Spectrum occupancy reconstruction is an important issue often encountered in collaborative
spectrum sensing in distributed cognitive radio networks (CRNs). This issue arises when the spectrum
sensing data that are collaborated by secondary users have gaps of missing entries. Many data imputation
techniques, such as matrix completion techniques, have shown great promise in dealing with missing
spectrum sensing observations by reconstructing the spectrum occupancy data matrix. However, matrix
completion approaches achieve lower reconstruction resolution due to the use of standard singular value
decomposition (SVD), which is designed for more general matrices. In this paper, we consider the problem
of spectrum occupancy reconstruction where the spectrum sensing results across the CRN are represented as
a plenary grid on a Markov random eld. We formulate the problem as a magnetic excitation state recovery
problem, and the stochastic gradient descent (SGD) method is applied to solve the matrix factorization.
SGD is able to learn and impute the missing values with a low reconstruction error compared with SVD.
The graphical and numerical results show that the SGD algorithm competes favorably SVD in the matrix
factorization by taking advantage of correlations in multiple dimensions.