Method and system for image reconstruction using target attribute assisted compressive sensing

A system for image reconstruction using target attribute assisted compressive sensing, comprising:

• an initialization module, which is configured to initialize parameters comprising a residual vector rt-1, an atom set A and a number of iterations t, where rt-1 is initialized to an input compressive measurement vector y, A is initialized to an empty set, and t is initialized to 1;
• a subspace partitioning module, which is configured to generate a sequence matrix D∈Rw×h consistent with a size of an image having a width of w and a height of h, wherein R is a set of real numbers, Rw×h is a two-dimensional real matrix with w rows and h columns;
• store numbers of 1 to w×h in the sequence matrix D, and partition the sequence matrix D into a number of two-dimensional sub-blocks according to a preset size of a target and convert each of the partitioned sub-blocks in the sequence matrix D into a column vector in a column stacking manner;
• and select corresponding vectors from a dictionary space Φ with elements in each column-stacked vector as indices to form a dictionary subspace Φi, i=1, 2, . . . , k, so as to realize the partitioning of the dictionary space;
• an atom set updating module, which is configured to compute a projection
• P
• i
• =
• Φ
• i
• T
• ⁢
• r
• t
• -
• 1
• 
• Φ
• i
• 
• 2
• 2
• of the residual vector rt-1 on each of the partitioned dictionary subspaces Φi and calculate an energy Ei=∥Pi∥22, i=1, 2, . . . k of the projection, wherein T is a mathematical transpose function;
• and then find an index subscript λt=arg maxi=1kEi, which corresponds to a maximum energy of the projection, find a corresponding dictionary subspace Φλt according to the obtained index subscript λt, update the atom set to At=[At-1, Φλt], where At is the currently updated atom set and At-1 is the last iteratively updated atom set;
• and after the atom set At is updated every time, set the dictionary subspace Φλt corresponding to λt to 0 for ensuring that its value will not be repeatedly taken;
• a sparse coefficient updating module, which is configured to perform a least square estimation on sparse coefficients by utilizing the current iteratively updated atom set At, set the sparse coefficient xt=(AtTAt)−1AtTy of a signal on the atom set At, wherein T is a mathematical transpose function, and update the residual vector rt=y−Axt;
• and
• an outputting module, which is configured to perform an iteration termination determination according to the obtained updated residual vector rt, and when a norm of the residual vector rt is greater than a preset constant ε, jump to the atom set updating step for performing a next iteration, otherwise terminate the iteration and output a final estimated value of the sparse coefficient of the signal;
• wherein the subspace partitioning module is specifically configured to:
• set a size of a template to a×b, it is assumed that a size of the target is B=a×b, and generate a two-dimensional sequence matrix D∈Rw×h corresponding to the size of the image, where a and b are a priori width and a priori height of the target, respectively, and w and h are a width and a height of a small target image, respectively, w is divisible by a, and h is divisible by b, use elements in the two-dimensional sequence matrix D as column-stacking values corresponding to positions of pixels in the image, and partition the two-dimensional sequence matrix D according to a priori size of the target to obtain D={B1, B2, . . . , Bi, . . . Bk}, where
• k
• =
• h
• b
• ×
• w
• a
• ;
• set the size of the template to a value which is capable of completely covering the target and may divide the width and height of the image without remainder when the width w of the image is not divisible by the priori width of the target a and/or the image height h is not divisible by the priori height of the target b;
• and
• convert each of the partitioned sub-blocks in the sequence matrix D into a column vector in a column stacking manner, and select corresponding vectors from a dictionary subspace Φ with elements in each column-stacked vector as indices to form a dictionary subspace Φi, i=1, 2, . . . , k, that is, partition the dictionary subspace, Φi=Φ(Vec(Bi)), i=1, 2, . . . , k.