A COMPARATIVE STUDY OF DCT AND WAVELET-BASED IMAGE CODING & RECONSTRUCTION Mr. S Majumder & Dr. Md. A Hussain Department of Electronics & Communication Engineering NERIST (North Eastern Regional Institute of Science & Technology) (Deemed University), Arunachal Pradesh [email protected]& [email protected]
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A COMPARATIVE STUDY OF DCT AND WAVELET-BASED IMAGE CODING & RECONSTRUCTION Mr. S Majumder & Dr. Md. A Hussain Department of Electronics & Communication.
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A COMPARATIVE STUDY OF DCT AND WAVELET-BASED
IMAGE CODING & RECONSTRUCTION
Mr. S Majumder & Dr. Md. A Hussain
Department of Electronics & Communication Engineering NERIST (North Eastern Regional Institute of Science & Technology)
1. Spatial redundancy Correlation between neighboring pixels values
2. Spectral redundancy’ Correlation between different spectral bands
INTRODUCTION TO IMAGE COMPRESSION 1. Lossless compression2. Lossy compression
OBJECTIVE 1. Minimum distortion
2. High compression ratio3. Fast computation time
DCT-Based Image Coding Standard
The DCT can be regarded as a discrete-time version of the Fourier-Cosine series. It is a close relative of DFT, a technique for converting a signal into elementary frequency components. Thus DCT can be computed with a Fast Fourier Transform (FFT) like algorithm in O(n log n) operations. Unlike DFT, DCT is real-valued and provides a better approximation of a signal with fewer coefficients. The DCT of a discrete signal x(n), n=0, 1, .. , N-1 is defined as:
where, C(u) = 0.707 for u = 0 and
= 1 otherwise.
DCT based Encoder & Decoder
DISCRETE WAVELET TRANSFORM
FLOWCHART FOR 2D FORWARD DWT
2D DWT (4 Steps)
WAVELETS
ZIGZAG SCAN PROCEDURE
Zigzag Scanning converts the 2D data into 1D data
QUANTIZATION
Uniform Quantization
Non-Uniform Quantization Quantization
UNIFORM QUANTIZATION
FLOWCHART FOR UNIFORM QUANTIZER & DEQUANTIZER
ENTROPY ENCODING
The quantized data contains redundant information. It is a waste of storage space if we were to save the redundancies of the quantized data.
Run-Length Encoding
Huffman Encoding
ENTROPY ENCODING
RUN-LENGTH ENCODING
FLOWCHART FOR RUN LENGTH ENCODER & DECODER
HUFFMAN ENCODING
FLOWCHART FOR HUFFMAN ENCODER & DECODER
FLOWCHART FOR 2D INVERSE DWT
DCT and DWT (Daubechies 6-tap) output size, after coding indifferent coding techniques versus Quantization level (for 14,321 bytes)
Image Size after Coding in various schemes
0
2000
4000
6000
8000
10000
12000
2 4 6 8 10 12 14 16 18 20 22 24 26 28
Quantization Levels
No
. o
f B
ytes
DWT+RLE
DWT+Huff
DWT+Huff+RLE
DCT+RLE
DCT+Huff
DCT+Huff+RLE
Reconstructed image size versus Quantization levels for different encoding techniques
Reconstructed image size Comparison
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
2 4 6 8 10 12 14 16 18 20 22 24 26 28
Quantization Levels
No
. of
by
tes
Original size
DWT
DCT
CONCLUSION• For still images, the wavelet transform based
compression outperforms the DCT based compression typically in terms of the compressed output for different quantization levels, as well as the reconstructed image quality.
• For the same reconstructed image size of 14 Kb and equivalent image clarity, DWT based coded image requires less than half transmission bandwidth and storage requirement as compared to DCT based coded image.
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Academic Publishers, 1991[4] Nelson, M. The Data Compression Book,2nd ed., M&T books, Nov. 1995, [5] Tsai, M. J., Villasenor, J. D., and Chen, F. Stack-Run Image Coding, IEEE Trans.
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Noise, IEEE Transactions on Image Processing, Vol. 6, No. 8, August 2002.[7] O.N.Gerekand, A.E.Cetin, “Adaptive polyphase subband decomposition structures for
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