1. An integrated circuit architecture for compressive sensing (CS) reconstruction comprising: a vector computation core comprising a plurality of processing elements inter-connected in parallel that is dynamically configured to perform vector operations using microcode generated by a global control unit; a scalar computation core configured to perform scalar operations, wherein the scalar computation core comprises a comparator, a sequential divider, and a plurality of adders, wherein the vector computation core and the scalar computation core are linked by data-path memories and are configured to cascade in a pipeline as a processing unit and configured to execute correlation sorting, folded inner product, forward substitution, and backward substitution operations; a shift register logic configured to provide latency in feedback paths associated with the plurality of processing elements and in a global feedback path between the vector and scalar computation cores, wherein the global feedback path links an adder in the scalar computation core to the plurality of processing elements in the vector computation core into parallel loops configured to execute forward substitution and backward substitution operations; a plurality of data-path memories each comprising a memory controller and configured to connect the vector and scalar computation cores, where the plurality of data-path memories are configured to provide data-flow control using the plurality of memory controllers and the plurality of data-path memories comprises: at least one data-path memory configured to receive and store CS sampled input data; at least one data-path memory configured to store an active set of values; at least one data-path memory configured to store a residual error estimate; and at least one data-path memory configured to store an estimated output data signal; the global control unit that is a finite state machine configured to synchronize and coordinate the plurality of memory controllers and the vector and scalar computation cores to iterate between a plurality of configurations to jointly perform a selective set of vector and scalar operations using: a first atom searching configuration of the vector and scalar computation cores, and the plurality of data-path memories in which a single atom is selected by maximizing its correlation coefficients with the residual error estimate and added to the active set of values associated with the estimated output data signal; a second least squares solving configuration in which the shift register logic, the vector and scalar computation cores, and the plurality of data-path memories are configured to solve a series of linear equations relating the estimated output data signal to the CS sampled input data to determine updates for the estimated output data signal that minimizes an error measure determined using the updated estimated output data signal and the CS sampled input data; and a third estimation update configuration of the vector and scalar computation cores, and the plurality of data-path memories, in which the estimated output data signal estimate is updated based upon the solution to the series of linear equations and the residual error estimate; wherein the global control unit is configured to: set the residual error estimate to an initial value equal to the CS sampled input data; set the plurality of memory controllers of the plurality of data-path memories and the vector and scalar computation cores to their initial states; and iterate between the first, second and third configurations until the residual error estimate falls below a predetermined threshold, wherein the computation cores are time-multiplexed using dynamic configuration to iterate between the first, second, and third configurations.