The Image Compression Performance Analysis of SPIHT Coding Based on Reversible Non-recursive Bi-orthogonal Discrete Wavelets Transform

[[abstract]]傳統遞迴式雙正交離散小波轉換（recursive bi-orthogonal discrete wavelets transform 簡稱RBDWT）已成功應用於影像資料的壓縮。由於RBDWT係基於遞迴式金字塔演算法（recursive pyramid algorithm）的運算方式，其存在error propagation現象，此現象是造成位元長度成長效益的主要因素，而且位元長度成長效益會降低RBDWT於高階分解時的硬體實現效益。但是影像資料壓縮又必須於高階分解才可獲得高壓縮效益。 可逆式非遞迴式雙正交離散小波轉換（簡稱 可逆式NRBDWT）是結合NRBDWT與可逆四捨五入線性轉換理論（Reversible Round-Off Linear Transformation 簡稱RROLT）的一新式小波轉換演算法。可逆式NRBDWT首先利用NRBDWT阻斷error propagation效應，再使用RROLT方法最小化小波係數的動態區間。此兩機制可有效抑制高階分解時的位元長度成長效應且適於VLSI實現。 本論文的目的在探討可逆式NRBDWT應用於影像壓縮之效能。經由NRBDWT分解後的影像，我們使用SPIHT編碼法來分析在有限位元下的壓縮效能，並與使用傳統RBDWT壓縮方法之比較；在有限位元實驗模擬中，成功將PSNR提高10dB，而在透過SPIHT編碼後，也能有效的提升壓縮效能。[[abstract]]The traditional recursive bi-orthogonal discrete wavelets transform (RBDWT) has been successfully applied to image data compression. As RBDWT is built upon the recursive pyramid algorithm, error propagation is the main factor that causes the Word-length growth effect. The Word -length growth effect will reduce the hardware performance when RBDWT is used for high level decomposition. However, high level decomposition is required for a high compression performance of image data compression. Reversible non-recursive bi-orthogonal discrete wavelets transform (Reversible NRBDWT) is a new wavelet transform algorithm integrated with NRBDWT and Reversible Round-Off Linear Transformation (RROLT). Reversible NRBDWT first uses NRBDWT to block the effect of error propagation and applies RROLT to minimize the dynamic interval of wavelet coefficients. The two mechanisms are effective in inhibiting the Word-length growth effect in high level decomposition and applicable to the implementation of VLSI. The purpose of this study was to investigate the performance of NRBDWT in image compression. Images decomposed by NRBDWT were processed with the SPIHT encoding algorithm to analyze the compression performance under limited bits, and the performance was further compared with that of the traditional RBDWT compression algorithm. In the experiment with limited bits, the PSNR was successfully enhanced to 10dB, and the application of the SPIHT encoding algorithm also effectively improved the compression performance