Abstract: A method for iterative reconstruction of an object containing noise using the pixon method determines the pixon map from a variable that is used to update the object in the iteration. The updating variable is based on an optimized merit function, and smoothes the updating variable during each iteration. The updating variable depends on the reconstruction method, but is typically a gradient of a merit function or a multiplicative update factor. The updated object can optionally also be further smoothed at the end of the iteration, using the pixon map determined during the iteration.

Abstract: A curvature-preserving filter having a null covariance matrix is applied to an input image to produce a denoised output image for output to a graphic display device or to a machine analysis tool. In one embodiment, the input image is a small kernel consisting of a limited number of pixels and the filter is applied to the input image by direct summation. In another embodiment, a digital image is input into an image processor that executes a Fourier transform to produce a Fourier-transformed signal. The curvature-preserving filter is applied to the Fourier-transformed signal in Fourier space to produce a denoised signal, then the denoised signal is transformed by an inverse Fourier transform to generate a denoised output image In an alternate embodiment, the filter further produces a deblurred signal by including an inverse point-response function.

Abstract: A method for iterative reconstruction of an object containing noise using the pixon method determines the pixon map from a variable that is used to update the object in the iteration. The updating variable is based on an optimized merit function, and smoothes the updating variable during each iteration. The updating variable depends on the reconstruction method, but is typically a gradient of a merit function or a multiplicative update factor. The updated object can optionally also be further smoothed at the end of the iteration, using the pixon map determined during the iteration.