Abstract: The present disclosure provides a system for lens-free imaging that includes a processor in communication with a lens-free imaging sensor. The processor is programmed to operate the imaging sensor to obtain a holographic image and to extract, from the holographic image, a plurality of patches, wherein the plurality of patches is a set of all fixed-size patches of the holographic image. The processor is also programmed to generate a dictionary D comprising a plurality of atoms, wherein the dictionary is generated by solving min ? , D ? ? i = 1 N ? E ? ( x i , D , ? i ) + ? ? ? R ? ( ? i ) , where N is the number of patches in the plurality of patches, xi is the ith patch of the plurality of patches, ?i represents the coefficients encoding the ith patch, E(xi, D, ?i) is a function measuring the squared error of the approximation of xi by the weighted combination of dictionary elements, and ?R (?i) is sparsity term.

Abstract: A method for segmenting a digital image includes initializing object and background seed nodes in an image, where the image is represented as a graph G=(V, E) whose nodes i?V correspond to image points and whose edges e?E connect adjacent points, where set M?V contains locations of nodes marked as seeds, set U?V contains locations of unmarked nodes, set O?M contains locations of object seed nodes, and set B?M contains locations of background seed nodes, assigning to each seed node a membership value such that ?i?O,xi=1 and ?i?B,xi=0, where each node i?V is associated with a membership xi?[0,1], and finding a membership vector x?, whose ith entry is given by xi that minimizes E p ? ( x ) = ? eij ? E ? w ij ? ? x i - x j ? pij , where each edge eij?E connecting nodes i and j in V is associated with a weight wij and an exponent pij, and ?eij?E,1?pij<?, such that xi=1 if i?O and xi=0 if i?B.

Abstract: A method for segmenting a digital image includes initializing object and background seed nodes in an image, where the image is represented as a graph G=(V, E) whose nodes i?V correspond to image points and whose edges e?E connect adjacent points, where set M?V contains locations of nodes marked as seeds, set U?V contains locations of unmarked nodes, set O?M contains locations of object seed nodes, and set B?M contains locations of background seed nodes, assigning to each seed node a membership value such that ?i?O,xi=1 and ?i?B, xi=0, where each node i?V is associated with a membership xi?[0,1], and finding a membership vector x?, whose ith entry is given by xi that minimizes E p ? ( x ) = ? eij ? E ? w ij ? ? x i - x j ? pij , where each edge eij?E connecting nodes i and j in V is associated with a weight wij and an exponent pij, and ?eij?E,1?pij<?, such that xi=1 if i?O and xi=0 if i?B.