Unified dual optimisation and algorithms for image reconstruction and spectral estimation

Taking the linear transformations of the image into a finite number of one dimensional (1-D) continuous functions as constraints, a new dual optimization method is introduced for formally deriving existing and new models for linear systems. The results are applied to Tomography and Spectral Analysis where several orthogonal expansions based on the models are studied. A new, fast Walsh transform Tomographic algorithm is introduced and also an iterative algorithm which gives better reconstruction than the popular convolution algorithm with comparable speed; its convergence under various conditions is specified. Using the AR filter a new iterative algorithm based on maximum likelihood is also presented for fast computation of the filter coefficients.