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In these recent years, Compressive Sensing (CS) is becoming an attractive topic in the field of Information Theory. It is widely used in several area including networking, image processing and digital camera. In particular, image reconstruction based on small number of measured components is known as the most useful application. In this paper, SL0 algorithm is specially used for the reconstruction process. It significantly decrease the processing time by utilizing a matrix in which the number of row is much smaller than number of column. Therefore, SL0 is known as one of the fastest and most accurate algorithm in CS. However due to ill-posed condition, if the prior information of the original image is undetermined, the reconstruction procedure of SL0 is much affected by the noise. Unfortunately, the investigation for solving this SL0 ill-posed condition is very limited therefore SL0 is not widely applied in many application. Consequently, this paper proposes a novel regularization technique for SL0 algorithm in the frequency domain. In order to reduce and constraint the space of reconstructed image, the frequency domain Tikhonov regularization technique is employed. It is shown that the quality of the reconstructed image is much better compared to the traditional algorithm under the noisy environment. The experimental result is exclusively simulated for 3 images: Lena, Sussie and Cameraman under both Gaussian and Non-Gaussian noise models (such as AWGN, Poisson noise, Salt & Pepper noise and Speckle noise) at different noise powers.