Compressive Sensing DNA Microarrays

Compressive sensing microarrays (CSMs) are DNA-based sensors that operate using group testing and compressive sensing (CS) principles. In contrast to conventional DNA microarrays, in which each genetic sensor is designed to respond to a single target, in a CSM, each sensor responds to a set of targets. We study the problem of designing CSMs that simultaneously account for both the constraints from CS theory and the biochemistry of probe-target DNA hybridization. An appropriate cross-hybridization model is proposed for CSMs, and several methods are developed for probe design and CS signal recovery based on the new model. Lab experiments suggest that in order to achieve accurate hybridization profiling, consensus probe sequences are required to have sequence homology of at least 80% with all targets to be detected. Furthermore, out-of-equilibrium datasets are usually as accurate as those obtained from equilibrium conditions. Consequently, one can use CSMs in applications in which only short hybridization times are allowed

Compressive Sensing DNA Microarrays

sensors that operate using group testing and compressive sensing (CS) principles. In contrast to conventional DNA microarrays, in which each genetic sensor is designed to respond to a single target, in a CSM each sensor responds to a set of targets. We study the problem of designing CSMs that simultaneously account for both the constraints from compressive sensing theory and the biochemistry of probe-target DNA hybridization. An appropriate cross-hybridization model is proposed for CSMs, and several methods are developed for probe design and CS signal recovery based on the new model. Our lab experiments suggest that, in order to achieve accurate hybridization profiling, consensus probe sequences are required to have sequence homology of at least 80 % with all targets to be detected. Furthermore, outof-equilibrium datasets are usually as accurate as those obtained from equilibrium conditions. Consequently, one can use CSMs in applications for which only short hybridization times are allowed. Index Terms—Compressive sensing, DNA microarray, group testing, hybridization affinity, probe design I

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

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

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 $\ell_1$ 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 $\ell_1$-constrained minimal singular value ($\ell_1$-CMSV) of the measurement matrix determines, in a very concise manner, the recovery performance of $\ell_1$-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 $\ell_1$-CMSVs bounded away from zero, as long as the number of measurements is relatively large. To compute the $\ell_1$-CMSV and its lower bound, we design two algorithms based on the interior point algorithm and the semi-definite relaxation