A group of researchers working in France and USA, leaded by N. Ducros, has uploaded an interesting paper this week.

When doing **single-pixel imaging**, one of the most important aspects you need to take into account is the kind of structured patters (functions) you are going to use. This is quite relevant because it is greatly connected with the **speed** you are going to achieve (as the number of total measurements needed for obtaining good images strongly depends on the set of functions you choose). Usually, the go-to solution for single-pixel cameras is to either choose **random functions**, or a set (family) of **orthogonal functions** (Fourier, DCT, Hadamard, etc.).

The problem with random functions is that they are not orthogonal (it is very hard to distinguish between two different random functions, all of them are similar), so you usually need to project a high number of them (which is** time consuming**). Orthogonal functions that belong to a basis are a better choice, because you can send the full basis to get “perfect” quality (i.e., without losing information due to undersampling). However, usually these functions have positive and negative values, which is something you cannot directly implement in lots of **Spatial Light Modulators** (for example, in **Digital Micromirror Devices**). If you want to implement these patterns, there are multiple workarounds. The most common one is to implement two closely-related patterns **sequentially** in the SLM to generate one function. This solves the negative-positive problem, but increases the time it takes to obtain an image in a factor two.

What Lorente-Mur et al. show in this paper is a method to generate a new family of **positive-only patterns**, derived from the original positive-negative family. This makes it possible to obtain images with a reduced number of measurements when compared to the dual or splitting approach I mentioned earlier, but still with high quality. Nice way to tackle one of the most limiting factors of single-pixel architectures.

### Handling negative patterns for fast single-pixel lifetime imaging

by Antonio Lorente Mur et al., at https://hal.archives-ouvertes.fr/hal-02017598

Abstract:

Pattern generalization was proposed recently as an avenue to increase the acquisition speed of single-pixel imaging setups. This approach consists of designing some positive patterns that reproduce the target patterns with negative values through linear combinations. This avoids the typical burden of acquiring the positive and negative parts of each of the target patterns, which doubles the acquisition time. In this study, we consider the generalization of the Daubechies wavelet patterns and compare images reconstructed using our approach and using the regular splitting approach. Overall, the reduction in the number of illumination patterns should facilitate the implementation of compressive hyperspectral lifetime imaging for fluorescence-guided surgery.

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