IHT Algorithm Source Code Implementation - Classic Compressed Sensing Approach

The Iterative Hard Thresholding (IHT) algorithm represents a fundamental approach in compressed sensing, primarily designed to reconstruct sparse signals from limited measurement data. The core methodology involves iteratively refining signal estimates while enforcing sparsity through hard thresholding operations at each iteration cycle.

The IHT algorithm follows these key computational steps:

Initialization Phase: Set initial signal estimate (typically a zero vector) and define maximum iteration count. Code implementation requires initializing variables for signal reconstruction and convergence parameters.

Gradient Update: Compute the residual between current estimate and observed measurements, then update the signal estimate using gradient descent methodology. This step involves matrix multiplication operations between measurement matrices and residual vectors.

Hard Thresholding Operation: Apply hard thresholding to the updated signal by retaining only the K-largest coefficients (where K represents signal sparsity level) while setting all other coefficients to zero. This operation typically utilizes sorting algorithms to identify dominant coefficients.

Convergence Verification: Evaluate whether the current estimate meets convergence criteria (such as sufficiently small residual error or reaching maximum iterations). If conditions are satisfied, terminate the iterative process; otherwise, return to the gradient update step. Implementation requires error calculation and loop control structures.

The IHT algorithm offers significant advantages in computational efficiency and demonstrates robust performance in sparse signal recovery scenarios. However, its effectiveness depends heavily on the Restricted Isometry Property (RIP) condition of the measurement matrix and requires prior knowledge of signal sparsity level K.

In practical applications, IHT finds extensive usage in medical imaging systems, wireless communication protocols, and image restoration tasks-particularly where data acquisition is constrained. The algorithm enables substantial reduction in required measurements while maintaining reconstruction quality. Source code implementations typically incorporate matrix computation libraries, thresholding functions, and iterative control loops, making them directly applicable for simulation studies and real-world data processing pipelines.