### Image Reconstruction

I followed the big concept of reconstruction from the precedent research “Radio tomographic imaging with wireless networks.” They suggest a mathematical model using RSSI to obtain images of moving objects [1]. The following is the mathematical linear model that represents relationship of image vector and RSSI vector.

y is the vector of all difference RSS measurements, W is the weighting matrix, and x is the attenuation image to be estimated, all measured in decibels (dB). W is of dimension M × N , with each column representing a single voxel, and each row describing the weighting of each voxel for that link. σ_N^(-2) is node variance and C_x is priori covariance matrix.

Detailed mathematical description of each factor in the equation is skipped in this document because it is described in detail in the pater. On the other hand, In this document, I’ll go into more detail about the vector y because it can be vary depend on the environment and even at the pater, it looks like open issue.

y is the vector of all the differences between RSS measurements in the network, but also it can be the vector of standard deviations at a certain timestamp. I tried to reconstruct image using 3 difference vector y and all of them brought meaningful result.

First. I set up vector y as a difference of RSSI in T_n with T_(n-1) which is one cycle. In that way. It shows most accurate reconstruction image. However, moving object (or person) stop moving during the measurement, the object disappear on the reconstruction image because the network adapt to new stable environment.

Second, I set up vector as difference of RSSI in T_n with T_0. RSSI of T_0 means RSSI of start point that there’s no moving object or any person. So the system can detect object which is not moving much more effectively than fist method. However, considering that the RSSI can be affected easily from small changes of environment, this second method can be adapted during short time otherwise it will bring inaccurate image.

Third, as I mentioned above, I used standard deviations as y. It showed similar images of First approach and It showed more accurate images when the iteration number increased.

Consequently, I implemented device application and reconstruction algorithm with first approach which shows the best result but I think the other two approaches also would be good alternative plan depend on the environment or with additional algorithm

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[1] Wilson, Joey, and Neal Patwari. “Radio tomographic imaging with wireless networks.” IEEE Transactions on Mobile Computing 9.5 (2010): 621-632.