Single Pixel Imaging

Sorting of the Hadamard basis for Single Pixel Imaging

This repository contains the source code of a sorting method of the Hadamard basis applied for single pixel imaging (SPI). The sorting method is based on generalized orthogonal basis vectors which can be represented as a two-dimensional structure of Hadamard patterns. By taken advantage of the energy concentration of the Hadamard patterns at the left upper corner of the 2D structure, it is used a zigzag traversal in order to sort the patterns in descending order of importance. The obtained ordering of the patterns, within the framework of SPI, allows to reconstruct a given target image using a small number of patterns.

The source code was written in Matlab on Windows operating system.

For an introduction to single pixel imaging see the documents intro1 intro 2

This repository contains the following folders and files:

Structure

Files and folders:

• \TVAL3_beta2.4
• \coco-train2014
• \misc
• \data
• demo1.m
• demo2.m
• ...

Configuration and data request

Initially, the folders \coco-train2014 and \misc are empty since it requires externals image reporsitories which can be downloaded by permission of the creators.

Image Databases

Link to the images:

• [COCO dataset] (http://images.cocodataset.org/zips/train2014.zip)
• [The USC-SIPI Image Database] (https://sipi.usc.edu/database/misc.zip)

Please note that the previous links to the datasets might change with time, it is advisable to visit the web page of the providers, namely, https://cocodataset.org/ and https://sipi.usc.edu/database/. Once the .zip files have been downloaded, they must be uncompressed into the main directory, replacing the existing folders.

TVL3 Package

Link to the tool:

• [TVL3] (https://github.com/liuyang12/3DCS.git)

In the previous link, go to packages and download the folder \TVL3_beta2.4, then move it to the main directory.

\data folder

This folder can be used to save precalculated Hadamard matrices. This is convenient when the dimension of the Hadamard matrix is greater than 2^7, which is time consuming to compute.

Simulation and execution

To test the Matlab library, run the demo1.m, demo2.m, demo3.m, demo4.m, or demo5.m script.

Important:

• demo4.m and demo5.m require to rename the images of the COCO database before their execution. So, please, into the command prompt of the Matlab environment, type the script renameImages and wait until finished.
• demo4.m and demo5.m require the ssim function for computing the Optimized Structural Similarity Index between two images. Matlab supports an implementation of the ssim function since R2014a into the Image Processing Toolbox. An existing implementation can be obtained from the following link The SSIM Index for Image Quality Assessment. It was originally proposed in Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, "Image quality assessment: From error visibility to structural similarity," IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600-612, Apr. 2004.
• If the provided repository is helpful for your research, please cite the following paper: Lourdes López-García, William Cruz-Santos, Anmi García-Arellano, Pedro Filio-Aguilar, José A. Cisneros-Martínez, and Rubén Ramos-García, "Efficient ordering of the Hadamard basis for single pixel imaging," Opt. Express 30, 13714-13732 (2022)

Related references

• Donoho, D.L. (2006), For most large underdetermined systems of linear equations the minimal 𝓁1-norm solution is also the sparsest solution. Comm. Pure Appl. Math., 59: 797-829. https://doi.org/10.1002/cpa.20132
• Candes, E., Romberg, J. Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions. Found Comput Math 6, 227–254 (2006). https://doi.org/10.1007/s10208-004-0162-x
• Candès, Emmanuel & Romberg, Justin & Tao, Terence. (2006). Robust Uncertainty Principles : Exact Signal Frequency Information. Information Theory, IEEE Transactions on. 52. 489-509. https://doi.org/10.1109/TIT.2005.862083