Figure 1: Example of sparse representations in the wavelet domain: (a) piecewise smooth signal; (b) wavelet transform of piecewise smooth signal, only few coefficients are significant and they are compressible or near sparse; (c) the significant coefficients are well organized in tree structure across the scales; (d) binary tree for piecewise smooth signal, the significant wavelet coefficients arise from the discontinuities in the signal (the black circles denote the large wavelet coefficients). 
