# Collective sensing: a fixed-point approach in the metric space

@inproceedings{Li2010CollectiveSA, title={Collective sensing: a fixed-point approach in the metric space}, author={Xin Li}, booktitle={Visual Communications and Image Processing}, year={2010} }

Conventional wisdom in signal processing heavily relies on the concept of inner product defined in the Hilbert space. Despite the popularity of Hilbert-space formulation, we argue it is overly-structured to account for the complexity of signals arising from the real-world. Inspired by the works on fractal image decoding and nonlocal image processing, we propose to view an image as the fixed-point of some nonexpansive mapping in the metric space in this paper. Recently proposed BM3D-based…

## 9 Citations

### Fine-Granularity and Spatially-Adaptive Regularization for Projection-Based Image Deblurring

- MathematicsIEEE Transactions on Image Processing
- 2011

This paper studies two classes of regularization strategies to achieve an improved tradeoff between image recovery and noise suppression in projection-based image deblurring. The first is based on a…

### A Study of the Structural Similarity Image Quality Measure with Applications to Image Processing

- Computer Science
- 2012

It is demonstrated how the SSIM index can be transformed into a distance metric and the hypothesis that the main source of selfsimilarity of images lies in their regions of low variance is confirmed.

### Chapter 1 Patch-Based Image Processing : from Dictionary Learning to Structural Clustering

- Computer Science
- 2011

Under the context of JPEG compression, fast advances of communication and computing technologies in later 1980s and early 1990s stimulated the research into image compression especially the development of standard.

### On the Mathematical Properties of the Structural Similarity Index

- Computer ScienceIEEE Transactions on Image Processing
- 2012

A series of normalized and generalized metrics based on the important ingredients of SSIM are constructed and it is shown that such modified measures are valid distance metrics and have many useful properties, among which the most significant ones include quasi-convexity, a region of convexity around the minimizer, and distance preservation under orthogonal or unitary transformations.

### SSIM-based non-local means image denoising

- Computer Science2011 18th IEEE International Conference on Image Processing
- 2011

This work makes one of the first efforts to incorporate the structural similarity (SSIM) index, a successful perceptual image quality assessment measure, into the framework of non-local means (NLM) image denoising, which is a state-of-the-art method that delivers superior desnoising performance.

### A Class of Image Metrics Based on the Structural Similarity Quality Index

- Mathematics, Computer ScienceICIAR
- 2011

A class of metrics for signals and images, considered as elements of RN, that are based upon the structural similarity (SSIM) index are derived, which shows that a suitable norm of an ordered pair of metrics defines a metric in RN.

### SSIM-Inspired Quality Assessment, Compression, and Processing for Visual Communications

- Computer Science
- 2013

The goal of this research is to break the tradition of using MSE as the optimization criterion for image and video processing algorithms and tackle several important problems in visual communication applications by exploiting SSIM-inspired design and optimization to achieve significantly better performance.

### Fractal Imaging Theory and Applications beyond Compression

- Physics
- 2012

The Natural Sciences and Engineering Research Council and the University of Guelph helped to provide financial support for this research.

### Patch-Based Image Processing: From Dictionary Learning to Structural Clustering

- Computer Science
- 2017

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