1. A computer-implemented method involving a fast nonlinear regression problem for use in classifying an image for an image classification system, said method comprising: receiving, at a hardware processor of a computer system, input data corresponding to a image feature design matrix (A) of values representing an image, wherein matrix (A) is an n×d matrix where n>d, and receiving data representing a corresponding output data target vector (b), and forming, at the hardware processor, a nonlinear regression problem to be solved, said nonlinear regression problem being of a form min xϵC ∥Ax−b∥ p , where x is a matrix, p is an 1-2 norm, and C is a constraint set; and modifying said nonlinear regression problem by: applying, using said hardware processor, a matrix operator T q to said matrix (A) to generate data representing a block-Vandermonde structured matrix T q (A), said T q (A) expanding matrix (A) to an (n×(dq)) matrix, said block-Vandermonde structured matrix having a fast vector-matrix method associated therewith; generating, using said hardware processor, a sparse embedding matrix for said 1-2 norm with an associated hash function; multiplying, using said hardware processor, said spare embedding matrix with said T q (A) to obtain a first product; multiplying, using said hardware processor, said spare embedding matrix with said vector (b) to obtain a second product; and running an iterative regression solver device on said modified nonlinear regression problem with p=2 to generate an output vector for said image classification system, said regression solver generating said output vector in an accelerated time according to: O(nnz(A)log 2 q) +poly(dq/ϵ) , where nnz(A) represents a number of non-zero entries of the matrix A and ϵ is a pre-specified accuracy parameter ϵ>0, wherein said output vector is used in classifying said image.