Radially symmetric wavelets possessing multiresolution framework are found to be useful in different fields like Pattern recognition, Computed Tomography (CT) etc. The compactly supported wavelets are known to be useful for localized operations in applications such as reconstruction, enhancement etc. In this work we introduce a novel way of designing compactly supported radial wavelets in L 2 pR 2 q from a 1D Daubechies wavelets and obtain a reconstruction formula possessing multiresolution framework. Further, we demonstrate the usefulness of our radial wavelets in Tomography.

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Local reconstruction from localized projections attains importance in Computed Tomography (CT). Several researchers addressed the local recovery (or interior) problem in different frameworks. The recent sparsity based optimization techniques in Compressed Sensing (CS) are shown to be useful for CT reconstruction. The CS based methods provide hardware-friendly algorithms, while using lesser data compared to other methods. The interior reconstruction in CT, being ill-posed, in general admits several solutions. Consequently, a question arises pertaining to the presence of target (or interior-centric) pixels in the recovered solution. In this paper, we address this problem by posing the local CT problem in the prior support constrained CS framework. In particular, we provide certain analytical guarantees for the presence of intended pixels in the recovered solution, while demonstrating the efficacy of our method empirically.