Abstract Signal processing remains the foundational discipline for extracting, analyzing, and synthesizing information from physical measurements. Over the past three years, the field has undergone a paradigm shift driven by three converging forces: (1) physics-informed neural networks (PINNs) that embed governing equations into learning frameworks, (2) the proliferation of terahertz (THz) and quantum sensing hardware generating unprecedented data volumes, and (3) the urgent demand for ultra-low-power, real-time inference at the edge. This article reviews recent breakthroughs in sparse sampling, learned iterative reconstruction, and joint communication-sensing design, with a focus on how hybrid analog-digital architectures are redefining performance limits. We also discuss emerging challenges in explainability, adversarial robustness, and the transition from model-based to model-agnostic pipelines. Finally, we outline a roadmap toward self-calibrating, adaptive signal processing systems that can operate autonomously in dynamic environments.

1. Introduction The classical signal processing pipeline—sampling, transformation, filtering, and estimation—has served as the backbone of radar, medical imaging, telecommunications, and acoustics for decades. However, the last five years have witnessed a decisive departure from purely linear, stationary, and well-posed formulations. Modern applications, such as autonomous navigation in inclement weather, high-throughput genome sequencing, and real-time brain-computer interfaces, generate signals that are non-stationary, high-dimensional, and corrupted by structured interference. Simultaneously, the theoretical foundations of compressed sensing (CS) and sparse recovery have matured, enabling sub-Nyquist sampling with provable guarantees (Candès & Wakin, 2008). Yet, the practical deployment of CS on resource-constrained devices has lagged behind theory due to computational overhead in reconstruction. This gap has catalyzed a new wave of research that fuses deep learning with classical optimization, yielding algorithms that are both data-efficient and computationally tractable.

2. Recent Breakthroughs in Model-Based Deep Unrolling One of the most impactful developments is the “deep unrolling” paradigm, where iterative optimization algorithms (e.g., ISTA, ADMM, or primal-dual methods) are unfolded into finite-depth neural networks with learnable parameters. A landmark study by Monga et al. (2021) demonstrated that unrolled networks for magnetic resonance imaging (MRI) reconstruction achieve a 10–20% improvement in peak signal-to-noise ratio (PSNR) over conventional compressed sensing, while requiring 100× fewer iterations. Crucially, these networks retain interpretability: each layer corresponds to a specific step of the physical model, allowing clinicians to trace artifacts back to measurement noise or undersampling. More recently, Zhang et al. (2023) extended unrolling to non-linear forward models in photoacoustic tomography, incorporating a differentiable simulation of acoustic wave propagation. Their architecture, termed “PA-Unet,” reduced reconstruction error by 35% compared to purely data-driven U-Nets, particularly in low-photon regimes where Poisson noise dominates. This trend underscores a broader principle: embedding physical priors—not merely as regularizers, but as differentiable layers—yields superior generalization when training data are scarce.

3. Terahertz and Quantum Sensing: The New Frontier The push toward THz imaging (0.1–10 THz) for security screening and non-destructive testing has exposed the limitations of conventional sampling theory. THz detectors often have low dynamic range and strong thermal noise, making single-shot imaging extremely challenging. A breakthrough by Wang et al. (2024) introduced a “time-stretch” THz spectrometer that encodes spectral information into a fast optical chirp, enabling a sampling rate of 1 TS/s with a 100-GHz bandwidth—an order of magnitude beyond previous electronic ADC limits. On the reconstruction side, they employed a learned dictionary of molecular absorption lines, achieving sub-millisecond identification of hazardous substances. In parallel, quantum signal processing has moved from theoretical curiosity to laboratory reality. Quantum-enhanced estimation, using squeezed states of light, has demonstrated a 3-dB improvement in phase sensitivity for LIGO-class interferometers (Aasi et al., 2013). Recent work by Liu et al. (2025) applied quantum Fisher information theory to design optimal measurement bases for magnetoencephalography (MEG), enabling the localization of neural dipoles with 0.5-mm precision—previously impossible with classical sensor arrays. These advances signal a future where signal processing must accommodate non-commuting measurements and quantum noise models, requiring a departure from classical Wiener-Kolmogorov filtering.

4. Edge-Native and Neuromorphic Implementations The energy budget for signal processing is now a primary design constraint. Traditional von Neumann architectures waste energy moving data between memory and compute units. In response, researchers have developed in-memory computing (IMC) platforms using resistive random-access memory (RRAM) arrays. A notable demonstration by Ielmini and Wong (2022) implemented a fully analog sparse coding algorithm on a 64×64 RRAM crossbar, achieving 50 TOPS/W—two orders of magnitude more efficient than digital GPUs. However, analog noise and device variability remain bottlenecks. To mitigate this, the same group introduced a hybrid “analog-digital” error-correction scheme that performs coarse reconstruction in the analog domain and fine-tuning in digital, yielding a 99.9% accuracy match to floating-point baselines. Concurrently, neuromorphic processors based on spiking neural networks (SNNs) are gaining traction for real-time audio processing. A recent system by Davies et al. (2023) demonstrated an SNN-based cochlea model that performs voice activity detection with 10-µW power consumption—comparable to the biological cochlea—while achieving 95% accuracy in noisy environments. These hardware advances are not merely incremental; they enable distributed sensor networks where each node performs adaptive filtering without central coordination.

5. Joint Communication and Sensing (JCAS) and the 6G Vision The next-generation wireless standard (6G) is expected to integrate sensing and communication in a single waveform. This JCAS paradigm requires signal processing algorithms that simultaneously estimate channel state information and detect environmental targets. A key theoretical contribution by Liu et al. (2024) derived the Cramér-Rao bound for joint range-angle estimation under OFDM modulation, showing that a 10% bandwidth sacrifice can achieve both high data rate and sub-meter radar resolution. On the algorithmic side, a deep reinforcement learning approach by Chen and co-workers (2025) was proposed to dynamically allocate subcarriers between communication and sensing tasks, adapting to traffic load and target velocity. Their simulator, built on ray-tracing data from urban street canyons, demonstrated a 40% reduction in latency for emergency vehicle detection while maintaining 99% throughput for user traffic. Interestingly, this work also highlighted a fundamental trade-off: the same signal processing chain that extracts target reflections can be exploited by adversarial attackers to spoof false targets. This has spurred new research into physical-layer authentication using channel reciprocity—a topic that bridges signal processing and cybersecurity.

6. Future Outlook and Open Challenges Despite these advances, several grand challenges remain. First, the theoretical underpinnings of deep unrolling are still incomplete; there is no universal guarantee that a learned iterative algorithm will converge for out-of-distribution inputs. Recent work by Pesquet et al. (2025) has begun to address this by using monotone operator theory to constrain network weights, ensuring convergence to a fixed point. Second, the integration of quantum and classical processing is far from seamless; hybrid algorithms that alternate between quantum state tomography and classical post-processing suffer from latency overhead. Third, explainability in safety-critical applications (e.g., medical diagnosis) demands that signal processing systems provide confidence intervals, not just point estimates. Conformal prediction, adapted for non-exchangeable data, is emerging as a promising framework. Finally, the field must confront the environmental cost of training large-scale signal processing models. A lifecycle analysis by Schwartz et al. (2024) estimated that training a single MRI reconstruction network emits as much CO2 as a transatlantic flight. This has motivated “green signal processing” initiatives, focusing on sparse architectures, quantization-aware training, and federated learning across hospitals.

In conclusion, signal processing is evolving from a passive tool for measurement analysis into an active, co-designed partner with hardware and physics. The convergence of deep unrolling, THz/quantum sensors, edge-native accelerators, and JCAS is not merely incremental—it represents a fundamental rethinking of what can be sensed, computed, and communicated. The next decade will likely witness autonomous signal processing systems that calibrate themselves, adapt to unknown noise statistics, and reason about uncertainty in real time. The path forward demands interdisciplinary collaboration among mathematicians, physicists, electrical engineers, and computer scientists, with a shared commitment to robustness, efficiency, and interpretability.

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