EIT for tactile sensing: considering artefacts in hyperparameter selection

Abstract

Electrical impedance tomography (EIT) is employed in tactile sensing to create an image of impedance changes within a continuous sensor using electrodes placed only at the perimeter. Noise destabilizes EIT images, and the onset of instability is associated with the appearance of artefacts, which are spurious image features that are not associated with sensor responses to contacts. Artefacts are detrimental because the essential features of contacts, or targets, must be correctly represented, including how many there are and their approximate shapes and locations, yet their presence has not previously been used as a performance measure. Regularization, the extent of which is determined by the hyperparameter λ, is used to manage the destabilization, but it results in spatially non-uniform defocusing of image features. We therefore introduce an efficient criterion for evaluating tactile sensor image quality based on the onset of artefacts. Using simulated data and the one-step Gauss-Newton reconstruction algorithm with the Laplace prior, the noise level at which artefacts first appear at a given hyperparameter, or noise threshold Nth(λ), is found. How the relationship depends on target characteristics and other factors is shown, and Nth can vary by orders of magnitude. The conceptually similar BestRes method and the classical L-curve and generalized cross-validation (GCV) methods for determining an optimal hyperparameter are evaluated using the criterion of artefact-free images. The L-curve generates hyperparameters that are well matched to the onset of artefacts, except at high noise; the other two result in artefacts. For high dynamic range tactile inputs, setting the threshold at a fixed value using a method such as Nth is not advisable, and automatic regularization tailored to the input may be needed using a method such as the L-curve or GCV, provided that the computational overhead is tolerable.

EIT for tactile sensing:considerations regarding the injection-measurement pattern

“…The mesh size used for the forward problem was the finest j2d4c, and for the inverse it was h2d4c. Prior work showed that results were mesh invariant [5]. The threshold f = 2 was used for the 1/f max amplitude set (e.g.…”

“…The I-M patterns were next challenged by adding noise. A useful metric for evaluating the effects of noise on tactile sensing images is the onset of artefacts [5]. Susceptibility to noise was determined by finding the noise level at which artifacts just started to appear for a given λ.…”

“…Since the resistance between electrodes is proportional to their separation, for a fixed injection current, greater electrode separation results in larger potential differences. Because the electrodes for I or M = 1 are closer together than for other positions, the maximum values in the measurement frame are smaller, and this lowers the signal to noise ratio, necessitating the use of larger hyperparameters [5].…”

Improving the spatial resolution of electrical impedance tomography using logical operation as post-processing

“…In previous studies, some reports have been evaluated using position error and resolution. 8,10,20) To evaluate more quantitatively, the following evaluation method was defined. The normalized size error (NSE) shown in Eq.…”

“…6) Various optimization approaches for hyperparameters have been reported. [9][10][11][12][13] However, determining the optimal hyperparameter remains a challenging task.…”