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Remote sensing images often suffer from stripe noise, which greatly degrades the image quality. Destriping of remote sensing images is to recover a good image from the image containing stripe noise. Since the stripes in remote sensing images have a directional characteristic (horizontal or vertical), the unidirectional total variation has been used to consider the directional information and preserve the edges. The remote sensing image contaminated by heavy stripe noise always has large width stripes and the pixels in the stripes have low correlations with the true pixels. On this occasion, the destriping process can be viewed as inpainting the wide stripe domains. In many works, high-order total variation has been proved to be a powerful tool to inpainting wide domains. Therefore, in this paper, we propose a variational destriping model that combines unidirectional total variation and second-order total variation regularization to employ the directional information and handle the wide stripes. In particular, the split Bregman iteration method is employed to solve the proposed model. Experimental results demonstrate the effectiveness of the proposed method.

The stripe noise is a common phenomenon that appears in multidetector imaging systems, including the atomic force microscope (AFM) [

A considerable effort has been made to remove stripe noise. The process of removing stripe noise in the striped image is called image destriping. Many methods have been proposed for destriping problems. The first kind of approaches employs digital filtering in the transform domain and suppresses the specific frequency caused by stripes [

It is known that destriping is an ill-posed problem to reconstruct a high quality image from one degraded image. Recently, the maximum a posteriori (MAP) estimation method becomes popular in image denoising [

The total variation (TV) model [

The main contributions of this paper include two aspects. First, we propose unidirectional TV and second-order TV (USTV) model for destriping of remote sensing images. Second, we present an efficient algorithm based on the split Bregman method to solve the proposed USTV model. Experiments demonstrate that it can get better visual sense and quantitative results. The rest of this paper is organized as follows. In Section

A model should be constructed to relate the true image to the contaminated image, by which we can analyze the destriping problem. The model can be linearly described as in [

To get the true image

Two probability density functions (PDF) should be established to get the true image

Substituting (

As we can see in Shen-MAP model, the Huber-Markov prior is a symmetrical regularization term which does not consider the directional characteristic of stripes in remote sensing images. Bouali and Ladjal [

Without loss of generality, we represent a gray image as

We use

We denote backward difference operators with periodic boundary condition as

It is easy to know that

We will present a split Bregman method to solve the above minimization problem in the next subsection.

We first change the unconstrained minimum problem (

We use the split Bregman method to solve problem (

From (

It is worth noting that the periodic boundary condition is a popular boundary assumption used in image processing. Under this assumption, the matrices corresponding to the gradient operator and second-order divergence operator have block circulant with circulant blocks (BCCB) structure, which have a particular spectral decomposition. The matrix-vector multiplications can be calculated by fast Fourier transform more quickly. We can also choose other boundary conditions, for example, zero or reflexive boundary condition, but it may be more difficult or slow to solve

According to (

Due to (

Because of (

Input:

Initialization:

Output: Destriping image

In this work, we use split Bregman method to solve the optimization problem in (

The optimization problem is well structured since the four variables

There are three matrices

In our experiments, we test the proposed model on Terra and Aqua MODIS images provided by Shen and Zhang [

MODIS images before destriping. (a) Aqua MODIS band 30. (b) Terra MODIS band 28. (c) Terra MODIS band 30.

Destriped results of Aqua MODIS band 30. (a) Original striped image. (b) Moment matching [

Destriped results of Terra MODIS band 28. (a) Original striped image. (b) Moment matching [

Destriped results of Terra MODIS band 30. (a) Original striped image. (b) Moment matching [

Figure

Mean cross-track profiles of MODIS images before (blue line) and after (red line) destriping. (a) Aqua MODIS band 30. (b) Terra MODIS band 28. (c) Terra MODIS band 30.

Mean column power spectrum of the MODIS images before (blue line) and after (red line) destriping. (a) Aqua MODIS band 30. (b) Terra MODIS band 28. (c) Terra MODIS band 30.

We use two quality indexes to evaluate the performance of the proposed USTV model. The first index is inverse coefficient of variation (ICV) [

ICVs and NRs of the comparison experiments.

Original | Moment | Shen-MAP | USTV | |
---|---|---|---|---|

Aqua band 30 | ||||

Sample 1 (ICV) | 8.17 | 29.51 | 37.96 | |

Sample 2 (ICV) | 13.01 | 23.14 | 25.29 | |

Sample 3 (ICV) | 8.78 | 14.84 | 18.45 | |

NR | 1.00 | 2.41 | 2.59 | |

Terra band 28 | ||||

Sample 1 (ICV) | 10.94 | 20.59 | 25.18 | |

Sample 2 (ICV) | 25.31 | 22.10 | 38.29 | |

Sample 3 (ICV) | 15.19 | 14.09 | 16.77 | |

NR | 1.00 | 2.92 | 3.64 | |

Terra band 30 | ||||

Sample 1 (ICV) | 31.45 | 75.41 | 80.88 | |

Sample 2 (ICV) | 39.91 | 85.55 | 105.29 | |

Sample 3 (ICV) | 33.26 | 52.84 | 67.52 | |

NR | 1.00 | 1.44 | 1.60 | |

In this paper, we proposed unidirectional TV and second-order TV model for destriping of the remote sensing images. The split Bregman iteration method was used to solve the proposed model. To the best of our knowledge, this is the first work to combine unidirectional TV and second-order TV for the destriping of remote sensing images. In addition, we employed two image quality indexes ICV and NR to evaluate the performance of different methods. Experiments demonstrated that the proposed model obtained better destriping effects than the moment matching method and the Shen-MAP model in terms of both visual sense and quantitative assessments. However, the degradation process in (

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work is supported by 973 Program (2013CB329404) and NSFC (61370147, 61402082).