Data fusion as a way to perform compressive sensing

Some time ago I started working on some kind of data fusion problem where we have access to several imaging systems working in parallel, each one gathering a different multidimensional dataset with mixed spectral, temporal, and/or spatial resolutions. The idea is to perform 4D imaging at high spectral, temporal, and spatial resolutions using some single-pixel/multi-pixel detectors, where each detector is specialized on measuring one dimension in high detail while subsampling the others. Using ideas from regularization/compressive sensing, the goal is to merge all the information we acquire individually in a way that makes sense, and while doing so, achieve very high compression ratios.

Looking for similar approaches, I stumbled with a series of papers from people doing remote sensing that basically do the same thing. While the idea is fundamentally the same, their fusion model relies on a Bayesian approach, which is something I have never seen before, and seems quite interesting. They try to estimate a 4D object that maximizes the coherence between the data they acquire (the low-resolution 2D/3D projections) and their estimation. This is quite close to what we usually do in compressive sensing experiments on imaging, but with a minimization based on a sparsity prior.

An Integrated Framework for the Spatio–Temporal–Spectral Fusion of Remote Sensing Images

By Huanfeng Shen ; Xiangchao Meng , and Liangpei Zhang, at IEEE Transactions on Geoscience and Remote Sensing

Abstract:

Remote sensing satellite sensors feature a tradeoff between the spatial, temporal, and spectral resolutions. In this paper, we propose an integrated framework for the spatio-temporal-spectral fusion of remote sensing images. There are two main advantages of the proposed integrated fusion framework: it can accomplish different kinds of fusion tasks, such as multiview spatial fusion, spatio-spectral fusion, and spatio-temporal fusion, based on a single unified model, and it can achieve the integrated fusion of multisource observations to obtain high spatio-temporal-spectral resolution images, without limitations on the number of remote sensing sensors. The proposed integrated fusion framework was comprehensively tested and verified in a variety of image fusion experiments. In the experiments, a number of different remote sensing satellites were utilized, including IKONOS, the Enhanced Thematic Mapper Plus (ETM+), the Moderate Resolution Imaging Spectroradiometer (MODIS), the Hyperspectral Digital Imagery Collection Experiment (HYDICE), and Systeme Pour l’ Observation de la Terre-5 (SPOT-5). The experimental results confirm the effectiveness of the proposed method.

Operation principle of the technique. Multiple images with different resolutions are combined to obtain a high-resolution multidimensional reconstruction of the data. Extracted from Fig.1 of the manuscript.

As sensors evolve, the amount of information we can gather grows at an alarming rate: we have gone from just hundreds or thousands of pixels to millions in just a few decades. Also, now we gather hundreds of spectral channels at hundreds or thousands of frames per second. This implies that we usually suffer from bottlenecks in the acquisition and storage of multidimensional datasets. Using approaches like this, one can make it possible to obtain very good object estimations while measuring very little data in a fast way, which is always a must.

Bonus: Of course, they have also been doing the same but using Machine Learning ideas:

Spatial–Spectral Fusion by Combining Deep Learning and Variational Model

By Huanfeng Shen, Menghui Jiang, Jie Li, Qiangqiang Yuan, Yanchong Wei, and Liangpei Zhang, at IEEE Transactions on Geoscience and Remote Sensing

Single frame wide-field Nanoscopy based on Ghost Imaging via Sparsity Constraints (GISC Nanoscopy)

This just got posted on the arXiv, and has some interesting ideas inside. Using a ground glass diffuser before a pixelated detector, and after a calibrating procedure where you measure the associated speckle patterns when scanning the sample plane, a single shot of the fluorescence signal speckle pattern can be used to retrieve high spatial resolution images of a sample. Also, the authors claim that the approach should work on STORM setups, achieving really fast and sharp fluorescence images. Nice single-shot example of Compressive Sensing and Ghost Imaging!

Single frame wide-field Nanoscopy based on Ghost Imaging via Sparsity Constraints (GISC Nanoscopy)

by Wenwen Li, Zhishen Tong, Kang Xiao, Zhentao Liu, Qi Gao, Jing Sun, Shupeng Liu, Shensheng Han, and Zhongyang Wang, at arXiv.org

Abstract:

The applications of present nanoscopy techniques for live cell imaging are limited by the long sampling time and low emitter density. Here we developed a new single frame wide-field nanoscopy based on ghost imaging via sparsity constraints (GISC Nanoscopy), in which a spatial random phase modulator is applied in a wide-field microscopy to achieve random measurement for fluorescence signals. This new method can effectively utilize the sparsity of fluorescence emitters to dramatically enhance the imaging resolution to 80 nm by compressive sensing (CS) reconstruction for one raw image. The ultra-high emitter density of 143 {\mu}m-2 has been achieved while the precision of single-molecule localization below 25 nm has been maintained. Thereby working with high-density of photo-switchable fluorophores GISC nanoscopy can reduce orders of magnitude sampling frames compared with previous single-molecule localization based super-resolution imaging methods.

Experimental setup and fundamentals of the calibration and recovery process. Extracted from Fig.1 of the manuscript.