# 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) (Deemed University), Arunachal Pradesh swanirbhar@gmail.com & bubuli_99@yahoo.com

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

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)

Reconstructed image size versus Quantization levels for different encoding techniques

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.

REFERENCES [1] Ahmed, N., Natarajan, T., and Rao, K. R. Discrete Cosine Transform, IEEE Trans. Computers, vol. C-23, Jan. 1974, pp. 90-93. [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. 519-521, [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 2002. [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. 2000. [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

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