Signal and Image Processing Algorithms Using Interval Convex Programming and Sparsity (2012)
Abstract / truncated to 115 words
In this thesis, signal and image processing algorithms based on sparsity and interval convex programming are developed for inverse problems. Inverse signal processing problems are solved by minimizing the ℓ1 norm or the Total Variation (TV) based cost functions in the literature. A modiﬁed entropy functional approximating the absolute value function is deﬁned. This functional is also used to approximate the ℓ1 norm, which is the most widely used cost function in sparse signal processing problems. The modiﬁed entropy functional is continuously diﬀerentiable, and convex. As a result, it is possible to develop iterative, globally convergent algorithms for compressive sensing, denoising and restoration problems using the modiﬁed entropy functional. Iterative interval convex programming algorithms are ... toggle 4 keywordssparsity – compressive sensing – filtered variation – total variation
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