编写一个matlab程序，对输入的图像进行哈夫曼编码，显示原图像的熵、编码后的平均码字长度以及编码效率

好的，以下是基于MATLAB的哈夫曼编码程序，您可以输入图像并进行编码。程序使用MATLAB内置函数`imread`和`imwrite`读取和写入图像，使用MATLAB的`entropy`函数计算熵，使用自定义函数`huffman_encode`计算编码和统计信息。

function huffman_image_encoding(image_path)
    % 读取图像
    image = imread(image_path);
    [height, width, channels] = size(image);
    
    % 转换为灰度图像
    if channels > 1
        image = rgb2gray(image);
    end
    
    % 将图像像素值存储为一维数组
    pixels = reshape(image, 1, []);
    
    % 计算像素值出现的频率
    freq_dict = histcounts(pixels, 0:255);
    
    % 构建哈夫曼树并获取编码映射表
    root = build_tree(freq_dict);
    codes = get_codes(root);
    
    % 对原图像进行编码
    encoded_data = "";
    for i = 1:length(pixels)
        encoded_data = strcat(encoded_data, codes{pixels(i)+1});
    end
    
    % 计算熵和平均码字长度
    entropy = entropy(pixels);
    avg_code_len = mean(cellfun('length', codes));
    
    % 计算编码效率
    original_size = dir(image_path).bytes;
    compressed_size = length(encoded_data) / 8;
    compression_ratio = original_size / compressed_size;
    efficiency = 1 / compression_ratio;
    
    % 输出统计信息
    fprintf("Entropy: %.2f\n", entropy);
    fprintf("Average Code Length: %.2f\n", avg_code_len);
    fprintf("Efficiency: %.2f\n", efficiency);
    
    % 将编码后的数据写入文件
    [filepath, name, ext] = fileparts(image_path);
    encoded_image_path = fullfile(filepath, strcat(name, "_encoded", ext));
    write_encoded_image(encoded_data, height, width, encoded_image_path);
end

% 构建哈夫曼树
function root = build_tree(freq_dict)
    heap = [];
    for i = 1:256
        if freq_dict(i) > 0
            node = Node(freq_dict(i), i-1);
            heap = [heap node];
        end
    end
    while length(heap) > 1
        node1 = heap(1);
        heap(1) = [];
        node2 = heap(1);
        heap(1) = [];
        merged = Node(node1.freq + node2.freq, [], node1, node2);
        heap = [heap merged];
        heap = heapify(heap);
    end
    root = heap(1);
end

% 获取编码映射表
function codes = get_codes(node, prefix, codes)
    if nargin < 3
        codes = cell(1, 256);
    end
    if node.is_leaf
        codes{node.symbol+1} = prefix;
    else
        codes = get_codes(node.left, strcat(prefix, "0"), codes);
        codes = get_codes(node.right, strcat(prefix, "1"), codes);
    end
end

% 堆排序
function heap = heapify(heap)
    for i = floor(length(heap)/2):-1:1
        heap = sift_down(heap, i);
    end
end

% 下滤
function heap = sift_down(heap, i)
    while i*2 <= length(heap)
        child = i*2;
        if child+1 <= length(heap) && heap(child+1).freq < heap(child).freq
            child = child + 1;
        end
        if heap(child).freq < heap(i).freq
            heap([child i]) = heap([i child]);
            i = child;
        else
            break;
        end
    end
end

% 写入编码后的图像
function write_encoded_image(encoded_data, height, width, encoded_image_path)
    num_zeros = mod(-length(encoded_data), 8);
    encoded_data = strcat(encoded_data, repmat('0', 1, num_zeros));
    encoded_data = reshape(encoded_data, 8, [])';
    encoded_data = bin2dec(encoded_data);
    encoded_data = reshape(encoded_data, height, width);
    imwrite(uint8(encoded_data), encoded_image_path);
end

% 定义节点类
classdef Node
    properties
        freq
        symbol
        left
        right
    end
    methods
        function obj = Node(freq, symbol, left, right)
            obj.freq = freq;
            obj.symbol = symbol;
            obj.left = left;
            obj.right = right;
        end
        function is_leaf = get.is_leaf(obj)
            is_leaf = isempty(obj.left) && isempty(obj.right);
        end
    end
end

请确保您已经将图像路径传递给huffman_image_encoding函数。程序将输出原图像的熵、编码后的平均码字长度和编码效率，并将编码后的图像写入与原图像相同的文件夹中（文件名中添加了“_encoded”后缀）。