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The 2D phase correlation and the 2D cepstrum technique are known as two solutions to the translation-based image registration problem. However, both methods have a large computational load. Satisfactory results were obtained in a smaller translation range by applying phase correlations to the 1D projections of images to reduce the computational load (Alliney, S. and Morandi, C., 1986). The paper presents a new algorithm based on applying the cepstrum technique to image projections in a similar way. An enhanced cepstrum technique is developed by subtracting the cepstrum of the projection differences from the cepstrum of the projection additions. A superior performance compared to that of the 1D phase correlation can be obtained by whitening the power spectrum by the square-root instead of the logarithm and using a high-pass filter afterwards. The algorithm yields larger translation ranges in registering noisy images and remarkably outperforms the phase correlation method in the case of different degrees of blurring between images.