1. Experiment
We will test whether the choice of samples will affect the estimation of sensors' spectral responsitivity with a calibrated device(HP Scanjet IIC). To achieve it, first we add 1% noise to sensors' RGB response. Then we compare the estimated curves with three different methods: Pseudo-Inverse directly(PI), Principal eigenvector with random selected patches (PE) and PE with selected patches based on Hardeberg's algorithm(SPE).
Below shows the estimated results with 12 patches. For PI and PE method, w simply choose the first 12 patches. The SPE method will select [ 16 18 17 4 15 7 9 13 19 12 5 11] patches as the most significant patches. PE and SPE will use only 5 largest singular values. The last graph show the estimated results with all 24 patches using PE method.
2. Conclusion
From these graphes, we can see directly that SPE method give us the best results. There is a large improvement from PI to PE. The improvement from PE to SPE is not so large, but we can still see it. More tests show that the difference between PE and SPE's results decrease with the increasing patches used in pseudo-inverse increase. It's quite natural since we have less choice then.
In this study, we also find that using only 12 patches, SPE method will give us almost the same results as PE with all 24 patches. This will quite encouraging since it will save us a lot of measurements.