Afshin Abdi

Optimal sensor selection in the presence of noise and interference

The sensor selection problem arises in many applications ranging from sensor networks for event detection to determining concentrations of bio-markers for disease detection. In this paper, we assume that in addition to noise, there exist interference signals (which can be correlated with the desired signals) corrupting the measurements. We consider two different criteria to measure the performance of the selected sensors; average error and minimax analysis. For each case, the cost function is defined over the reconstruction algorithm (or matrix in the linear case), which in turn, explicitly determines the selected sensors. Therefore, minimizing the cost function with some sparsity constraints on the reconstruction algorithm results in the best subset of sensors and as to how we recover the desired signals from the selected measurements. In this paper, we consider the problem for the linear measurement system in various settings and derive the optimization problems. Finally, we propose various methods to solve these problems, and show the effectiveness of the proposed algorithms through simulations.

Learning dictionary for efficient signal compression

We consider the problem of learning dictionaries for data compression. Different from ordinary learning methods, the objective is to design a dictionary such that the signal has a low entropy representation in the basis of the dictionary, rather than giving a sparse or low-energy representation. To achieve this goal, we need to consider the effect of quantization on the rate-distortion curve as well as an estimation of the distributions of the coefficients. Based on this probability estimation, the coefficients are computed, quantized and then entropy-coded. As such, we have developed algorithms for different classes of dictionaries; orthonormal, union of orthonormals and general dictionaries with unit-norm atoms, to iteratively learn the dictionary and the distribution models of the coefficients. A mixture of Gaussians is adopted to estimate the probability and is updated using the expectation maximization algorithm together with the dictionary learning. Simulation results on the real seismic data show the effectiveness of the proposed algorithm compared to ordinary dictionary learning methods.

Mixture source identification in non-stationary data streams with applications in compression

We consider a non-stationary data stream in which the data statistics may change abruptly from one sample to another, i.e. each sample might be generated from a different (unknown) source in a mixture of K sources. The problem of identifying the models and parameters of K sources, as well as the source switching model is investigated. We proposed an algorithm based on Bayesian Information Criterion and Expectation Maximization to determine the models and estimate the mixture parameters. The estimated data generation model can be used in memory-assisted universal compression to decrease the coding rate further. Simulation results confirmed that using the proposed algorithm for source identification and universal compression can significantly decrease the compression redundancy.

Quantization in Molecular Signal Sensing via Biological Agents

One of the long-term goals of synthetic biology is to reliably engineer biological systems that perform human-defined functions such as sensing, monitoring, and processing. Molecular sensing via biological cells is often performed through receptors which interact with the signal molecules. The ligand receptors in bacteria are one of the most studied examples of such phenomenon. In this paper, we study the distortion in sensing and estimation of the concentration of molecular signals by synthetic biological agents equipped with ligand receptors. The sensing distortion is caused by random measurement of the molecular signal by the ligand receptors and the quantization of the cell output via finite number of levels. First, we consider the case where the prior distribution of the molecules in the environment is known and study the performance of the optimum as well as uniform quantizers. Next, we consider robust (minimax) quantizers, where the distribution of the molecules is unknown a priori. We study the behavior of the quantizer as a function of the number of ligand receptors and number of quantization levels. By comparing with the theoretical limits, we derive approximate bounds for the number of quantization levels versus the number of ligand receptors for good quantization performance.

Near optimal representative subset selection from short sequences generated by a stationary source

We consider the problem of representative subset selection for model training and identification, particularly for the applications in universal compression. We used the Kullback-Leibler divergence to measure the distance between the estimated model from the representative subset and the source model resulting from the entire data in the set. As directly solving the original projection problem is NP-hard and not practical for large data-sets, we proposed a different approximate algorithm, based on ℓ2 optimization with ℓ0 constraints. Furthermore, we derive an upper bound for the KL-Divergence that relates monotonically (increasingly) to the ℓ2 cost function. Hence, we can bound KL-divergence penalty by minimizing the ℓ2-norm. Using experimental results, we confirm the effectiveness of the proposed ℓ2-norm method.

Micro-RNA profile detection via factor graphs

Recent studies have shown that micro-RNAs (miRNAs) play a key role in inter-cell communication in humans. More importantly, irregular patterns over specific miRNAs have been linked to certain types of cancer and cardiac diseases. In this paper, we introduce a general framework to sense environmental miRNAs and detect certain irregular patterns. We use a sensor cell (i.e., biosensor) array comprising of various genes whose expression can be suppressed through miRNAs of interest. Interference and noise are major issues in miRNA sensing via such a cell array. In particular, every miRNA may have a footprint on multiple biosensors and each biosensor in the array may be affected by multiple miRNAs. We present a probabilistic model capturing this phenomenon and solve the detection problem via a factor graph. Since, the exact values of the input miRNAs are not needed, fewer observation are required to achieve the same level of pattern-detection accuracy relative to directly measuring the concentration. Finally, we use Belief Propagation, a message-passing algorithm, to infer the presence of irregular patterns. Our model-based data suggests significant improvement in performance.

Error correction for approximate computing

Approximate computing, which sacrifices the accuracy during computation, is a promising technology to save energy. However, large number of computation errors may violate the accuracy requirement of certain applications and should be corrected. Consider a Graphical Processing Unit (GPU) with multiple Streaming Multiprocessors (SMs), where some of these SMs perform accurate computation while the others perform approximate computation. Provided the approximate outputs are correlated with other accurate outputs, we exploit this relation and model the approximate computation process as a communication process. Then the problem of error correction transforms to a problem of decoding and we want to solve it with certain error correction code. Different from the classical communications process, approximate computing raises additional constraints on the code design. In this paper, we propose a semi-regular LDPC code satisfying these constraints and prove this code can be perfectly decoded. Certain properties of the code are analyzed and simulations are provided to verify the statement.