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Cartoon-Texture Image Decomposition Using
Blockwise Low-Rank Texture Characterization
Abstract—Using a novel characterization of texture, we propose an image decomposition
technique that can effectively decomposes an image into its cartoon and texture components. The
characterization rests on our observation that the texture component enjoys a blockwise low-rank
nature with possible overlap and shear, because texture, in general, is globally dissimilar but
locally well patterned. More specifically, one can observe that any local block of the texture
component consists of only a few individual patterns. Based on this premise, we first introduce a
new convex prior, named the block nuclear norm (BNN), leading to a suitable characterization of
the texture component. We then formulate a cartoon-texture decomposition model as a convex
optimization problem, where the simultaneous estimation of the cartoon and texture components

2. from a given image or degraded observation is executed by minimizing the total variation and
BNN. In addition, patterns of texture extending in different directions are extracted separately,
which is a specialfeature of the proposed model and of benefit to texture analysis and other
applications. Furthermore, the model can handle various types of degradation occurring in image
processing, including blur + missing pixels with several types of noise. By rewriting the problem
via variable splitting, the so-called alternating direction method of multipliers becomes
applicable, resulting in an efficient algorithmic solution to the problem. Numerical examples
illustrate that the proposed model is very selective to patterns of texture, which makes it produce
better results than state-of-the-art decomposition models.

3. Existing method:
The paper is organized as follows.we introduce minimal mathematical tools necessary for the
following discussion. devoted to establishing BNN with several of its theoretical properties and
elaborating on the difference between BNN and existing priors for texture characterization.
Proposed method:
In addition, the proposed model is designed to accept various degradation scenarios, including
blur + missing pixels with noise. Such a scenario was considered in a recent study [19] under a
Gaussian noise assumption. Notably the proposed model can also handle several non-Gaussian
noise cases in a unified way with the associated convex optimization problem solvable using
proximal splitting techniques. Specifically, for simplicity, we adopt a convex optimization
algorithm called the Alternating Direction Method of Multipliers] (ADMM), resulting in an
efficient algorithmic solution.

4. Merits:
1. Better PSNR values
2. Output image more enhancement.
3. Low BER rate
Demerits:
1.noise level is very high
2. restoration process time is very high.

5. Results: