Enhanced total variation minimization for stable image reconstruction. (English) Zbl 1518.94004
In this paper, a combination of a backward diffusion process and a total variation regularization method (“enhanced TV model”) is proposed in order to obtain an image reconstruction method that reduces the loss of contrasts. Some details of the mathematics necessary to understand the statements and proofs of results underlying the proposed method are presented. To fully understand the mathematics of this paper it is necessary to be familiar with concepts and results stated in earlier papers by other authors, as cited in this paper. Detailed and rigorous proofs of the theoretical properties of the new method are provided. The authors show the advantages of the new method through preliminary experiments on some synthetic, real, and medical images. This proposed method’s effectiveness is compared with that obtained by two previous methods also based on total variation models, using eight images, four synthetic, two real, and two medical images. As the authors themselves put it “it is worth noting that the enhanced TV model may not perform as effectively for natural images as it does for the images (in the other examples)”, possibly because the edges of objects in real images are not piecewise constant, in general, or other complications. All data for the examples presented are available. Four appendices conclude the paper, which helps to understand the theory underlying the new proposal and its subsequent computer implementation. Reference lists are extensive, detailed, and up-to-date (only 9 of the 73 papers cited are prior to 2000).
Reviewer: Oscar Bustos (Córdoba)
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 68U10 | Computing methodologies for image processing |
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
| 60H50 | Regularization by noise |
| 60J60 | Diffusion processes |
Keywords:
total variation; image reconstruction; backward diffusion; anisotropic; loss of contrast; stability; difference-of-convex regularizationReferences:
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