The concept of compressed sensing has become a crucial topic in the information research field since its introduction.In theory of compressed sensing

the sampling and compression of information are conducted simultaneously

thereby reducing storage space and computation amount.The sampling rate exceeds the limitation of the sampling rate of Shannon's theorem

which is greater than or equal to twice the bandwidth.Consequently

the sampling rate is reduced.Therefore

we can reconstruct the signal rapidly through minimal sampling.The block compressed sensing reconstruction algorithm uses the same sampling rate for each image block

which results in an unreasonable allocation of resources

and the reconstruction process will produce the block effect.The multi-scale block compressed sensing reconstruction algorithm also exhibits the following problems:1) The algorithm reduces block size to decrease storage space

which increases computation amount.2) A rough block edge remains when reconstructing a complex image.The edge and direction-based block compression sensing algorithm allocates the total sampling rate to the layers of sub-band by utilizing the characteristics of edge and direction.The adaptive multi-scale block compressed sensing algorithm allocates the sampling rate to each block image by using the texture and directionality of an image.These two algorithms reduce the number of samples to a certain extent

which considerably saves resources and improves reconstruction performance.Among the two

adaptive sampling is more effective for images with a large gap between smooth and complicated regions.The two algorithms reconstruct the low-frequency coefficients after wavelet transformation;thus

the details of the reconstruction effect on a complex image are non-ideal.An improved adaptive multi-scale block compressed sensing algorithm is proposed in this study to solve the aforementioned problems.This improved algorithm is expected to reasonably use the low-and high-frequency information of an image and enhance the quality of image reconstruction when the concerned image has high detail complexity. In the algorithm

three-layer wavelet transform is conducted to obtain a low-frequency signal and nine ways of a high-frequency signal

which are then inverted with wavelet transform and divided into non-overlapping blocks with the same size.After wavelet transform

a significant amount of energy of the original image focuses on the low-frequency signal

which leads to strong resistance and good stability.The low-frequency signal is processed using a 2D adjacent block edge adaptive weighted filter method.The same jump of the edge pixel gray scale among adjacent blocks produces the block effect.Thus

the four adjacent block edge characteristics around the pixel should be used for filtering.The edge pixel value of the adjacent block is weighted based on distance to obtain the updated pixel value.The wavelet transform of an image can be expressed as the superposition of the approximation signal of the low-resolution image and all the details of the signal.These details are obtained by decomposing each stage that belongs to the high-frequency signal.An adaptive texture block-sampling method is adopted for the high-frequency signal

and the smooth projected Landweber algorithm is used to reconstruct the image.The flat image is overlapped after weighted filtering

and higher-resolution reconstructed images can be obtained. Compared with existing algorithms

such as the block compression sensing algorithm

the edge and direction-based block compression sensing algorithm

and the texture-based block compression algorithm

the proposed algorithm exhibits improved performance under different sampling rates.The high-frequency signal that represents image details is fully reconstructed.The reconstructed images obtained from the improved algorithm have higher resolution

particularly the images with considerable details.The reconstructed images also obtain a high peak signal-to-noise-ratio.The 2D adjacent block edge adaptive weighted filter is an effective method for removing the block effect on the reconstructed image

and reconstruction time is reduced by 0.3 s. After conducting three-layer wavelet transform

the high-frequency signal is used as part of the texture

and an adaptive multi-scale block compressed sensing algorithm is adopted to reconstruct the contours and edges of the image.The low-frequency signal is regarded as the flat part

and the neighbor block-relied filtering method is used to reconstruct image details.Reconstruction time is effectively shortened by reasonably utilizing the low-and high-frequency information of an image and reducing the process to detect the flat block.After the experiment

the quality of the reconstructed images is evidently improved

particularly the images with significant details.The block effect on the images is also apparently eliminated

and the reconstructed images have clear edges and texture details.Thus

an adaptive multi-scale block compressed sensing algorithm is mainly applied to images with complex texture

such as face

architectural

and remote sensing images.