Math Research

It is a method for single image dehazing using a convolutional neural network. Outdoor images have been used on which particular filters are applied to find the haze in image. Hazy images contain small value in only one-color alpha channel from Red, Blue, green RGB channel.-  by Wencheng Wang

Comparison between hazy image and hazy free image 

Image by Wencheng Wang

Locate the latest information on "image dehazing" that utilizes mathematical models and concepts and provide references.

I cannot directly "locate" and provide the very latest research papers in real-time. Scientific publications are constantly being updated. However, I can guide you on how to find the most current information on image dehazing using mathematical models and concepts:

Where to Search for the Latest Research:

1. IEEE Xplore Digital Library: This digital library is a treasure trove of papers on signal processing, computer vision, and image processing, all areas crucial to image dehazing. Search for keywords like "image dehazing," "atmospheric scattering model," "dark channel prior," "transmission map estimation," "deep learning dehazing," and combine them with terms related to specific mathematical techniques (e.g., "PDE-based dehazing," "optimization methods for dehazing"). Filter by publication date to see the most recent papers.

2. ACM Digital Library: Similar to IEEE Xplore, the ACM Digital Library contains a wealth of computer science literature, including many relevant papers on image dehazing. Use the same keywords as above.

3. Google Scholar: A powerful search engine for scholarly literature. Use the same keywords, but also experiment with different combinations and variations to broaden or narrow your search. Pay attention to the citation counts, which can indicate the influence and importance of a paper.

4. arXiv: This preprint server hosts many papers before they are published in journals. It's a good place to find very recent research, but be aware that preprints haven't undergone peer review. Use the same keywords as above.

5. ResearchGate and Academia.edu: These platforms allow researchers to share their work. You can find papers and even contact authors directly.

Mathematical Models and Concepts Commonly Used in Image Dehazing:

When searching, keep an eye out for papers employing these mathematical frameworks:

• Atmospheric Scattering Model: This is the fundamental model describing how haze affects images. It typically involves parameters like the transmission map (describing how much light is transmitted through the haze) and the atmospheric light (the color of the haze).

• Dark Channel Prior (DCP): A widely used prior assumption stating that the darkest pixel in a local patch of a haze-free image is likely to be close to zero in the absence of illumination. Many advanced methods build upon or refine this concept. See Chia-Chi Tsai+++

• Partial Differential Equations (PDEs): PDE-based methods often model the image dehazing process as a diffusion or regularization problem, aiming to recover sharp details while removing haze smoothly.

• Optimization Methods: Various optimization techniques, such as gradient descent, are frequently used to estimate the transmission map and atmospheric light, minimizing a cost function representing the difference between the observed hazy image and the estimated haze-free image.

• Deep Learning Methods: Convolutional Neural Networks (CNNs) and other deep learning architectures have become very popular, often learning complex relationships between hazy and haze-free images directly from data. These implicitly learn mathematical relationships but are less explicitly described using traditional mathematical notation.

Tips for Your Search:

• Combine keywords: Use a combination of general keywords (image dehazing) and specific mathematical keywords (PDE, optimization).

• Filter by date: Focus on the most recent publications.

• Look at citations: Highly cited papers are often considered influential and important.

• Read abstracts carefully: Identify papers that directly address your interests.

Remember to critically evaluate the papers you find, considering the methodology, results, and limitations. The field is constantly evolving, so staying updated through regular searches on the resources mentioned above is key.

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I cannot provide direct citations in the same way a traditional literature review would. My knowledge is based on a massive dataset of text and code, and I don't have direct access to a bibliographic database to pull specific citations with DOIs or PMIDs. To find relevant citations, you must perform the searches I described previously on the databases like IEEE Xplore, ACM Digital Library, Google Scholar, and arXiv.

However, I can give you some landmark papers and influential concepts that frequently appear in the image dehazing literature, allowing you to use these as search terms or starting points in your own literature search:

Landmark Papers and Concepts (use these as search terms):

• He, K., Sun, J., Tang, X., & Shum, H. Y. (2009). Single image haze removal using dark channel prior. IEEE transactions on pattern analysis and machine intelligence, 33(12), 2341-2353. This is the seminal paper introducing the Dark Channel Prior (DCP), a highly influential concept in image dehazing. Many subsequent papers build upon or improve upon this method.

• Tan, R. T. (2008). Visibility in bad weather from a single image. In Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on (pp. 1-8). IEEE. An earlier work exploring single-image dehazing, often cited as a precursor to DCP.

• Many papers using Partial Differential Equations (PDEs): Searching for "image dehazing PDE" will yield many results. These papers often don't have a single, universally cited foundational paper but instead represent a family of approaches based on solving differential equations to model the image formation process and haze removal.

• Numerous deep learning papers: Searching for "image dehazing deep learning" or "image dehazing CNN" will bring up a large number of recent publications. This area is highly active, with continuous improvements in network architectures and training techniques. Specific citations would vary depending on the exact type of deep learning architecture (e.g., U-Net, ResNet variations).

To find the absolute latest research:

1. Start with the papers listed above: Use the "cited by" feature on Google Scholar or other databases to find more recent papers that build upon these seminal works.

2. Use advanced search operators: Refine your search on databases like IEEE Xplore and ACM Digital Library by specifying date ranges, keywords, and other criteria.

3. Look at conference proceedings: Many leading-edge research findings are first presented at conferences like CVPR (Computer Vision and Pattern Recognition), ICCV (International Conference on Computer Vision), IEEE/CVF Winter Conference on Applications of Computer Vision (WACV) and ECCV (European Conference on Computer Vision).

By using these starting points and search strategies, you will be able to locate the most current research papers on image dehazing employing various mathematical models and concepts. Remember to always critically evaluate the methodology, results, and limitations of each paper.

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