Design and Implementation of Lifting Based Daubechies Wavelet Transforms Using Algebraic Integers

Over the past few decades, the demand for digital information has increased drastically. This enormous demand poses serious difficulties on the storage and transmission bandwidth of the current technologies. One possible solution to overcome this approach is to compress the amount of information by discarding all the redundancies. In multimedia technology, various lossy compression techniques are used to compress the raw image data to facilitate storage and to fit the transmission bandwidth. In this thesis, we propose a new approach using algebraic integers to reduce the complexity of the Daubechies-4 (D4) and Daubechies-6 (D6) Lifting based Discrete Wavelet Transforms. The resulting architecture is completely integer based, which is free from the round-off error that is caused in floating point calculations. The filter coefficients of the two transforms of Daubechies family are individually converted to integers by multiplying it with value of 2 , where, x is a random value selected at a point where the quantity of losses is negligible. The wavelet coefficients are then quantized using the proposed iterative individual-subband coding algorithm. The proposed coding algorithm is adopted from the well-known Embedded Zerotree Wavelet (EZW) coding. The results obtained from simulation shows that the proposed coding algorithm proves to be much faster than its predecessor, and at the same time, produces good Peak Signal to Noise Ratio (PSNR) at very low bit rates. Finally, the two proposed transform architectures are implemented on Virtex-E Field Programmable Gate Array (FPGA) to test the hardware cost (in terms of multipliers, adders and registers) and throughput rate. From the synthesis results, we see that the proposed algorithm has low hardware cost and a high throughput rate.