Principles of Modern Radar - Volume 2 1891121537

5.3 SR Algorithms 175of the TV norm and nondiagonal weighting on the l 1 portion of the cost function consideredhere. Another strong contribution of [61] is an extensive numerical comparison of severalleading algorithms, including examples not considered in this chapter, on a series of testproblems.5.3.2.2 Hard ThresholdingWe now turn our attention toward hard thresholding algorithms. Iterative Hard Thresholding(IHT) applies the operator η h {x, s} after each gradient step. This hard thresholdingfunction leaves the s coefficients of x with the largest magnitudes 30 unchanged and setsall others to zero. In particular, the IHT algorithm [80] is given byˆx k+1 = η h{ ˆx k − μ∇ f ( ˆx k ), s } (5.33)By construction every iteration produces a solution such that ∥ ˆx k∥ ∥0≤ s. Thus, if thealgorithm parameter is set too low, we are guaranteed a priori to never find the correctsolution. Naturally, this choice is analogous to the choice of λ, τ,orσ when using the l pnorm-based algorithms.A RIP-based performance guarantee for IHT is provided in [80,Theorem 4]. After weselect the sparsity parameter s for IHT, then provided that R 3s (A)