arXiv subjects

Luke Pfister

Publications and source records attributed to Luke Pfister.

5 recordsLinked to original sources

arXiv2019

Composition-Aware Spectroscopic Tomography

Chemical imaging provides information about the distribution of chemicals within a target. When combined with structural information about the target, in situ chemical imaging opens the door to applications ranging from tissue classification to industrial process monitoring. The combination of infrared spectroscopy and optical microscopy is a powerful tool for chemical imaging of thin targets. Unfortunately, extending this technique to targets with appreciable depth is prohibitively slow. We combine confocal microscopy and infrared spectroscopy to provide chemical imaging in three spatial dimensions. Interferometric measurements are acquired at a small number of focal depths, and images are formed by solving a regularized inverse scattering problem. A low-dimensional signal model is key to our approach: we assume the target comprises a finite number of distinct chemical species. We establish conditions on the constituent spectra and the number of measurements needed for unique recovery of the target. Simulations illustrate imaging of cellular phantoms and sub-wavelength targets from noisy measurements.

eess.IV↗

arXiv2019

A deep learning framework for morphologic detail beyond the diffraction limit in infrared spectroscopic imaging

Infrared (IR) microscopes measure spectral information that quantifies molecular content to assign the identity of biomedical cells but lack the spatial quality of optical microscopy to appreciate morphologic features. Here, we propose a method to utilize the semantic information of cellular identity from IR imaging with the morphologic detail of pathology images in a deep learning-based approach to image super-resolution. Using Generative Adversarial Networks (GANs), we enhance the spatial detail in IR imaging beyond the diffraction limit while retaining their spectral contrast. This technique can be rapidly integrated with modern IR microscopes to provide a framework useful for routine pathology.

eess.IV↗

arXiv2019

Transform Learning for Magnetic Resonance Image Reconstruction: From Model-based Learning to Building Neural Networks

Magnetic resonance imaging (MRI) is widely used in clinical practice, but it has been traditionally limited by its slow data acquisition. Recent advances in compressed sensing (CS) techniques for MRI reduce acquisition time while maintaining high image quality. Whereas classical CS assumes the images are sparse in known analytical dictionaries or transform domains, methods using learned image models for reconstruction have become popular. The model could be pre-learned from datasets, or learned simultaneously with the reconstruction, i.e., blind CS (BCS). Besides the well-known synthesis dictionary model, recent advances in transform learning (TL) provide an efficient alternative framework for sparse modeling in MRI. TL-based methods enjoy numerous advantages including exact sparse coding, transform update, and clustering solutions, cheap computation, and convergence guarantees, and provide high-quality results in MRI compared to popular competing methods. This paper provides a review of some recent works in MRI reconstruction from limited data, with focus on the recent TL-based methods. A unified framework for incorporating various TL-based models is presented. We discuss the connections between transform learning and convolutional or filter bank models and corresponding multi-layer extensions, with connections to deep learning. Finally, we discuss recent trends in MRI, open problems, and future directions for the field.

eess.IV↗

arXiv2018

Bounding Multivariate Trigonometric Polynomials with Applications to Filter Bank Design

The extremal values of multivariate trigonometric polynomials are of interest in fields ranging from control theory to filter design, but finding the extremal values of such a polynomial is generally NP-Hard. In this paper, we develop simple and efficiently computable estimates of the extremal values of a multivariate trigonometric polynomial directly from its samples. We provide an upper bound on the modulus of a complex trigonometric polynomial, and develop upper and lower bounds for real trigonometric polynomials. For a univarite polynomial, these bounds are tighter than existing bounds, and the extension to multivariate polynomials is new. As an application, the lower bound provides a sufficient condition to certify global positivity of a real trigonometric polynomial. We use this condition to motivate a new algorithm for multi-dimensional, multirate, perfect reconstruction filter bank design. We demonstrate our algorithm by designing a 2D perfect reconstruction filter bank.

eess.SP↗

arXiv2018

Learning Filter Bank Sparsifying Transforms

Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data, and data-adaptive sparsifying transforms have demonstrated excellent performance in signal restoration tasks. Sparsifying transforms are typically learned using small sub-regions of data called patches, but these algorithms often ignore redundant information shared between neighboring patches. We show that many existing transform and analysis sparse representations can be viewed as filter banks, thus linking the local properties of patch-based model to the global properties of a convolutional model. We propose a new transform learning framework where the sparsifying transform is an undecimated perfect reconstruction filter bank. Unlike previous transform learning algorithms, the filter length can be chosen independently of the number of filter bank channels. Numerical results indicate filter bank sparsifying transforms outperform existing patch-based transform learning for image denoising while benefiting from additional flexibility in the design process.

stat.ML↗