616 research outputs found
Sparse measurements, compressed sampling, and DNA microarrays
DNA microarrays comprising tens of thousands of probe spots are currently being employed to test multitude of targets in a single experiment. Typically, each microarray spot contains a large number of copies of a single probe designed to capture a single target, and hence collects only a single data point. This is a wasteful use of the sensing resources in comparative DNA microarray experiments, where a test sample is measured relative to a reference sample. Since only a small fraction of the total number of genes represented by the two samples is differentially expressed, a vast number of probe spots will not provide any useful information. To this end we consider an alternative design, the so-called compressed microarrays, wherein each spot is a composite of several different probes and the total number of spots is potentially much smaller than the number of targets being tested. Fewer spots directly translates to significantly lower costs due to cheaper array manufacturing, simpler image acquisition and processing, and smaller amount of genomic material needed for experiments. To recover signals from compressed microarray measurements, we leverage ideas from compressive sampling. Moreover, we propose an algorithm which has far less computational complexity than the widely-used linear-programming-based methods, and can also recover signals with less sparsity
Recovering Sparse Signals Using Sparse Measurement Matrices in Compressed DNA Microarrays
Microarrays (DNA, protein, etc.) are massively parallel affinity-based biosensors capable of detecting and quantifying a large number of different genomic particles simultaneously. Among them, DNA microarrays comprising tens of thousands of probe spots are currently being employed to test multitude of targets in a single experiment. In conventional microarrays, each spot contains a large number of copies of a single probe designed to capture a single target, and, hence, collects only a single data point. This is a wasteful use of the sensing resources in comparative DNA microarray experiments, where a test sample is measured relative to a reference sample. Typically, only a fraction of the total number of genes represented by the two samples is differentially expressed, and, thus, a vast number of probe spots may not provide any useful information. To this end, we propose an alternative design, the so-called compressed microarrays, wherein each spot contains copies of several different probes and the total number of spots is potentially much smaller than the number of targets being tested. Fewer spots directly translates to significantly lower costs due to cheaper array manufacturing, simpler image acquisition and processing, and smaller amount of genomic material needed for experiments. To recover signals from compressed microarray measurements, we leverage ideas from compressive sampling. For sparse measurement matrices, we propose an algorithm that has significantly lower computational complexity than the widely used linear-programming-based methods, and can also recover signals with less sparsity
On Recovery of Sparse Signals in Compressed DNA Microarrays
Currently, DNA micro arrays comprising tens of thousands of probe spots are employed to test entire genomes in a single experiment. Typically, each microarray spot contains a large number of copies of a single probe, and hence collects only a single data point. This is a wasteful use of the sensing resources in comparative DNA microarray experiments, where a test sample is measured relative to a reference sample. Since only a small fraction of the total number of genes represented by the two samples is differentially expressed, a large fraction of a microarray does not provide any useful information. To this end, in this paper we consider an alternative microarray design wherein each spot is a composite of several different probes, and the total number of spots is potentially much smaller than the number of genes being tested. Fewer spots directly translates to significantly lower costs due to cheaper array manufacturing, simpler image acquisition and processing, and smaller amount of genomic material needed for experiments. To recover signals from compressed microarray measurements, we leverage ideas from compressive sampling. Experimental verification of the proposed methodology is presented
Performance Analysis of Sparse Recovery Based on Constrained Minimal Singular Values
The stability of sparse signal reconstruction is investigated in this paper.
We design efficient algorithms to verify the sufficient condition for unique
sparse recovery. One of our algorithm produces comparable results with
the state-of-the-art technique and performs orders of magnitude faster. We show
that the -constrained minimal singular value (-CMSV) of the
measurement matrix determines, in a very concise manner, the recovery
performance of -based algorithms such as the Basis Pursuit, the Dantzig
selector, and the LASSO estimator. Compared with performance analysis involving
the Restricted Isometry Constant, the arguments in this paper are much less
complicated and provide more intuition on the stability of sparse signal
recovery. We show also that, with high probability, the subgaussian ensemble
generates measurement matrices with -CMSVs bounded away from zero, as
long as the number of measurements is relatively large. To compute the
-CMSV and its lower bound, we design two algorithms based on the
interior point algorithm and the semi-definite relaxation
Bacterial Community Reconstruction Using A Single Sequencing Reaction
Bacteria are the unseen majority on our planet, with millions of species and
comprising most of the living protoplasm. While current methods enable in-depth
study of a small number of communities, a simple tool for breadth studies of
bacterial population composition in a large number of samples is lacking. We
propose a novel approach for reconstruction of the composition of an unknown
mixture of bacteria using a single Sanger-sequencing reaction of the mixture.
This method is based on compressive sensing theory, which deals with
reconstruction of a sparse signal using a small number of measurements.
Utilizing the fact that in many cases each bacterial community is comprised of
a small subset of the known bacterial species, we show the feasibility of this
approach for determining the composition of a bacterial mixture. Using
simulations, we show that sequencing a few hundred base-pairs of the 16S rRNA
gene sequence may provide enough information for reconstruction of mixtures
containing tens of species, out of tens of thousands, even in the presence of
realistic measurement noise. Finally, we show initial promising results when
applying our method for the reconstruction of a toy experimental mixture with
five species. Our approach may have a potential for a practical and efficient
way for identifying bacterial species compositions in biological samples.Comment: 28 pages, 12 figure
Explicit measurements with almost optimal thresholds for compressed sensing
We consider the deterministic construction of a measurement
matrix and a recovery method for signals that are block
sparse. A signal that has dimension N = nd, which consists
of n blocks of size d, is called (s, d)-block sparse if
only s blocks out of n are nonzero. We construct an explicit
linear mapping Φ that maps the (s, d)-block sparse signal
to a measurement vector of dimension M, where s•d <N(1-(1-M/N)^(d/(d+1))-o(1).
We show that if the (s, d)-
block sparse signal is chosen uniformly at random then the
signal can almost surely be reconstructed from the measurement
vector in O(N^3) computations
- …