Image recovery from reduced sparse measurements by compressed sensing based on wavelet transform

In traditional sampling methods, images are sampled at the Nyquist rate for perfect reconstruction. But most of these acquired data samples are discarded during compression. Compressed Sensing (CS) overcomes this problem by combining the acquisition and compression process. Most of the images are sparse in some domain and thus can be recovered from reduced number of samples than the Nyquist rate. The quality of reconstruction depends upon the sparsity level of the image. Contourlet transform is used to obtain the sparse representation of the image while the wavelet transform reduces the complexity of the compressed sensing algorithm. Thus both the transforms are combined to achieve better recovery from reduced number of sparse measurements. The low frequency wavelet subband contains most of the information and thus more number of samples is taken from this band. The high frequency wavelet bands contain lesser amount of data and thus reduced number of samples is taken from these bands. The recovered image is smoothened by using the Hybrid Mean Median (HMM) Filter because of its nature of preserving the sharp edges in the image. Hence higher quality image is obtained from very less measurements.