Theory and algorithms for spatial transcriptomics denoising

Spatial transcriptomics goes one step beyond single-cell RNA sequencing, yielding high-dimensional images of gene expression in a tissue, which offer the prospect of understanding cell signaling. Recent breakthroughs in spatial transcriptomics have drastically increased the area of tissue which can be profiled. However, sequencing all RNA molecules over large spatial areas is prohibitively expensive. One would like to reduce the number of RNAs sequenced, but this results in excessive technical noise in the measured gene expression data. To counter this problem, we develop theory and algorithms for spatial transcriptomics denoising, based on low rank matrix recovery and spatial smoothing. We propose two novel procedures for estimating the true underlying gene expression image: (1) a low rank maximum-likelihood-type estimator with graph-based total variation regularization, and (2) a switching procedure that switches between 'risky' estimators that work well in practice, and 'safe' estimators which have well-known properties. Our methods are backed by theoretical recovery guarantees, as well as tests on real data which suggest that it is possible to reduce the number of RNAs sequenced by more than 10-fold, without significantly increasing recovery error. Finally, as a generalization of the analysis employed above, we establish some convergence rates for the estimation of structured discrete probability distributions.Science, Faculty ofMathematics, Department ofGraduat

Fast and adaptive hyperspectral imaging for biological and biochemical characterization

Hyperspectral images comprise of light intensity information resolved into two spatial dimensions and a spectral (wavelength) dimension. Hyperspectral imaging (HSI) provides much more information than regular optical microscopy and spectroscopy, making it valuable for non-invasive materials characterization in areas such as cell monitoring and food safety. However, HSI is challenging because of the large amount of data that has to be acquired. Traditional scanning methods suffer large measurement times, and possibly, data storage costs. Hence there is a need for subsampling approaches to HSI, such that measurements can be made more efficient without losing critical information. Standard compressive sensing approaches to hyperspectral imaging can achieve this, albeit subject to tradeoffs between image reconstruction accuracy, speed and generalizability to different samples. A promising approach to compressive HSI is adaptive basis scan, which overcomes these tradeoffs by achieving high-accuracy, generalizable imaging and fast reconstruction. However, existing adaptive methods are developed for imaging architectures that are inherently slow – the single spectrometer pixel camera, which can measure only a single spectrum at once. Here, we develop two methods to integrate multi-track spectral measurement with adaptive basis scan algorithms. We design and employ compound patterns on a DMD (digital micromirror device), which together with a multitrack acquisition architecture, can sample multiple wavelet coefficients at once. Simulation results show that the methods developed here are significantly faster than non-adaptive compressive HSI and full sampling HSI, without compromise to reconstruction accuracies across the different sample images tested.Bachelor of Engineering (Materials Engineering

Multitrack Compressed Sensing for Faster Hyperspectral Imaging

Hyperspectral imaging (HSI) provides additional information compared to regular color imaging, making it valuable in areas such as biomedicine, materials inspection and food safety. However, HSI is challenging because of the large amount of data and long measurement times involved. Compressed sensing (CS) approaches to HSI address this, albeit subject to tradeoffs between image reconstruction accuracy, time and generalizability to different types of scenes. Here, we develop improved CS approaches for HSI, based on parallelized multitrack acquisition of multiple spectra per shot. The multitrack architecture can be paired up with either of the two compatible CS algorithms developed here: (1) a sparse recovery algorithm based on block compressed sensing and (2) an adaptive CS algorithm based on sampling in the wavelet domain. As a result, the measurement speed can be drastically increased while maintaining reconstruction speed and accuracy. The methods were validated computationally both in noiseless as well as noisy simulated measurements. Multitrack adaptive CS has a ∼10 times shorter measurement plus reconstruction time as compared to full sampling HSI without compromising reconstruction accuracy across the sample images tested. Multitrack non-adaptive CS (sparse recovery) is most robust against Poisson noise at the expense of longer reconstruction times

Applications of neural networks to dynamics simulation of Landau-Zener transitions

We simulate the dynamics of a qubit-oscillator system obeying the Landau-Zener (LZ) model, by employing the nonlinear autoregressive neural network and the long short-term memory neural network. Initially, time-dependent transition probability of the LZ model is obtained by the Dirac-Frenkel time dependent variation with the multiple Davydov D2 Ansatz. With the first stage of a two-dimensional (2D) dataset (time versus transition probability), two different kinds of neural networks are trained and validated successfully with sufficient information to predict the future values of transition probability (the second stage) with considerable accuracy. Furthermore, we also develop a framework under which an entire time series of a LZ model with fixed tunneling strength Δ and a given qubit-bath coupling strength γ can be predicted, using neural networks that are trained on a set of pre-generated time series corresponding to various values of γ (3D data: time, γ and transition probability). Considerable accuracy is also achieved in 3D data prediction.Ministry of Education (MOE)Competitive Research Programme (CRP) under Project No. NRFCRP5-2009-04 and from the Singapore Ministry of Education Academic Research Fund Tier 1 (Grant Nos. RG106/15, RG102/17, and RG190/18) is gratefully acknowledged