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Sharpening filters are used to highlight fine image details, including object edges. However, sharpening filters are very specific to different types of images as they may create undesired edge effects, over-highlight fine details, or emphasize noise. Laplacian, Laplacian of Gaussian, high-boost, unsharp masking filters, and their extended algorithms are among most widely used sharpening spatial filters. This paper introduces a method that integrates anisotropic averaging with the Laplacian kernels for grayscale image sharpening. The proposed methodology is based on the concept of kriging computation in geostatistics for determining optimal interpolation weights in spatial domain. The convolution of kriging and Laplacian kernels is then carried out for image sharpening. Experimental results suggest certain advantages of the proposed linear convolution model for image sharpening over the Laplacian, Laplacian of Gaussian, high-boost, unsharp masking, and anisotropic diffusion methods in terms of the balance of sharpness and natural visualization. Another advantage of the proposed method is that it does not require any input statistical parameters.