Spiking Learned ISTA for Inverse Problems with Finite-Time Convergence Analysis

Deep unfolding offers an interpretable framework for learned sparse recovery. Learned Iterative Shrinkage-Thresholding Algorithm (LISTA) unfolds sparse-recovery iterations into a trainable reconstruction network. However, it represents the recovered coefficients as real-valued activations processed by dense multiply-accumulates. By contrast, a spiking implementation can represent them through sparse signed spike trains and replace dense coefficient multiplications with event-triggered accumulations. We therefore propose Spiking LISTA (S-LISTA), which replaces LISTA soft-thresholding with a Signed Soft-Threshold Integrate-and-Fire (SST-IF) unit that uses paired non-leaky integrate-and-fire neurons for the positive and negative branches and coordinate- and stage-specific scales to balance firing-rate resolution and saturation. We prove a finite-time approximation bound for SST-IF, with error proportional to the scale divided by the number of timesteps, and propagate this error through a fixed-depth unfolded network. The resulting bound shows that the spiking error of S-LISTA decreases as the number of timesteps increases. We evaluate S-LISTA on synthetic support recovery, natural-image compressive sensing, compressed-sensing MRI, and low-precision deployment. S-LISTA preserves the support-recovery behavior of its non-spiking counterpart, and after fine-tuning, it closely matches the corresponding backbone on Set11, BSD68, and MRI while remaining competitive with unfolded baselines. Under low-precision deployment, S-LISTA remains stable under reduced weight precision and avoids the sharp failures observed in its non-spiking counterpart under aggressive post-training quantization. Its measured spike activity further suggests that event-driven affine execution can reduce synaptic arithmetic.