System and methods of regularized optimization for matrix factorization and image and video reconstruction

摘要

An image and video processing system and methods based on amplitude-modulation frequency-modulation (“AM-FM”) demodulation to provide high quality reconstructions, both visually and quantitatively. The system and methods reconstructs an image based on a Regularized Optimization (“RO”) of estimates to attain a small number of locally coherent components and simultaneously enforce a piecewise smooth constrain for one or more amplitude functions.

主权项

1. A computer system method for modeling image content comprising the steps of:
providing an input image; attaining a small number of locally coherent components by solving for the minimum ofJ⁡(a,ζ)=1p⁢f⁡(a,ζ)-bpp+λa⁢T⁡(a)+λζ⁢ζ1,s.t.⁢a≥0,ζ≤1,wherein
J(a,) is a function that takes vectors as inputs, and whose output is a scalar, a is a one dimensional column vector of image content in terms of an amplitude function, is a one dimensional column vector of image content in terms of a cosine function applied to a phase function, f(a,) represents a matrix-times-vector notation of the image content in terms of the amplitude function and the phase function, b is a one dimensional column vector of the input image approximated by the summation of a and , p is a natural and positive number representing the p-norm for finite-dimensional vector spaces, λa represents a Lagrange multiplier of the total variation of vector a, T(a) refers to the total variation of vector a, λ represents a Lagrange multiplier of the vector norm of , ∥∥1 represents the vector norm of , s. t. represents “such that” the one dimensional column vector a is greater than or equal to zero and the absolute value of the one dimensional column vector is less than or equal to one; enforcing a piecewise smooth constrain for one or more instantaneous amplitude functions; calculating a resulting amplitude function and a resulting phase function; reconstructing the input image using the resulting amplitude function and the resulting phase function to obtain a reconstructed image; and displaying the reconstructed image on a display unit.