ReLU-based hard thresholding (RHT) and ReLU-based hard thresholding pursuit (RHTP) are recently developed algorithms for non-negative sparse signal recovery. Although the restricted isometry property of order$3s$guarantees robust recovery when the restricted isometric constants satisfy$\delta _{3s} < 0.618$for RHT and$\delta _{3s} < 0.57735$for RHTP, numerical results show that RHTP consistently outperforms RHT, highlighting a gap between theoretical guarantees and observed performance. This work addresses this gap by deriving relaxed sufficient conditions for robust recovery based on$\delta _{2s}$. Specifically, we establish bounds for$\delta _{2s}$, with$\delta _{2s}< 0.379514$for RHTP and$\delta _{2s}< 0.357282$for RHT, demonstrating the broader applicability of RHTP. These results strengthen the theoretical guarantees, bringing them closer to empirical observations and advancing the understanding of ReLU-based methods.

The Hard Thresholding Pursuit (HTP) algorithm is a widely recognized method for sparse signal recovery, supported by rigorous theoretical guarantees based on the restricted isometry constants$\delta _{3s}$and$\delta _{2s}$. However, the existing analysis framework has not been extended to lower-order restricted isometry conditions. In this work, we address this gap by establishing a novel recovery guarantee for HTP under a relaxed condition involving$\delta _{s+1}$. Specifically, we show that HTP achieves robust recovery whenever$\delta _{s+1} < \sqrt{1/37} \approx 0.1644$, which surpasses the IHT-based bound of$\delta _{s+1} < 0.1545$based on the optimal step-length 1. To our knowledge, this result provides the first lower-order restricted isometry guarantee for HTP, in terms of$\delta _{s+1}$.

Filter pruning method is an effective approach to eliminate redundant filters in convolutional neural networks. Most of the existing techniques rely on threshold parameters for filter selection and employ multi-shot pruning, resulting in increased computational overhead. In addition, many methods primarily optimize test accuracy while overlooking robustness to noise, which is critical in practical and safety-critical applications. Since Incoherent Unit Norm Tight Frames (IUNTFs) are inherently robust to noise, we propose a filter pruning technique that removes redundant filters such that the retained set approximates an IUNTF structure. This structure enhances noise robustness and promotes the extraction of diverse and complementary features. Unlike conventional approaches, the proposed framework requires no threshold tuning and adopts a one-shot pruning strategy. Experimental results on the CIFAR-10 dataset using VGG-16, ResNet-56, and GoogLeNet demonstrate that the proposed method achieves robustness under noise and improved accuracy compared to existing approaches while pruning 85.12%, 57%, and 59% of the parameters and 69.66%, 57%, and 58% of the FLOPs, respectively.

The construction of binary matrices has attained significance due to its potential for hardware-friendly implementation and appealing applications in compressed sensing (CS). A class of binary matrices with low coherence and flexible row sizes can be constructed from Euler Squares (ES). In this paper, we introduce a generalization of the ES concept, namely, Generalized Euler Square (GES). We show that the binary matrices designed from GES provide significant improvements in column size compared to the ones constructed from Euler square. Exploiting the properties of GES, we obtain that such constructed binary matrices possess block orthogonal structure. As a result, such binary matrices are suitable for the recovery of block sparse signals.

Frames with a large minimum angle between any two distinct frame vectors are desirable in many present day applications. For a unit norm frame, the absolute value of the cosine of the minimum frame angle is also known as coherence. Two frames are equivalent if one can be obtained from the other via left action of an invertible linear operator. Frame angles can change under the action of a linear operator. Most of the existing works solve different optimization problems to find an optimal linear operator that maximizes the minimal frame angle (in other words, minimizes the coherence). In the present work, nevertheless, we consider the question: Is it always possible to find an equivalent frame with smaller coherence for a given frame. In this paper, we derive properties of the initial unit norm frame that can ensure an equivalent frame with strictly larger minimal frame angle compared to the initial one. It turns out that the nullspace property of a certain matrix obtained from the initial frame can guarantee such an equivalent frame. We also present the numerical results that support our theoretical claims.

Disjunct matrices play a central role in non-adaptive group testing, as they provide necessary and sufficient conditions for identifying defective items from a large population using a small number of tests. In this paper, we show that binary disjunct matrices can also be very useful for recovering sparse signals from underdetermined linear measurements. They admit non-iterative, ultra-low complexity recovery of sparse signals. Binary measurement matrices have the added benefit of being friendly for hardware implementation. Further, we generalize the notion of disjunctness to matrices with arbitrary (non-binary) entries and show that such matrices also admit similar fast sparse vector recovery algorithms. We empirically demonstrate that disjunct matrices can recover denser signals than recent non-iterative sparse recovery algorithms.

In the recent past, various methods have been proposed to construct deterministic compressed sensing (CS) matrices. Of interest has been the construction of binary sensing matrices as they are useful for multiplierless and faster dimensionality reduction. In most of these binary constructions, the matrix size depends on primes or their powers. In this study, we propose a composition rule which exploits sparsity and block structure of existing binary CS matrices to construct matrices of general size. We also show that these matrices satisfy optimal theoretical guarantees and have similar density compared to matrices obtained using Kronecker product. Simulation work shows that the synthesized matrices provide comparable results against Gaussian random matrices.