Processing of data arrays and applications including image processing

A method for processing data, comprising:

• representing original data in form of a number array with one or more row elements and one or more column elements that are based on the original data;
• associating elements of the number array with a set of indices arranged in an index array having row and column numbers matching row and column number of the number array, wherein values of the indices are dependent on properties of corresponding elements in the number array, respectively, and properties of other elements of the number array;
• modifying values of elements of the number array by superposing a product of an amplitude variable A and values of a function F selecting from an ensemble of functions that are generated by using values of the indices in the index array as input variables to the function F, wherein the value of the amplitude variable A is computed to optimize a cost function associated with the amplitude variable A, the respective function F, values of elements of the number array, and values of the indices of the index array;
• and
• generating a modified number array using the modified values of elements of the number array.

A method of improving an image quality of a first image generated by an imaging apparatus and represented by a first number array, comprising:

• designating an index to each of a plurality of pixels of the first number array based on one or more features of the pixel relative to other pixels of the first number array;
• adjusting an amplitude variable for each of one or more functions to optimize a cost function associated with the amplitude variable, the respective function, a plurality of pixel values, and a plurality of designated indexes;
• updating the plurality of pixel values based on the adjusted amplitude variable after each amplitude variable corresponding to the one or more functions is adjusted to optimize the cost function to thereby produce updated pixel values for the plurality of pixel values;
• and
• generating an output image represented by a second number array having a plurality of output image pixels formed by the updated pixel values for the plurality of pixel values with an enhanced image quality.

A non-transitory computer readable storage medium comprising machine-readable instructions that upon execution by one or more processors, are configured to cause the one or more processors to perform a method comprising:

• obtaining an original image from an imaging apparatus;
• processing pixels in the original image to generate a first image having a plurality of first pixels with more pixels than the original image, the first image represented by a first number array;
• designating an index to each of a plurality of pixels of the first number array based on one or more features of the pixel relative to other pixels of the first number array;
• adjusting an amplitude variable for each of one or more functions to optimize a cost function associated with the amplitude variable, the respective function, a plurality of pixel values, and a plurality of designated indexes;
• updating the plurality of pixel values based on the adjusted amplitude variable after each amplitude variable corresponding to the one or more functions is adjusted to optimize the cost function to thereby produce updated pixel values for the plurality of pixel values;
• and
• generating an output image represented by a second number array having a plurality of output image pixels formed by the updated pixel values for the plurality of pixel values with an enhanced image quality.