**1. Introduction**

In a photoacoustic computed tomography (PACT) configuration, the ultrasonic waves are collected using ultrasonic transducers placed all around the tissue. The waves are then processed through a reconstruction algorithm, and an image is generated [1–4]. The number of transducers/view angles in PACT is directly proportional to the quality of the reconstructed image. In the past several years, researchers in the field of PACT have focused on two main topics: the design of the imaging system and image reconstruction algorithms [5–9]. In the case of system design, most of the attention has been on the arrangemen<sup>t</sup> of the transducers. The simplest proposed configuration has been using a single transducer swiping around the targeted object, and a more complicated one is to use a transducer array that covers either 360 degrees around the object (ring shape) or some parts of it. The type of transducers used in the configuration of PACT can be spherical, cylindrical, or flat [10–13]. The expansion of this concept is beyond the scope of this study. The literature cited here is a limited amount of PACT work. For a more complete list, please read [14]. Readers are referred to Figure 1 of [15] and Figure 11 of [16] for further explanation of PACT imaging systems.

Several reconstruction algorithms have been designed for PACT, where a circular or linear array has been used for data acquisition [17–19]. Back-Projection (BP) and its derivations e.g., filtered back projection (FBP), could be considered as the most eminent PACT reconstruction algorithm due to their simple implementation [20]. They use the fact that pressures propagating from an acoustic source reach the detectors at different time delays, which depends on the speed of sound, as well as the distance between the source and the detectors [6,8,21].

The requirement in the BP algorithm is to input a large number of signals collected from different view angles. As mentioned, for a circular detection, the signals can be collected either using a single transducer rotating around the object or a ring shape transducer array. Such systems are either too expensive (due to the transducer ring array) or have a poor temporal resolution (due to using single transducer). To address theses problems, iterative image reconstruction algorithms (known as model-based algorithms too) can be used where there is a model used for the reconstruction [22]. In other words, iterative algorithms build up a model to describe the relationship between the detected photoacoustic (PA) signals and the optical absorption distribution and iteratively reduce the artifacts [23–25].

One of the concepts which can be combined with the model-based algorithms is compressed sensing (CS) and sparsity [26]. Over the past few years, it has been shown that using sparsity with model-based image reconstruction algorithms can mitigate the artifacts caused by the limited view angles and improve the quality of the reconstructed PA images [24,27–29]. Donoho et al. proposed the CS theory in 2006, for the first time, which is based on a prior knowledge of unknowns [30]. This method can be used in data acquisition procedure of PACT [31], which leads to information reconstruction based on the convex optimization from some observations that seem highly incomplete [28]. This concept has been used in the reconstruction of magnetic resonance imaging (MRI) and Computed Tomography (CT)-MRI in order to reduce the scan time and have an inherent registration in space and time [32]. In addition, CS has been used for thermoacoustic imaging (TAI) [33].

Provost and Lesage [28] have used CS for PACT image reconstruction, where due to the advantages of sparse characteristic of a sample, fewer projections were used to reconstruct the optical absorption distribution map of the tissue [34]. Signal sparsification can be done in two different ways: (i) applying a dictionary learning and (ii) using standard transform functions. Even though dictionary learning-based methods outperform the standard transform functions, in order to make the signal sparser, they impose a higher complexity for reconstruction [35,36]. On the other hand, standard transform functions can simply translate the signal to a sparse shape. The Wavelet Transform (WT), Discrete Cosine Transform (DCT), and Total Variation (TV) are some of the popular sparsifying transforms. Such transformations result different sparse representations of the original signal. Similar to compression algorithms, the combination of the original signal in different transformation domains, can provide an image with an improved quality.

In this paper, we introduce a novel dictionary for sparse representation of PA signals in order to improve the quality of the reconstructed PA image. The proposed method consists of three sparsifying transformation functions: WT, DCT, and TV. Using the proposed method, users are able to highlight information provided by each of the functions. We compared the performance of the proposed algorithm with the performance of BP and sparse reconstruction based on different methods when the same number of view angles is used. We use two established quality assessment metrics—peak signal-to-noise ratio (PSNR) and edge preservation index (EPI)—for quantitative evaluation of the results. Quantitative and qualitative results indicate that the proposed method can be a proper option when we face a limited number of angle views.
