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2. A Smartphone-Based Disposable Hemoglobin Sensor Based on Colorimetric Analysis

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   Meng, Zhuolun; Tayyab, Muhammad; Lin, Zhongtian; Raji, Hassan; Javanmard, Mehdi (January 2023, Sensors)

   Hemoglobin is a biomarker of interest for the diagnosis and prognosis of various diseases such as anemia, sickle cell disease, and thalassemia. In this paper, we present a disposable device that has the potential of being used in a setting for accurately quantifying hemoglobin levels in whole blood based on colorimetric analysis using a smartphone camera. Our biosensor employs a disposable microfluidic chip which is made using medical-grade tapes and filter paper on a glass slide in conjunction with a custom-made PolyDimethylSiloaxane (PDMS) micropump for enhancing capillary flow. Once the blood flows through the device, the glass slide is imaged using a smartphone equipped with a custom 3D printed attachment. The attachment has a Light Emitting Diode (LED) that functions as an independent light source to reduce the noise caused by background illumination and external light sources. We then use the RGB values obtained from the image to quantify the hemoglobin levels. We demonstrated the capability of our device for quantifying hemoglobin in Bovine Hemoglobin Powder, Frozen Beef Blood, and human blood. We present a logarithmic model that specifies the relationship between the Red channel of the RGB values and Hemoglobin concentration. 

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3. Tightening methods based on nontrivial bounds on bilinear terms

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5. A new perspective on denoising based on optimal transport

   https://doi.org/10.1093/imaiai/iaae029  

   García_Trillos, Nicolás; Sen, Bodhisattva (September 2024, Information and Inference: A Journal of the IMA)

   Abstract In the standard formulation of the classical denoising problem, one is given a probabilistic model relating a latent variable $$\varTheta \in \varOmega \subset{\mathbb{R}}^{m} \; (m\ge 1)$$ and an observation $$Z \in{\mathbb{R}}^{d}$$ according to $$Z \mid \varTheta \sim p(\cdot \mid \varTheta )$$ and $$\varTheta \sim G^{*}$$, and the goal is to construct a map to recover the latent variable from the observation. The posterior mean, a natural candidate for estimating $$\varTheta $$ from $$Z$$, attains the minimum Bayes risk (under the squared error loss) but at the expense of over-shrinking the $$Z$$, and in general may fail to capture the geometric features of the prior distribution $$G^{*}$$ (e.g. low dimensionality, discreteness, sparsity). To rectify these drawbacks, in this paper we take a new perspective on this denoising problem that is inspired by optimal transport (OT) theory and use it to study a different, OT-based, denoiser at the population level setting. We rigorously prove that, under general assumptions on the model, this OT-based denoiser is mathematically well-defined and unique, and is closely connected to the solution to a Monge OT problem. We then prove that, under appropriate identifiability assumptions on the model, the OT-based denoiser can be recovered solely from information of the marginal distribution of $$Z$$ and the posterior mean of the model, after solving a linear relaxation problem over a suitable space of couplings that is reminiscent of standard multimarginal OT problems. In particular, due to Tweedie’s formula, when the likelihood model $$\{ p(\cdot \mid \theta ) \}_{\theta \in \varOmega }$$ is an exponential family of distributions, the OT-based denoiser can be recovered solely from the marginal distribution of $$Z$$. In general, our family of OT-like relaxations is of interest in its own right and for the denoising problem suggests alternative numerical methods inspired by the rich literature on computational OT. 

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