Hyperspectral image reconstruction via a compressed sensing framework

A hyperspectral video system for image reconstruction using a compressed sensing framework, the system comprising:

• a reference sensor having a total of N bands;
• a target hyperspectral camera having a multi-filter grid of a total of M bands where M<<N;
• a memory and a storage medium;
• and
• a processor in communication with said storage medium and said memory, said processor executing machine readable instructions for performing:
• constructing, for each of a plurality of sub-data cubes, a N×N representation matrix ψ, each of said sub-data cubes containing a 2D array of pixels and collectively comprising a first hyperspectral image data cube constructed from a first set of different spectral planes of a hyperspectral image captured using said reference sensor, wherein constructing each representation matrix comprises:
• creating a matrix of random numbers;
• deriving a set of natural basis vectors in a spectral direction;
• selecting a first few of said natural basis vectors to restrict said representation matrix to a space of interest;
• replacing a first few columns of said random number matrix with said selected first few natural basis vectors;
• and
• performing Gram-Schmidt ortho-normalization to obtain said representation matrix;
• retrieving, from said memory, a M×N sampling matrix φ comprising a non-square matrix filled with 1's at locations corresponding to the peak wavelengths of filters in said multi-filter grid and with remaining elements filled with 0's;
• using said constructed representation matrices and said sampling matrix to reconstruct a full signal ƒ* of a hyperspectral image captured by said target hyperspectral camera;
• and
• storing said reconstructed hyperspectral image to said storage medium.

A computer implemented method for image reconstruction using a compressed sensing framework for a hyperspectral video system, the method comprising:

• constructing, for each of a plurality of sub-data cubes a N×N representation matrix ψ, each of said sub-data cubes containing a 2D array of pixels and collectively comprising a first hyperspectral image data cube constructed from a first set of different spectral planes of a hyperspectral image captured using a reference sensor, where N is a total number of bands in said reference sensor, wherein constructing each representation matrix comprises:
• creating a matrix of random numbers;
• deriving a set of natural basis vectors in a spectral direction;
• selecting a first few of said natural basis vectors to restrict said representation matrix to a space of interest;
• replacing a first few columns of said random number matrix with said selected first few natural basis vectors;
• and
• performing Gram-Schmidt ortho-normalization to obtain said representation matrix;
• receiving a M×N sampling matrix φ comprising a non-square matrix filled with 1's at locations corresponding to the peak wavelengths of filters in a multi-filter grid of a target hyperspectral camera and with remaining elements filled with 0's, where M is a number of bands in said target camera such that M<<N;
• and
• using said constructed representation matrices and said sampling matrix to reconstruct a full signal ƒ* of a hyperspectral image captured by said target hyperspectral camera.