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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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Presentation on theme: "A COMPARATIVE STUDY OF DCT AND WAVELET-BASED IMAGE CODING & RECONSTRUCTION Mr. S Majumder & Dr. Md. A Hussain Department of Electronics & Communication."— Presentation transcript:

1 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 &

2 IMAGE COMPRESSION THE NEED FOR COMPRESSION 1.Spatial redundancy Correlation between neighboring pixels values 2. Spectral redundancy Correlation between different spectral bands INTRODUCTION TO IMAGE COMPRESSION 1.Lossless compression 2.Lossy compression OBJECTIVE 1.Minimum distortion 2.High compression ratio 3.Fast computation time

3 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) = for u = 0 and = 1 otherwise.

4 DCT based Encoder & Decoder

5 DISCRETE WAVELET TRANSFORM

6 FLOWCHART FOR 2D FORWARD DWT

7 2D DWT (4 Steps)

8 WAVELETS

9 ZIGZAG SCAN PROCEDURE Zigzag Scanning converts the 2D data into 1D data

10 QUANTIZATION Uniform Quantization Non-Uniform Quantization Quantization

11 UNIFORM QUANTIZATION

12 FLOWCHART FOR UNIFORM QUANTIZER & DEQUANTIZER

13 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

14 RUN-LENGTH ENCODING

15 FLOWCHART FOR RUN LENGTH ENCODER & DECODER

16 HUFFMAN ENCODING

17 FLOWCHART FOR HUFFMAN ENCODER & DECODER

18 FLOWCHART FOR 2D INVERSE DWT

19 DCT and DWT (Daubechies 6-tap) output size, after coding indifferent coding techniques versus Quantization level (for 14,321 bytes)

20 Reconstructed image size versus Quantization levels for different encoding techniques

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22 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.

23 REFERENCES [1] Ahmed, N., Natarajan, T., and Rao, K. R. Discrete Cosine Transform, IEEE Trans. Computers, vol. C-23, Jan. 1974, pp [2] Vetterli, M. and Kovacevic, J. Wavelets and Subband Coding, Englewood Cliffs, NJ, Prentice Hall, 1995, [3] Gersho, A. and Gray, R. M. Vector Quantization and Signal Compression, Kluwer 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. CSVT, vol. 6, no. 5, Oct. 1996, pp , [6] A.B.Watson, G.Yang, J.A.Solomon, and J Villasenor, Visibility of Wavelet Quantization Noise, IEEE Transactions on Image Processing, Vol. 6, No. 8, August [7] O.N.Gerekand, A.E.Cetin, Adaptive polyphase subband decomposition structures for image compression, IEEE Trans. Image Processing, vol. 9, pp. 1649–1659, Oct [8] S.D.Servetto, K.Ramchandran, V.A.Vaishampayan, and K Nahrstedt, Multiple Description Wavelet Based Image Coding, IEEE Trans on Image Processing, vol. 9, no. 5, may 2000 [9] Henrique S. Malvar, Fast Progressive Image Coding without Wavelets IEEE Data Compression Conference – Snowbird, Utah, March 2000

24 THANK YOU


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