Hadamard Row-Wise Generation Algorithm

In this paper, we introduce an efficient algorithm for generating specific Hadamard rows, addressing the memory demands of pre-computing the entire matrix. Leveraging Sylvester's recursive construction, our method generates the required $i$-th row on demand, significantly reducing computational resources. The algorithm uses the Kronecker product to construct the desired row from the binary representation of the index, without creating the full matrix. This approach is particularly useful for single-pixel imaging systems that need only one row at a time.

Designed Dithering Sign Activation for Binary Neural Networks

Binary Neural Networks emerged as a cost-effective and energy-efficient solution for computer vision tasks by binarizing either network weights or activations. However, common binary activations, such as the Sign activation function, abruptly binarize the values with a single threshold, losing fine-grained details in the feature outputs. This work proposes an activation that applies multiple thresholds following dithering principles, shifting the Sign activation function for each pixel according to a spatially periodic threshold kernel. Unlike literature methods, the shifting is defined jointly for a set of adjacent pixels, taking advantage of spatial correlations. Experiments over the classification task demonstrate the effectiveness of the designed dithering Sign activation function as an alternative activation for binary neural networks, without increasing the computational cost. Further, DeSign balances the preservation of details with the efficiency of binary operations.

JR2net: A Joint Non-Linear Representation and Recovery Network for Compressive Spectral Imaging

Deep learning models are state-of-the-art in compressive spectral imaging (CSI) recovery. These methods use a deep neural network (DNN) as an image generator to learn non-linear mapping from compressed measurements to the spectral image. For instance, the deep spectral prior approach uses a convolutional autoencoder network (CAE) in the optimization algorithm to recover the spectral image by using a non-linear representation. However, the CAE training is detached from the recovery problem, which does not guarantee optimal representation of the spectral images for the CSI problem. This work proposes a joint non-linear representation and recovery network (JR2net), linking the representation and recovery task into a single optimization problem. JR2net consists of an optimization-inspired network following an ADMM formulation that learns a non-linear low-dimensional representation and simultaneously performs the spectral image recovery, trained via the end-to-end approach. Experimental results show the superiority of the proposed method with improvements up to 2.57 dB in PSNR and performance around 2000 times faster than state-of-the-art methods.