Multilevel Wavelet Transform Based Sparsity Reduction for Compressive Sensing

Compressive sensing has become a popular technique in broad areas of science and engineering for data analysis, which leads to numerous applications in signal and image processing. It exploits the sparseness and compressibility of the data in order to reduce the size. Wavelet analysis is one of leading techniques for compressive sensing. In 2D discrete wavelet transform, the digital image is decomposed with a set of basis functions. At each level, wavelet transform is applied to compute the lowpass outcome (approximation) and highpass outcomes (three details), each with a quarter size of the source image. For the subsequent levels, the lower level outcomes turn out to be the inputs of the higher level to conduct further wavelet decompositions recursively, so that another set of approximation and detail components is generated. Discrete wavelet transform and discrete wavelet packet transform differ in higher levels other than the first level of decomposition. From the second level, discrete wavelet transform applies the transform to the lowpass outcomes exclusively, while wavelet packet transform applies the transform to lowpass and highpass outcomes simultaneously. As the more comprehensive approach, wavelet packet transform is selected for scene image compression on cases of both the lower and higher dynamic range images. Quantitative measures are then introduced to compare the outcomes of two cases.