In this paper, we formulate non-parametric spectral estimators as solutions of some linear inverse problems, and propose new methods for spectral estimation using regularization. The general form of quadratic regularization is discussed. Moreover, two new spectral estimators are proposed using oracle SVD operator based on Capon and APES respectively. Simulations using either one-dimensional or two-dimensional data have shown that our methods usually give more accurate spectral estimates but a little lower resolution than the methods they based on. The proposed 2-D spectral estimation methods are very suitable for SAR imaging especially in cases that the number of data sfamples is low.