are determined by 14 Discrete Cosine Transform  2D discrete cosine transform (2D DCT) – In JPEG  Where i , j, u , v = 1,2, ,7  2D inverse discrete cosine transform (2D IDCT) 15 Discrete Cosine Transform  1D discrete cosine transform (1D DCT)  Where i , u = 1,2, ,7  1D inverse discrete cosine transform (1D IDCT) 16 Basic functions of DCT 17 Basic functions of DCT 18 Example of 1D DCT 19 Example of 1D DCT 20  More things to read  Karhunen-Loeve Transform  Wavelet-based coding  JPEG 21 End of the lecture 22 ...  Lossless compression algorithms not deliver compression ratios that are high enough Hence, most multimedia compression algorithms are lossy  In order to achieve higher rate of compression, ... compression, we give up complete reconstruction and consider lossy compression technique  So we need a way to measure how good the compression technique is meaning that how close to the original... Ratio  Peak Signal to Noise Ratio Rate-Distortion Theory  We trade-off rate (number of bits per symbol) versus distortion this is represented by a rate-distortion function R(D) Lecture contents