Recursive Compressed Sensing for Noisy Streaming Data Windows

The patent divides streaming data into overlapping windows of length L with step size τ, processing each window separately through compressed sensing. This segmentation allows the system to handle infinite streaming data with finite computational resources at each step, reducing overall computational complexity while maintaining signal recovery accuracy through the overlapping structure that provides redundancy across windows.

The patent applies preliminary orthogonal transformation (such as DFT or wavelet transform) to convert streaming data into a sparse domain before compressed sensing measurement. This preliminary action exploits the sparsity of signals in transformed domains, enabling accurate signal recovery from fewer measurements and reducing computational complexity compared to processing in the original domain.

The patent applies different processing strategies to different parts of the signal processing pipeline: orthogonal transformation is applied to exploit local sparsity in transformed domains, while compressed sensing measurements are applied to capture global signal characteristics. This local quality approach allows efficient representation of signals with fewer coefficients than Nyquist rate while maintaining bandwidth capture through the combined effect of sparsity exploitation and compressed measurement.

The patent changes the representation parameters of the signal by transforming from the time domain to sparse domains (frequency domain via DFT or other transform domains). This parameter change allows the same signal to be represented with fewer non-zero coefficients in the transformed domain, enabling compressed sensing to capture signal information with fewer measurements than traditional Nyquist sampling.