Spectral unmixing for visualization of samples

1. A computer-implemented method comprising:

a. acquiring a first sequence of multiple images of a sample, with each image in the first sequence corresponding to a different spectral weighting function and with the sample comprising multiple components each having a different spectral signature;

b. unmixing the first sequence of images into data corresponding to a first set of unmixed images, wherein each unmixed image in the first set corresponds to a spatial distribution in the sample of a different one of the multiple components at a first time;

c. acquiring one or more additional images of the sample, with each of the additional images corresponding to a different one of the spectral weighting functions and combining the additional images with one or more of the images in the first sequence to form a second sequence of images;

d. unmixing the second sequence of images into data corresponding to a second set of unmixed images, wherein each unmixed image in the second set corresponds to a spatial distribution in the sample of a different one of the multiple components at a second time; and

e. displaying information about the sample as a function of time based on the data corresponding to the first and second sets of unmixed images.

2. The method of claim 1 , further comprising:

a. acquiring one or more further additional images of the sample, with each of the further additional images corresponding to a different one of the spectral weighting functions and combining the further additional images with one or more of the images in the second sequence to form a third sequence of images; and

b. unmixing the third sequence of images into data corresponding to a third set of unmixed images, wherein each unmixed image in the third set corresponds to a spatial distribution in the sample of a different one of the multiple components at a third time,

c. wherein the displaying of the information as a function of time is based on the data corresponding to the first, second, and third sets of unmixed images.

3. The method of claim 2 , further comprising

a. acquiring a fourth sequence of multiple images of the sample, with each image in the fourth sequence corresponding to a different one of the spectral weighting functions and wherein none of the images in the fourth sequence were acquired as part of any of the first, second, and third sequences;

b. unmixing the fourth sequence of images into data corresponding to a fourth set of unmixed images, wherein each unmixed image in the fourth set corresponds to a spatial distribution in the sample of a different one of the multiple components at a fourth time;

c. thereafter acquiring one or more additional images of the sample, with each of the thereafter-acquired additional images corresponding to a different one of the spectral weighting functions and combining the thereafter-acquired additional images with one or more of the images in the fourth sequence to form a fifth sequence of images; and

d. unmixing the fifth sequence of images into data corresponding to a fifth set of unmixed images, wherein each unmixed image in the fifth set corresponds to a spatial distribution in the sample of a different one of the multiple components at a fifth time,

e. wherein the displaying of the information as a function of time is based on the data corresponding to at least the five sets of unmixed images.

4. The method of claim 1 ,

a. wherein each sequence comprises M images corresponding to a common set of the different spectral weighting functions, and

b. wherein the one or more additional images comprise K<M additional image(s).

5. The method of claim 4 , wherein there are N<M unmixed images in each set of unmixed images.

6. The method of claim 4 , wherein K=1.

7. The method of claim 1 , further comprising repeating the acquiring of additional images and the unmixing of additional sequences to provide a real-time display of information about the sample as a function of time, wherein each additional sequence comprises at least some images from a prior sequence and one or more newly acquired images so that each additional sequence comprises at least M>1 images corresponding to a common set of the different spectral weighting functions.

8. The method of claim 1 , wherein the unmixing steps comprise a linear decomposition into the spectral signatures of the components of the sample.

9. The method of claim 1 , wherein unmixing the second sequence of images into the data corresponding to the second set of images comprises:

for each of the images in the first set of unmixed images, determining a difference between the image in the first set of unmixed images and an image in the second set of unmixed images that corresponds to a common spectral weighting function; and

adjusting the data corresponding to the image in the first set of unmixed images by an amount proportional to the difference.

10. The method of claim 9 , wherein for each of the images in the first set of unmixed images, the amount proportional to the difference corresponds to a proportionality constant for a component corresponding to the image, and wherein the proportionality constants for the components are given by a vector corresponding to an inverse of a matrix formed by the spectral signatures of the components.

11. The method of claim 1 , wherein the displaying comprises displaying any change between the first and second sets of unmixed images at a rate faster than 1 Hz.

12. The method of claim 1 , further comprising:

a. combining the second set of unmixed images to form an estimated spectrum of the sample;

b. combining the second sequence of images to form an actual spectrum of the sample;

c. comparing the actual spectrum of the sample to the estimated spectrum of the sample to determine an extent of errors in the second set of unmixed images; and

d. displaying information indicative of the comparison.

13. The method of claim 8 , further comprising

a. for one or more locations of the sample, comparing actual signal corresponding to at least one of the sequences of images to a reconstructed signal based on the corresponding linear decomposition to determine a residual error for the linear decomposition; and

b. displaying information indicative of the comparison.

14. The apparatus of claim 1 , wherein the electronic processor is configured to unmix the second sequence of images into the data corresponding to the second set of images by:

for each of the images in the first set of unmixed images, determining a difference between the image in the first set of unmixed images and an image in the second set of unmixed images that corresponds to a common spectral weighting function; and

adjusting the data corresponding to the image in the first set of unmixed images by an amount proportional to the difference.

15. The apparatus of claim 14 , wherein the electronic processor is configured so that, for each of the images in the first set of unmixed images, the amount proportional to the difference corresponds to a proportionality constant for a component corresponding to the image, and wherein the proportionality constants for the components are given by a vector corresponding to an inverse of a matrix formed by the spectral signatures of the components.

16. An apparatus, comprising:

a radiation source configured to direct radiation to a sample comprising multiple components each having a different spectral signature;

a detector configured to receive radiation from the sample; and

an electronic processor configured to:

a. acquire a first sequence of multiple images of the sample based on radiation measured by the detector, with each image in the first sequence corresponding to a different spectral weighting function;

b. unmix the first sequence of images into data corresponding to a first set of unmixed images, wherein each unmixed image in the first set corresponds to a spatial distribution in the sample of a different one of the multiple components at a first time;

c. acquire one or more additional images of the sample, with each of the additional images corresponding to a different one of the spectral weighting functions;

d. combine the additional images with one or more of the images in the first sequence to form a second sequence of images;

e. unmix the second sequence of images into data corresponding to a second set of unmixed images, wherein each unmixed image in the second set corresponds to a spatial distribution in the sample of a different one of the multiple components at a second time; and

f. display information about the sample as a function of time based on the data corresponding to the first and second sets of unmixed images.

17. The apparatus of claim 16 , wherein the electronic processor is further configured to:

a. acquire one or more further additional images of the sample, with each of the further additional images corresponding to a different one of the spectral weighting functions, and combine the further additional images with one or more of the images in the second sequence to form a third sequence of images; and

b. unmix the third sequence of images into data corresponding to a third set of unmixed images, wherein each unmixed image in the third set corresponds to a spatial distribution in the sample of a different one of the multiple components at a third time,

c. wherein the displaying of the information as a function of time is based on the data corresponding to the first, second, and third sets of unmixed images.

18. The apparatus of claim 17 , wherein the electronic processor is further configured to:

a. acquire a fourth sequence of multiple images of the sample, with each image in the fourth sequence corresponding to a different one of the spectral weighting functions and wherein none of the images in the fourth sequence were acquired as part of any of the first, second, and third sequences;

b. unmix the fourth sequence of images into data corresponding to a fourth set of unmixed images, wherein each unmixed image in the fourth set corresponds to a spatial distribution in the sample of a different one of the multiple components at a fourth time;

c. thereafter acquire one or more additional images of the sample, with each of the thereafter-acquired additional images corresponding to a different one of the spectral weighting functions and combining the thereafter-acquired additional images with one or more of the images in the fourth sequence to form a fifth sequence of images; and

d. unmix the fifth sequence of images into data corresponding to a fifth set of unmixed images, wherein each unmixed image in the fifth set corresponds to a spatial distribution in the sample of a different one of the multiple components at a fifth time,

e. wherein the displaying of the information as a function of time is based on the data corresponding to at least the five sets of unmixed images.

19. The apparatus of claim 16 , wherein the electronic processor is configured so that:

a. each sequence comprises M images corresponding to a common set of the different spectral weighting functions, and

b. the one or more additional images comprise K<M additional image(s).

20. The apparatus of claim 19 , wherein the electronic processor is configured so that there are N<M unmixed images in each set of unmixed images.

21. The apparatus of claim 19 , wherein the electronic processor is configured so that K=1.

22. The apparatus of claim 16 , wherein the electronic processor is further configured to repeat the acquiring of additional images and the unmixing of additional sequences to provide a real-time display of information about the sample as a function of time, wherein each additional sequence comprises at least some images from a prior sequence and one or more newly acquired images so that each additional sequence comprises at least M>1 images corresponding to a common set of the different spectral weighting functions.

23. The apparatus of claim 16 , wherein the electronic processor is configured to perform unmixing steps that comprise a linear decomposition into the spectral signatures of the components of the sample.

24. The apparatus of claim 23 , wherein the electronic processor is further configured to:

a. for one or more locations of the sample, compare actual signal corresponding to at least one of the sequences of images to a reconstructed signal based on the corresponding linear decomposition to determine a residual error for the linear decomposition; and

b. display information indicative of the comparison.

25. The apparatus of claim 16 , wherein the electronic processor is configured to display any change between the first and second sets of unmixed images at a rate faster than 1 Hz.

26. The apparatus of claim 16 , wherein the electronic processor is further configured to:

a. combine the second set of unmixed images to form an estimated spectrum of the sample;

b. combine the second sequence of images to form an actual spectrum of the sample;

c. compare the actual spectrum of the sample to the estimated spectrum of the sample to determine an extent of errors in the second set of unmixed images; and

d. display information indicative of the comparison.

27. An apparatus comprising a non-transitory computer-readable medium storing a program that causes an electronic processor to:

a. acquire a first sequence of multiple images of a sample, with each image in the first sequence corresponding to a different spectral weighting function and with the sample comprising multiple components each having a different spectral signature;

b. unmix the first sequence of images into data corresponding to a first set of unmixed images, wherein each unmixed image in the first set corresponds to a spatial distribution in the sample of a different one of the multiple components at a first time;

c. acquire one or more additional images of the sample, with each of the additional images corresponding to a different one of the spectral weighting functions;

d. combine the additional images with one or more of the images in the first sequence to form a second sequence of images;

e. unmix the second sequence of images into data corresponding to a second set of unmixed images, wherein each unmixed image in the second set corresponds to a spatial distribution in the sample of a different one of the multiple components at a second time; and

f. display information about the sample as a function of time based on the data corresponding to the first and second sets of unmixed images.