Signal restoration from randomly sampling is needed in many different application environments, like time efficiency and low-power device or hardware failure. In this paper, we use the Analogical Basis Decomposition (ABD) theory to restore the signal by randomized sampling data in frequency domain. Based on the ABD theory, once standard basis are defined in the signal domain, the corresponding analogical basis can be obtained by randomized sampling each base in the frequency domain. Randomly sampled signal can be represented as sum of weighted analogical basis. We developed a fast matching pursuit technique to estimate the weights of analogical basis and then restore the signal. Actually, ABD theory can be used for signal restoration in other transformation domain (like wavelet transformation). Finally, we apply the ABD theory to reconstruct 2-D MR image based on partial sampling data in k-space.