# A Communication Framework for Image Transmission through LPWAN Technology
## 3 Proposed Framework
### Stage II: Compressive Sensing  
A picture is a rectangular array of dots with m rows and n columns. The expression \(m\times n\) is known as image resolution, and the dots are commonly referred to as pixels. The term resolution is also used to describe the number of pixels in an image per unit length. A monochromatic image (also known as a bilevel image) has pixels with one of two values, 0 or 1, that correspond to black or white colors and is considered the simplest type of image. A pixel in a grayscale image can have one of the \(n\) values be 0 through \(n-1\), indicating one of \(2^{n}\), where n can be \(4,8,12,16,\ldots\). A continuous-tone image can have many similar colors (or grayscales) that are difficult for the eye to distinguish. A discrete-tone image is typically an artificial image with a few or many colors that lacks the noise and blurring of a natural image. A cartoon image has a color image made up of uniform areas, with each area having a uniform color but adjacent areas having very different colors. Each type of image clearly has feature redundancy, but they are redundant in different ways. As a result, any given compression method may not work well for all images, and different methods are required to compress the various image types [86]. Because modern hardware can display many colors, a pixel is commonly represented as a 24-bit number (R-G-B components, each of which occupies 8 bits). As a result, a 24-bit pixel can specify 1 to \(2^{24}\) million colors, so an image with a resolution of \(128\ \times\ 128\) pixels occupies 49,152 bytes (16,384 in each component), one with 512 \(\times\) 512 pixels occupies 786,432 bytes, and one with 1024 \(\times\) 1024 pixels occupies 3,145,728 bytes. Then, image compression is critical. In general, information can be compressed if it is redundant; however, there is a concept known as \"remove irrelevancy\", which allows an image to be compressed with loss by removing irrelevant information even if the image contains no redundancy [86]. The spatial redundancy principle is used in image compression; as a result, if we select a random pixel in an image, its neighbors may have the same or similar colors, implying that the neighboring pixels are highly correlated. It is possible to rebuild the original data with high efficiency using this information. Compressive Sensing (CS) can reduce information by up to 95% of its original size. Only 5% of the original vector information can be rebuilt with high precision. This allows for a reduction in the amount of data that must be transported into LoRa. CS is a technique for creating and retrieving sparse signals with low noise using far fewer samples than the Nyquist sampling theorem requires [89; 90]. To implement CS, a program that represents the original signal in a sparse signal using an appropriate sparse representation was used. The original signal can be represented as a \(N\times 1\) vector, where N is equal to \(N=n\times n\ \left[rows\right]\times\left[columns\right]\). CS employs a sparsity technique to transform an information signal denoted as \(s\) into a vector \(S\ \in\ R^{N}\) in discrete form. \(k\) (data value dispersion relation) and \(s\) are elements of the original signal that differ from zero (the most representative). Signals with low dispersion (high value of \(k\)) can be converted to signals with greater dispersion via lineal transformation \(f\) by \(f=s\) and \(f\in R^{N\times N}\), which in our case represents data on wavelet transform [82; 91; 92; 93; 94; 95]. A k-disperse signal in which \(f\in R^{N}\) are sampled with CS to produce the \(g\in R^{M}\) signal, where \(M<<N\). A system sampling matrix is a representation of the sampling in matrix form as \(g=f\) and \(\in\ R^{M\times N}\). If \(f\) is unknown, an indeterminate system of linear equations can be found (infinite solutions). It could be solved for this purpose with an optimization problem that can be converted into a complex mathematical problem that is not convex.