Convex Optimization
Lossless image compression with projection-based and adaptive reversible integer wavelet transforms
IEEE Transactions on Image Processing
Adaptively quadratic (AQua) image interpolation
IEEE Transactions on Image Processing
Design of signal-adapted multidimensional lifting scheme for lossy coding
IEEE Transactions on Image Processing
Optimization of integer wavelet transforms based on difference correlation structures
IEEE Transactions on Image Processing
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A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.