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Electrical Impedance Tomography (EIT) is a well-known imaging technique for detecting the electrical properties of an object in order to detect anomalies, such as conductive or resistive targets. More specifically, EIT has many applications in medical imaging for the detection and location of bodily tumors since it is an affordable and non-invasive method, which aims to recover the internal conductivity of a body using voltage measurements resulting from applying low frequency current at electrodes placed at its surface. Mathematically, the reconstruction of the internal conductivity is a severely ill-posed inverse problem and yields a poor quality image reconstruction. To remedy this difficulty, at least in part, we regularize and solve the nonlinear minimization problem by the aid of a Krylov subspace-type method for the linear sub problem during each iteration. In EIT, a tumor or general anomaly can be modeled as a piecewise constant perturbation of a smooth background, hence, we solve the regularized problem on a subspace of relatively small dimension by the Flexible Golub-Kahan process that provides solutions that have sparse representation. For comparison, we use a well-known modified Gauss–Newton algorithm as a benchmark. Using simulations, we demonstrate the effectiveness of the proposed method. The obtained reconstructions indicate that the Krylov subspace method is better adapted to solve the ill-posed EIT problem and results in higher resolution images and faster convergence compared to reconstructions using the modified Gauss–Newton algorithm. 

We report a novel colorimetric sensing paradigm using multi-chromatic light from an RGB laser combined with a structural color sensor for fast, ultra-sensitive, and spatio-temporally resolved detection of surface biomolecules by human eye or smartphone. 

Colorimetric sensors offer the prospect for on-demand sensing diagnostics in simple and low-cost form factors, enabling rapid spatiotemporal inspection by digital cameras or the naked eye. However, realizing strong dynamic color variations in response to small changes in sample properties has remained a considerable challenge, which is often pursued through the use of highly responsive materials under broadband illumination. In this work, we demonstrate a general colorimetric sensing technique that overcomes the performance limitations of existing chromatic and luminance-based sensing techniques. Our approach combines structural color optical filters as sensing elements alongside a multichromatic laser illuminant. We experimentally demonstrate our approach in the context of label-free biosensing and achieve ultrasensitive and perceptually enhanced chromatic color changes in response to refractive index changes and small molecule surface attachment. Using structurally enabled chromaticity variations, the human eye is able to resolve ∼0.1-nm spectral shifts with low-quality factor (e.g., Q ∼ 15) structural filters. This enables spatially resolved biosensing in large area (approximately centimeters squared) lithography-free sensing films with a naked eye limit of detection of ∼3 pg/mm 2 , lower than industry standard sensors based on surface plasmon resonance that require spectral or angular interrogation. This work highlights the key roles played by both the choice of illuminant and design of structural color filter, and it offers a promising pathway for colorimetric devices to meet the strong demand for high-performance, rapid, and portable (or point-of-care) diagnostic sensors in applications spanning from biomedicine to environmental/structural monitoring.