Digital Image Reconstruction: Deblurring and Denoising

Digital image reconstruction is a robust means by which the underlying images hidden in blurry and noisy data can be revealed. The main challenge is sensitivity to measurement noise in the input data, which can be magnified strongly, resulting in large artifacts in the reconstructed image. The cure is to restrict the permitted images. This review summarizes image reconstruction methods in current use. Progressively more sophisticated image restrictions have been developed, including (a) filtering the input data, (b) regularization by global penalty functions, and (c) spatially adaptive methods that impose a variable degree of restriction across the image. The most reliable reconstruction is the most conservative one, which seeks the simplest underlying image consistent with the input data. Simplicity is context-dependent, but for most imaging applications, the simplest reconstructed image is the smoothest one. Imposing the maximum, spatially adaptive smoothing permitted by the data results in the best image reconstruction.