2011/01/03 by Gitta Kutyniok, Kutyniok, Gitta, Wang‐Q Lim +1 · 1 citation
Computer Science · Engineering · #65T60 #68U10 #Advanced Image Fusion Techniques #FOS: Mathematics #Image and Signal Denoising Methods #Medical Image Segmentation Techniques #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1101.0553
openalex publication_date 2011/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present an image separation method for separating images into point- and curvelike parts by employing a combined dictionary consisting of wavelets and compactly supported shearlets utilizing the fact that they sparsely represent point and curvilinear singularities, respectively. Our methodology is based on the very recently introduced mathematical theory of geometric separation, which shows that highly precise separation of the morphologically distinct features of points and curves can be achieved by ℓ1 minimization. Finally, we present some experimental results showing the effectiveness of our algorithm, in particular, the ability to accurately separate points from curves even if the curvature is relatively large due to the excellent localization property of compactly supported shearlets.