Compressed Sensing Using Adaptive Wavelet Transform and Overcomplete Dictionary

In this paper, we present a new compressed sensing implementation process for one dimension signal reconstruction. Firstly, one level wavelet decomposition of the one dimensional signal was finished. For using the adaptive wavelet transform based on lifting wavelet transforms, we can achieve the detail signals being zero (or almost zero) at big probability, so the signal has the better linear approximation. Secondly, the signal can be reconstructed using compressed sensing method. Because the length of the low frequency coefficients is half of the original signal length, the measurement matrix can be reduced. The redundancy of overcomplete dictionary can make it effectively capture the characteristics of the signals. The overcomplete dictionary which combined the DCT base with the unit matrix can be used for the compressed sensing. Thirdly, using the inverse adaptive wavelet transform, the signal can be reconstructed with the low frequency coefficients. Finally experimental results demonstrate the application effectiveness for this scheme in compressed sensing fields.