Method for Determining a Spectrum from Time-Varying Data

A computer product comprising a non-transitory computer readable medium storing a plurality of instructions that when executed control a computer system to determine a spectrum of a sample, the instructions comprising:

• receiving a data set obtained by:
• at each of a plurality of time steps:
• operating a spectrometer to detect particles having a specified range of values of a parameter, the detecting obtaining a measurement corresponding to a number of particles detected during the time step;
• receiving an auto-correlation matrix A corresponding to a set of reference basis functions, each corresponding to a different value of the parameter;
• calculating a cross-correlation vector b by:
• for each reference basis function:
• convolving the data set with the reference basis function to obtain a cross-correlation value;
• performing for each of a plurality of iterations:
• determining a Kth estimated vector by minimizing a Kth objective function, the Kth objective function including a residual between the cross-correlation vector b and a (K−1)th estimated vector multiplied by the auto-correlation matrix A;
• performing a truncation operation using the Kth estimated vector to obtain a Kth truncated vector that is constrained to have values equal to or greater than a truncation threshold;
• accumulating a Kth noise vector that includes a (K−1)th noise vector and that includes a difference between the Kth estimated vector and the Kth truncated vector;
• and
• using the Kth noise vector to determine a (K+1)th objective function for the (K+1)th iteration;
• and
• determining the spectrum based on a final vector, the final vector being a truncated vector or an estimated vector after the K iterations.

A method of determining a mass spectrum, the method comprising:

• at each of a plurality of time steps:
• operating a spectrometer to detect particles having a specified range of values of a parameter, the detecting obtaining a measurement corresponding to a number of particles detected during the time step, thereby obtaining a data set;
• receiving, at a computer system, a first auto-correlation matrix A1 corresponding to a set of reference basis functions, each corresponding to a different time step;
• calculating, by a computer system, a first cross-correlation vector b1 by:
• for each reference basis function:
• convolving the data set with the reference basis function to obtain a cross-correlation value;
• identifying N values greater than a threshold for a first solution vector x1 that minimizes a first objective function that includes a residual between A1 and b1, the N values corresponding to N reference basis functions that have a contribution to the data set that is above the threshold;
• determining a second auto-correlation matrix A2 corresponding to the N reference basis functions;
• determining a second cross-correlation vector b2 for the N reference basis functions and the data set;
• and
• determining the mass spectrum based on a second solution vector x2 that minimizes a second objective function that includes a residual between A2 and b2.

A method of determining a spectrum of a sample, the method comprising:

• at each of a plurality of time steps:
• operating a spectrometer to detect particles having a specified range of values of a parameter, the detecting obtaining a measurement corresponding to a number of particles detected during the time step, thereby obtaining a data set;
• receiving, at a computer system, an auto-correlation matrix A corresponding to a set of reference basis functions, each corresponding to a different value of the parameter;
• calculating, by a computer system, a cross-correlation vector b by:
• for each reference basis function:
• convolving the data set with the reference basis function to obtain a cross-correlation value;
• estimating a noise vector u that corresponds to noise in the data set;
• calculating a solution vector x that solves Ax=b−u;
• and
• using the solution vector x to determine the spectrum.

A method of determining a mass spectrum of a sample, the method comprising:

• at each of a plurality of time steps:
• operating a spectrometer to detect ions, derived from the sample, having a range of values of mass to charge ratio, the detecting obtaining a measurement corresponding to a number of ions detected during the time step, thereby obtaining a data set;
• receiving, at a computer system, an auto-correlation matrix A corresponding to a set of reference basis functions, each corresponding to a different value of the mass to charge ratio;
• calculating, by a computer system, a cross-correlation vector b by:
• for each reference basis function:
• convolving the data set with the reference basis function to obtain a cross-correlation value;
• estimating, by a computer system, a solution vector x that solves Ax=b, subject to a constraint requiring all values of x to be non-negative;
• and
• using the solution vector x to determine the mass spectrum.