73 research outputs found
Sparse image reconstruction for molecular imaging
The application that motivates this paper is molecular imaging at the atomic
level. When discretized at sub-atomic distances, the volume is inherently
sparse. Noiseless measurements from an imaging technology can be modeled by
convolution of the image with the system point spread function (psf). Such is
the case with magnetic resonance force microscopy (MRFM), an emerging
technology where imaging of an individual tobacco mosaic virus was recently
demonstrated with nanometer resolution. We also consider additive white
Gaussian noise (AWGN) in the measurements. Many prior works of sparse
estimators have focused on the case when H has low coherence; however, the
system matrix H in our application is the convolution matrix for the system
psf. A typical convolution matrix has high coherence. The paper therefore does
not assume a low coherence H. A discrete-continuous form of the Laplacian and
atom at zero (LAZE) p.d.f. used by Johnstone and Silverman is formulated, and
two sparse estimators derived by maximizing the joint p.d.f. of the observation
and image conditioned on the hyperparameters. A thresholding rule that
generalizes the hard and soft thresholding rule appears in the course of the
derivation. This so-called hybrid thresholding rule, when used in the iterative
thresholding framework, gives rise to the hybrid estimator, a generalization of
the lasso. Unbiased estimates of the hyperparameters for the lasso and hybrid
estimator are obtained via Stein's unbiased risk estimate (SURE). A numerical
study with a Gaussian psf and two sparse images shows that the hybrid estimator
outperforms the lasso.Comment: 12 pages, 8 figure
Information Preserving Component Analysis: Data Projections for Flow Cytometry Analysis
Flow cytometry is often used to characterize the malignant cells in leukemia
and lymphoma patients, traced to the level of the individual cell. Typically,
flow cytometric data analysis is performed through a series of 2-dimensional
projections onto the axes of the data set. Through the years, clinicians have
determined combinations of different fluorescent markers which generate
relatively known expression patterns for specific subtypes of leukemia and
lymphoma -- cancers of the hematopoietic system. By only viewing a series of
2-dimensional projections, the high-dimensional nature of the data is rarely
exploited. In this paper we present a means of determining a low-dimensional
projection which maintains the high-dimensional relationships (i.e.
information) between differing oncological data sets. By using machine learning
techniques, we allow clinicians to visualize data in a low dimension defined by
a linear combination of all of the available markers, rather than just 2 at a
time. This provides an aid in diagnosing similar forms of cancer, as well as a
means for variable selection in exploratory flow cytometric research. We refer
to our method as Information Preserving Component Analysis (IPCA).Comment: 26 page
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