Compressive sensing with local geometric features
Methods and apparatuses for compressive sensing that enable efficient recovery of features in an input signal based on acquiring a few measurements corresponding to the input signal. One method of compressive sensing includes folding an image to generate first and second folds, and recovering a feature of the image based on the first and second folds without reconstructing the image. One example of a compressive sensing apparatus includes a lens, a focal plane array coupled to the lens and configured to generate first and second folds based on the image, and a decoder configured to receive the first and second folds and to recover a feature of the image without reconstructing the image. The feature may be a local geometric feature or a corner. Compressive sensing methods and apparatuses for determining translation and rotation between two images are also disclosed.
1. An apparatus for compressive sensing comprising:
a lens;
a focal plane array (FPA) coupled to the lens so as to receive an image, the FPA being configured to generate a compressed image at least in part by folding the image, the compressed image including at least one folded image; and
a decoder configured to receive the compressed image and to recover at least one feature of the image based on the compressed image and without reconstructing the image.
2. An apparatus for compressive sensing comprising:
a lens;
a focal plane array (FPA) coupled to the lens so as to receive an image, the FPA being configured to generate a compressed image at least in part by generating a hashed image by applying a hashing function to the image and applying an error correcting code to the hashed image; and
a decoder configured to receive the compressed image and to recover at least one feature of the image based on the compressed image and without reconstructing the image.
3. The apparatus of claim 2 , wherein the hashing function is a pairwise independent hashing function.
4. The apparatus of claim 2 , wherein the error correcting code includes at least one of the Chinese Remainder Theorem (CRT) code and the Reed Solomon code.
5. The apparatus of claim 1 , further comprising a digitizer configured to receive the compressed image and to output a digitized compressed image, and wherein the decoder is further configured to receive the digitized compressed image and to recover the at least one feature of the image based on the digitized compressed image.
6. The apparatus of claim 1 , wherein the decoder is further configured to recover the at least one feature of the image at least in part by:
generating a plurality of feature vectors based on the compressed image;
thresholding the plurality of feature vectors to generate a plurality of thresholded feature vectors;
clustering the plurality of thresholded feature vectors to generate a plurality of clusters; and
decoding at least one cluster of the plurality of clusters.
7. The apparatus of claim 1 , wherein the at least one feature includes at least one of a corner, a muzzle flash, and a star in the received image.
8. The apparatus of claim 1 , wherein the FPA is further configured to receive at least two images and generate at least two compressed images at least in part by folding the at least two images, and wherein the decoder is further configured to recover the at least one feature based on the at least two compressed images.
9. The apparatus of claim 8 , wherein the at least one feature includes at least one of a rotation between the at least two images and a translation between the at least two images.
10. A method of compressive sensing, comprising:
receiving, by a focal plane array (FPA) coupled to a lens, an image to provide a received image;
folding the received image to generate at least one folded image, folding the received image including superimposing a plurality of non-overlapping subsections of the image to generate the at least one folded image; and
recovering from the at least one folded image, by at least one processor coupled to the FPA, at least one feature of the image without reconstructing the received image.
11. The method of claim 10 , wherein folding the received image includes:
generating a hashed image by applying a hashing function to the received image; and
applying an error correcting code to the hashed image.
12. The method of claim 10 , wherein the at least one feature includes at least one of a corner, a muzzle flash, and a star in the received image.
13. The method of claim 10 , wherein receiving the image includes receiving at least two images, and wherein folding the received image includes folding the at least two images to generate at least two folded images.
14. The method of claim 13 , wherein recovering the at least one feature includes recovering, based on the at least two folded images, at least one of a rotation between the two images and a translation between the two images.
15. The method of claim 10 , further comprising digitizing, by a digitizer, the at least one folded image to generate a corresponding at least one digitized folded image, and wherein recovering from the at least one folded image includes recovering from the corresponding at least one digitized folded image.
16. An apparatus for compressive sensing, comprising:
a memory;
at least one processor coupled to the memory, the at least one processor configured to:
receive a compressed image, the compressed image being compressed at least in part by folding an original image, such that the compressed image includes at least one folded image;
generate a plurality of feature vectors based on the compressed image;
threshold the plurality of feature vectors to produce a plurality of thresholded feature vectors;
cluster the plurality of thresholded feature vectors to generate a plurality of clusters; and
recover at least one feature of the original image by decoding at least one cluster of the plurality of clusters.
17. The apparatus of claim 16 , wherein the at least one feature includes at least one of a corner, a muzzle flash, and a star in the original image.
18. The apparatus of claim 2 , further comprising a digitizer configured to receive the compressed image and to output a digitized compressed image, and wherein the decoder is further configured to receive the digitized compressed image and to recover the at least one feature of the image based on the digitized compressed image.
19. The apparatus of claim 2 , wherein the decoder is further configured to recover the at least one feature of the image at least in part by:
generating a plurality of feature vectors based on the compressed image;
thresholding the plurality of feature vectors to generate a plurality of thresholded feature vectors;
clustering the plurality of thresholded feature vectors to generate a plurality of clusters; and
decoding at least one cluster of the plurality of clusters.
20. The apparatus of claim 2 , wherein the FPA is further configured to receive at least two images and generate at least two compressed images, and wherein the decoder is further configured to recover the at least one feature based on the at least two compressed images.
21. The apparatus of claim 20 , wherein the at least one feature includes at least one of a rotation between the at least two images and a translation between the at least two images.