Modulo Sampling in Shift-Invariant Spaces: Recovery and Stability Enhancement

Sampling shift-invariant (SI) signals with a high dynamic range poses a notable challenge in the domain of analog-to-digital conversion (ADC). It is essential for the ADC's dynamic range to exceed that of the incoming analog signal to ensure no vital information is lost during the conversion process. Modulo sampling, an approach initially explored with bandlimited (BL) signals, offers a promising solution to overcome the constraints of dynamic range. In this paper, we expand on the recent advancements in modulo sampling to encompass a broader range of SI signals. Our proposed strategy incorporates analog preprocessing, including the use of a mixer and a low-pass filter (LPF), to transform the signal into a bandlimited one. This BL signal can be accurately reconstructed from its modulo samples if sampled at slightly above its Nyquist frequency. The recovery of the original SI signal from this BL representation is then achieved through suitable filtering. We also examine the efficacy of this system across various noise conditions. Careful choice of the mixer plays a pivotal role in enhancing the method's reliability, especially with generators prone to instability. Our approach thus broadens the framework of modulo sampling's utility in efficiently recovering SI signals, pushing its boundaries beyond BL signals while sampling only slightly above the rate needed for a SI signal.

Efficient Convolutional Forward Modeling and Sparse Coding in Multichannel Imaging

This study considers the Block-Toeplitz structural properties inherent in traditional multichannel forward model matrices, using Full Matrix Capture (FMC) in ultrasonic testing as a case study. We propose an analytical convolutional forward model that transforms reflectivity maps into FMC data. Our findings demonstrate that the convolutional model excels over its matrix-based counterpart in terms of computational efficiency and storage requirements. This accelerated forward modeling approach holds significant potential for various inverse problems, notably enhancing Sparse Signal Recovery (SSR) within the context LASSO regression, which facilitates efficient Convolutional Sparse Coding (CSC) algorithms. Additionally, we explore the integration of Convolutional Neural Networks (CNNs) for the forward model, employing deep unfolding to implement the Learned Block Convolutional ISTA (BC-LISTA).