Abstract: An exemplified methods and systems provides a Volterra filter network architecture that employs a cascaded implementation and a plurality of kernels, a set of which is configured to execute an nth order filter, wherein the plurality of kernels of the nth order filters are repeatedly configured in a plurality of cascading layers of interconnected kernels to form a cascading hierarchical structure that approximates a high-order filter.

Abstract: An exemplified methods and systems provides a Volterra filter network architecture that employs a cascaded implementation and a plurality of kernels, a set of which is configured to execute an nth order filter, wherein the plurality of kernels of the nth order filters are repeatedly configured in a plurality of cascading layers of interconnected kernels to form a cascading hierarchical structure that approximates a high-order filter.

Abstract: A computer-implemented method of detecting a foreground data in an image sequence using a dual sparse model framework includes creating an image matrix based on a continuous image sequence and initializing three matrices: a background matrix, a foreground matrix, and a coefficient matrix. Next, a subspace recovery process is performed over multiple iterations. This process includes updating the background matrix based on the image matrix and the foreground matrix; minimizing an L?1 norm of the coefficient matrix using a first linearized soft-thresholding process; and minimizing an L?1 norm of the foreground matrix using a second linearized soft-thresholding process. Then, background images and foreground images are generated based on the background and foreground matrices, respectively.

Abstract: A computer-implemented method of detecting a foreground data in an image sequence using a dual sparse model framework includes creating an image matrix based on a continuous image sequence and initializing three matrices: a background matrix, a foreground matrix, and a coefficient matrix. Next, a subspace recovery process is performed over multiple iterations. This process includes updating the background matrix based on the image matrix and the foreground matrix; minimizing an L?1 norm of the coefficient matrix using a first linearized soft-thresholding process; and minimizing an L?1 norm of the foreground matrix using a second linearized soft-thresholding process. Then, background images and foreground images are generated based on the background and foreground matrices, respectively.