Fractal Image Coding as Projections Onto Convex Sets

2008

J. Phys.: Conf. Ser.

In this paper we introduce and analyze a set of regularization expressions based on self-similarity properties of images in order to address the classical inverse problem of image denoising and the ill-posed inverse problem of single-frame image zooming. The regularization expressions introduced are constructed using either the fractal image transform or the newly developed "Nonlocal-means (NL-means) image denoising filter" of Buades et al. (2005). We exploit these regularization terms in a global MAP-based formulation and produce analytical and computational solutions. Analytical comparisions are made with results based on classical methods (e.g., fractal-based denoising and zooming, and NL-means image denoising).

Section: The Role Of Self-similarity In Various Imaging Inverse Problmentioning

confidence: 99%

Regularization schemes involving self-similarity in imaging inverse problems

2008

J. Phys.: Conf. Ser.

“…More details on fractal image coding can be found in many places [1], [3], [7], [11], [9], including one of our recent papers on generalized fractal image coding using projections onto convex sets [5]. Fractal image coding seeks to approximate an image by a union of spatially-contracted and greyscale-modified copies of subblocks of itself.…”

Section: Basics Of Fractal Image Encoding and Decodingmentioning

confidence: 99%

“…In [5] we introduced the problem of restoration of an image with an incomplete fractal code, and used the method of projection onto convex sets (POCS) to address this problem. Here we use the regularization approach introduced above.…”

Section: Application To Restoration Of An Image With An Incomplete Frmentioning

confidence: 99%

See 1 more Smart Citation

Regularized Fractal Image Decoding

2006 Canadian Conference on Electrical and Computer Engineering

2006

Self Cite

“…Another major drawback of traditional fractal-based methods is that their output is quite restricted, i.e., no prior knowledge, extra regularization method or tuning (regularization) parameters can be combined with these methods. Recently, we have examined various possibilities to address this problem in [12,13]. In this paper, we shall combine some of the ideas in the above works in a natural and complementary fashion.…”

Section: Fractal-based Methodsmentioning

confidence: 99%

Solving the Inverse Problem of Image Zooming Using “Self-Examples”

Lecture Notes in Computer Science

Self Cite

Abstract. In this paper we present a novel single-frame image zooming technique based on so-called "self-examples". Our method combines the ideas of fractal-based image zooming, example-based zooming, and nonlocal-means image denoising in a consistent and improved framework. In Bayesian terms, this example-based zooming technique targets the MMSE estimate by learning the posterior directly from examples taken from the image itself at a different scale, similar to fractal-based techniques. The examples are weighted according to a scheme introduced by Buades et al. to perform nonlocal-means image denoising. Finally, various computational issues are addressed and some results of this image zooming method applied to natural images are presented.