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A frequency‐based image deblurring method is proposed. Unlike the traditional ways of replicating target images, a periodic point spread function (PSF) is constructed. By investigating the periodic PSF under the Fourier domain, it has been found that noises at different frequencies produce significantly varying impacts on the reconstruction quality. Therefore, the Fourier slice theorem is utilised to select partial Fourier samples and to avoid the noises that can severely damage performance. A sparse‐inducing method is then developed to recover a clear image from the selected Fourier samples. [ABSTRACT FROM AUTHOR]