A measurement method of batch solution concentration based on normalized compressed sensing

Measuring large batches of solution concentrations is a cumbersome task that is time consuming and involves many reagents. Determining how to improve the measurement efficiency of batch concentrations is an urgent problem to be solved. This paper introduces an efficient method for the measurement of batch solution concentrations based on normalized compressed sensing. The method is based on the sparsity of natural signals and can reconstruct the original batch concentration signals with a high level of accuracy while taking fewer measurements. The proposed method extracts subsamples from the original samples according to a sampling matrix; the number of subsamples can be much smaller than the original number of samples. Then the solution concentration of the original samples can be reconstructed by measuring the subsamples. The specific process includes sparse signal representation, non-related observation, and nonlinear optimization reconstruction. Compared with the traditional measurement method, the proposed method is demonstrably superior for the measurement of batch solution concentrations; satisfactory batch solution concentration distribution results can be obtained with a number of measurements that is much smaller than the number of samples. The proposed method will greatly reduce the time and cost of measurement.

[1]  M. Ng,et al.  The Convex Relaxation Method on Deconvolution Model withMultiplicative Noise , 2013 .

[2]  M. Lustig,et al.  Compressed Sensing MRI , 2008, IEEE Signal Processing Magazine.

[3]  D. Donoho.  For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solution , 2006 .

[4]  Bhaskar D. Rao,et al.  Sparse channel estimation via matching pursuit with application to equalization , 2002, IEEE Trans. Commun..

[5]  Faramarz Farahi,et al.  Active illumination single-pixel camera based on compressive sensing. , 2011, Applied optics.

[6]  Ali Pourmohammad,et al.  Image Denoising Based on Compressed Sensing , 2012 .

[7]  Laurent Jacques,et al.  Consistent Basis Pursuit for Signal and Matrix Estimates in Quantized Compressed Sensing , 2015, IEEE Signal Processing Letters.

[8]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[9]  Zhang Tie-shan.  Research of image reconstruction of Compressed Sensing using basis pursuit algorithm , 2011 .

[10]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[11]  A. Barron,et al.  Approximation and learning by greedy algorithms , 2008, 0803.1718.

[12]  Xun Wang,et al.  General image denoising framework based on compressive sensing theory , 2014, Comput. Graph..

[13]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[14]  Thong T. Do,et al.  Sparsity adaptive matching pursuit algorithm for practical compressed sensing , 2008, 2008 42nd Asilomar Conference on Signals, Systems and Computers.

[15]  Yunhai Xiao,et al.  A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing , 2013 .

[16]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[17]  Jie Tang,et al.  Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms , 2009, Physics in medicine and biology.

[18]  Yaakov Tsaig,et al.  Extensions of compressed sensing , 2006, Signal Process..