The Application Of Vector Quantization To The Remote Sensing Images Based Wavelet Theory

Compared Fourier transforms, wavelet transform displays advantage to the unstationary singles,and WT can process singles in time and frequency fields together. It has been employed in manyfields and applications, such as signal processing, image analysis, pattern recognition, biomedical imaging, andso on. We take advantage of the superiorty of the WT and VQ, do some work as follows:In this paper, we study wavelet theory and propose a perfect reconstructed bi-orthogonalitywavelet basis method. We know traditional wavelet basis constructed is difficult. Firstly, weknow a two-scale function and a set of nesting close subspaces {V_j,j∈Z}; secondly, wedecompose every close subspace V_j+1=V_j⊕W_j; thirstly, we construct wavelet function in W_j.The new method only knows a 2×2 unitary matrix that we can get a series of new waveletbases. Forthmore, we give a solution about 2×2 unitary matrix.Vector quantization has simple structure and the algorithm is mature. So VQ appliesextensively to data compress. But conventional VQ algorithm has some defect. Firstly, its speedis slowly. Secondly, its codebook isn't global optimal. So, many scholars do a lot of work toimprove VQ algorithm. Through these improved algorithms have some advantage, they don'tadapt to different questions. Thus VQ is an open question. In this paper, we propose a fastalterable rate VQ algorithm for compressing remote sensing images. The test shows that thisalgorithm performance is very good. Especially, in very low rate, the performance is better. Andit can compress remote sensing images in alterable rate in time. Compared LBG algorithm, ourspeed improves 96%.We know that high resolution (or high-rate or asymptotic) quantization theory is an openquestion. In this paper, we outline this problem in three aspects: (1) empirically designedquantizers of a fixed vector dimension to the best quantizer of the same dimension for the truesource, as the training set size grows; (2) optimal vector quantizer for the true source to thedistortion-rate function, as the vector dimension grows; (3) empirically desighed quantizers tothe distortion-rate function, as the number of input samples grows. We state the important resultsof high resolution theory. It can give some guidance in our works.