In this chapter, we consider an estimation problem in a tensor regression model with high and ultra-high-dimensional data. In particular, we consider the case where the tensor regression coefficients may satisfy a restriction. In addition to the imposed restriction, the particularity of such a problem is the high-dimensionality settings. In order to overcome this problem, we utilize a block relaxation algorithm. Thus, we obtain the unrestricted estimator (UE) and restricted estimator (RE). We also derive the joint asymptotic normality of the UE and RE. We then propose shrinkage estimators (SEs) that combine the UE and RE. Further, by using the asymptotic distributional risk (ADR) criterion, we show that the SEs are more efficient than the UE. Moreover, we present some simulations which support the established theoretical results. Finally, in order to illustrate the application of the proposed method, we analyze a real neuroimaging data set.